Corporate Finance Exam

Calculating APR Find the APR in each of the following cases: APR Number of Times Compounded EAR Semiannually 14.2% Monthly 18.4 Weekly 11.1 Infinite 8.9

((1 + EAR)^(1/m) - 1)*m = APR A) APR Semiannually m = 2 EAR = (( 1 + .142)^(1/2) - 1)*2 = 13.73% B) APR monthly m =12 EAR = (( 1 + .184)^(1/12) - 1)*12 = 17.01% C)APR weekly m =52 EAR = (( 1 + .111)^(1/52) - 1)*52 = 10.54% EAR = e^(APR*t) for continous compounding here value of t = 1 (1 + EAR) = e^APR Taking ln both sides we get Ln(1 + EAR) =APR APR = Ln(1.089) = .08525 = 8.53%

The Financial Manager

The financial manager's primary goal is to increase the value of the firm by: 1.Selecting value-creating projects. like buying assets, machines, building property, research brands that generate more money than cost creating 2.Making smart financing decisions. borrowing at the lowest rate

Perpetuities A prestigious investment bank designed a new security that pays a quarterly dividend of $5 in perpetuity. The first dividend occurs one quarter from today. What is the price of the security if the APR is 8.5 percent compounded quarterly?

The formula to calculate the PV of a perpetual cash flow = PMT / (I/Y) Here, PMT = The periodic payment = $5 I/Y = Interest rate per period = 8.5% / 4 = 2.1250% (Interest is compounded quarterly and the payment is made quarterly hence we want a quarterly interest rate) PV of the perpetuity = $5 / 0.021250 PV of perpetuity = $235.29$ is the PV or the price of the security.

Firm TTT has sales of $15,000, total assets of $10,000, and a debt-equity ratio of 1. If its return on equity is 15 percent, what is its net income? (answer format: no comma and no dollar sign. For example, 100000)

Total assets = $10,000 Debt equity ratio = 1 Return on equity = 15% Let Debt = 0.5x Equity = x 10000 = 1x + x 10000 = 2x 10000/2 = x .15 = Net income / 5000 5000 x .15 = 750

Growing Perpetuities Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be $225,000, received two years from today. Subsequent annual cash flows will grow at 3.2 percent in perpetuity. What is the present value of the technology if the discount rate is 10.1 percent?

Value of technology in 1 year = Cashflow in year 2 / (discount rate - growth rate) Value of technology in 1 year = $225,000 / (10.1% - 3.2%) Value of technology in 1 year = $3,260,869.565 Present value of the technology = Value of technology in 1 year / (1 + discount rate)1 Present value of the technology = $3,260,869.565 / (1 + 10.1%)1 Present value of the technology = $2,961,734.39

Calculating Annuities Due You want to buy a new sports car from Muscle Motors for $64,500. The contract is in the form of a 60-month annuity due at an APR of 5.4 percent. What will your monthly payment be?

We have the periodic payment of annuity due, PMT = PV x r x ((1+r)^(n-1))/ ((1+r)^(n)-1) PV = -$64,500 I/Y = 5.4/12 N = 60 CPT PMT = $1,223.54 PMT=64,500×0.0045×(1.0045^(60−1))/(1.0045^60−1) PMT=290.25×(1.0045^59/1.0045^60−1)=1,223.54 The required monthly payment = 1,223.54

Calculating Rates of Return During 2003, Sotheby's sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $10,311,500. Unfortunately for the previous owner, he had purchased it in 1999 at a price of $12,377,500. What was his annual rate of return on this sculpture?

We use the formula: A=P(1+r/100)^n where A=future value P=present value r=rate of interest n=time period. 10,311,500=12,377,500*(1+r/100)^4 (10,311,500/12,377,500)^(1/4)=(1+r/100) (1+r/100)=0.955371382 r=0.955371382-1 =(4.46%)(Approx)(Negative).

What is the difference between average and marginal tax rates? Which should we use when making financial decisions?

We wanna think about the marginal even though we'll pay the average tax rate

Statement 1: when an asset can be quickly converted into cash, it is illiquid. Statement 2: balance sheet accounts are listed in order of increasing liquidity. Those statements are _____.

both false Supplying money to the firm in the form of Current Liabilities. Long-Term Debt. bank debt or bondsShareholders' Equity.

3. A firm's ______ refers to the management of firm's fixed assets; a firm's ______ refers to the firm's proportions of financing from current and long-term debt and equity; a firm's ______ refers to the firm's net working capital

capital budgeting; capital structure; short-term management

Treasury Quotations going to be typically some date followed by some coupon. then there's going to be typically two numbers, which it was going to be a bid number and an offer number. What is the coupon rate on the bond? When does the bond mature? What is the bid price? What does this mean? What is the ask price? What does this mean? How much did the price change from the previous day? What is the yield based on the ask price?

2028 Aug 15 2.875 118.116 118.126 -.03 .517 Coupon rate = 2.875% Matures in August 15, 2028 (assumes 2020 pricing date) Bid price is 118.116. If you want to sell $100,000 par value T-bonds, the dealer is willing to pay $118,116. Ask price is 118.126. If you want to buy $100,000 par value T-bonds, the dealer is willing to sell them for $118,126. The difference between the bid and ask prices is called the bid-ask spread, and it is how the dealer makes money. The price decreased by .03 percent, or $.30, in value from the previous day, so $30 on $100,000 worth of bonds. The yield is .517%.

Bond Yields Ashburn Corp. issued 25-year bonds two years ago at a coupon rate of 5.6 percent. The bonds make semiannual payments. If these bonds currently sell for 97 percent of par value, what is the YTM?

25 - 2 = 23 x 2 = 46 pmt is the coupon payment i.e 1000 * 5.6% = 56 / 2 = 28 (Since the coupon payment is made semiannually therefore divided by 2) pv is the last price i.e 970 (1000 * 0.97) Note : pv should be taken as negative figure. fv is the face value i.e 1000 =RATE(46,28,-970,1000) YTM is 2.92% (Semiannual) YTM is 2.92% * 2 = 5.84% (Annual)

Calculating Discounted Payback An investment project costs $19,000 and has annual cash flows of $5,100 for six years. What is the discounted payback period if the discount rate is zero percent? What if the discount rate is 5 percent? If it is 19 percent?

645x2=1290 1800-1290=510 510/645 = + 2 = 2.79 645x5=3225 3500-3225=275 275/645 = + 5 = 5.43 0, won't ever pay back

12. Nonconstant Growth Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years because the firm needs to plow back its earnings to fuel growth. The company will pay a dividend of $10 per share 10 years from today and will increase the dividend by 6 percent per year thereafter. If the required return on this stock is 11 percent, what is the current share price?

=$10/(.11 − .06) =$200 =200.00/1.11^9 =$78.18

8.1 Bonds and Bond Valuation

A bond is a legally binding agreement between a borrower and a lender that specifies the: •Par (face) value: notional value that's attached to the bond •Coupon rate: the United States, the common rate is semiannual for government and corporate bonds. •Coupon payment: interest rate, they're talking about percentages of par face value and then bonds. •Maturity date: fixed time at the end when the bond is expected to pay you back. The yield to maturity is the required market interest rate on the bond. Corporations and governments borrow money routinely from people and from and from institutions based on and in the structure that they call a bond.

Which one of the following statements is correct concerning ratio analysis?

A single ratio is often computed differently by different individuals

Aftertax Yields

A taxable bond has a yield of 8 percent, and a municipal bond has a yield of 6 percent. If you are in a 30 percent tax bracket, which bond do you prefer? •.08(1 − .3) = .056, or 5.6% •The aftertax return on the corporate bond is 5.6 percent, compared to a 6 percent return on the municipal. At what tax rate would you be indifferent between the two bonds? •.08(1 − T) = .06, or 6% •T = .25, or 25%

Using Stock Quotes You have found the following stock quote for RWJ Enterprises, Inc., in the financial pages of today's newspaper. What was the closing price for this stock that appeared in yesterday's paper? If the company currently has 25 million shares of stock outstanding, what was net income for the most recent four quarters? HI LO Stock (DIV) SYM YLD% PE VOL 100s CLOSE Net Chg 95.13 63.17 RWJ 1.85 RWJ 2.15 19 17652 ?? .27

A). Dividend Yield = Dividend / Stock Price 0.0215 = $1.85 / Stock Price Stock Price = $1.85 / 0.0215 = $86.05 Yesterday's Closing Price = Stock Price + Net Change = $86.05 + $0.27 = $86.32 B). PE Ratio = Stock Price / EPS 19 = $86.05 / EPS EPS = $86.05 / 19 = $4.53 EPS = Net Income / Shares Outstanding $4.53 = Net Income / 25,000,000 Net Income = $4.53 * 25,000,000 = $113,219,094

Calculating Payback An investment project provides cash inflows of $835 per year for eight years. What is the project payback period if the initial cost is $1,900? What if the initial cost is $3,600? What if it is $7,400?

Annual Cash Flow = $835 per year a) Initial Cost = $1,900 So, Payback period = Initial Cost / Annual Cash Flow = $1,900 / $835 So, Payback period = 2.276 years b) Initial Cost = $3,600 So, Payback period = Initial Cost / Annual Cash Flow = $3,600 / $835 So, Payback period = 4.311 years c) Initial Cost = $7,400 So, Payback period = Initial Cost / Annual Cash Flow = $7,400 / $835 So, Payback period = 8.8622 years , Since the cash flow stops after 8 years, so the payback period is never which is 0.

Finding the Bond Maturity Milton Corp. has 8 percent coupon bonds making annual payments with a YTM of 7.2 percent. The current yield on these bonds is 7.55 percent. How many years do these bonds have left until they mature?

Annual payments on a 1,000 bond are 8%, or 80. If the current yield is 7.55%, i.e. 80 / Current Price, then Current Price is 80 / .0755, or 1,059.60. With PV 1,059.60, FV 1,000, PMT 80, YTM 7.2%, N must be 11.057 yrs.

Coupon rateBid priceAsked price Locate the Treasury issue in Figure 7.4 maturing in February 2031. Assume a par value of $10,000.The coupon rate, located in the second column of the quote, is 5.375 percent. The bid price is:

Bid price = 125.8984 = 125.8984% Bid price = (125.8984 / 100)($10,000) Bid price = $12,589.84 The previous day's asked price is found by: Previous day's asked price = Today's asked price - Change Previous day's asked price = 125.9766 - (-.7266) Previous day's asked price = 126.7032 The previous day's price in dollars was: Previous day's dollar price = 126.7032 = 126.7032% Previous day's dollar price = (126.7032 / 100)($10,000) Previous day's dollar price = $12,670.32

C Inc., issued 15 Year bonds 2 years ago at a coupon rate of 6.40% percent. The bonds make semi- annual payments. If these bonds currently sell for 106 percent of par value, what is the YTM?Settlement date 1/1/2000Maturity date 1/1/2013Annual coupon rate =6.40%Coupons per year =2Face value (% of par) =100Bond price (% of par) =106

Bond price =C* [ 1-(1+r)^-n ] / r + $1000/ (1+r)^n Note: Semi-annual coupon bond Coupon payment = 0.064/2 * $1000= 32 N= 13 years*2=26 r=YTM? Price PV = - 1 060 FV=$1000 $1 060= $32 *[ 1-(1+r)^26]/ r + $1000/ (1+r)^26 Using Excel =Rate() function is determined as follows : =Rate ( Nper, PMT, PV, FV) =Rate( 26 , 32, -1060, 1000)*2 YTM =5.74%

Bond Concepts

Bond prices and market interest rates move in opposite directions. When coupon rate = YTM, price = par value When coupon rate > YTM, price > par value (premium bond) When coupon rate < YTM, price < par value (discount bond) Price Risk: •Change in price due to changes in interest rates. •Long-term bonds have more price risk than short-term bonds. •Low-coupon-rate bonds have more price risk than high coupon rate bonds. Reinvestment Rate Risk: •Uncertainty concerning rates at which cash flows can be reinvested. •Short-term bonds have more reinvestment rate risk than long-term bonds. •High-coupon-rate bonds have more reinvestment rate risk than low coupon rate bonds.

Calculating Profitability Index Suppose the following two independent investment opportunities are available to a company. The appropriate discount rate is 8.5 percent. Year Project Alpha Project Beta 0 −$3,700 −$4,300 1 1,900 1,500 2 1,800 3,100 3 1,400 2,400 a. Compute the profitability index for each of the two projects. b. Which project(s) should the company accept based on the profitability index rule?

CALCULATOR CF, DOWN CO1: 1900 Enter, DOWN CO2: 1800 ENTER, Down CO3: 1400 NPV 8.5 Enter Down, CPT

Calculating Rates A financial planning service offers a college savings program. The plan calls for you to make six annual payments of $15,000 each, with the first payment occurring today, your child's 12th birthday. Beginning on your child's 18th birthday, the plan will provide $27,000 per year for four years.

Calculate internal rate of return: Internal rate of return=Initial cash payment−Annual cash payment1+rn=−15,000−15,000/1+r−15,000/(1+r)^2−15,000/(1+r)^3−15,000/(1+r)^4−15,000/(1+r)^5+27,000/(1+r)^6+27,000/(1+r)^7+27,000/(1+r)^8+27,000/(1+r)^9=3.69%

Dividend Growth Four years ago, Bling Diamond, Inc., paid a dividend of $1.95 per share. The company paid a dividend of $2.75 per share yesterday. Dividends will grow over the next five years at the same rate they grew over the last four years. Thereafter, dividends will grow at 4.5 percent per year. What will the company's dividend be in seven years?

Calculation of growth rate over last 4 years: Growth Rate = (Last Dividend / Dividend 4 years ago)^(1/4) - 1 Growth Rate = ($2.75 / $1.95)^(1/4) - 1 Growth Rate = 1.41025641^(1/4) - 1 Growth Rate = 1.08974409 - 1 Growth Rate = 0.08974409 or 8.974% Last Dividend, D0 = $2.75 Growth rate over next 5 years is 8.974%, followed by a constant growth rate of 4.5% Dividend in 5 years = $2.75 * 1.08974^5 Dividend in 5 years = $4.22617187 Dividend in 7 years = $4.22617187 * 1.045^2 Dividend in 7 years = $4.62 So according to the question. Dividend in 7 years = $ 4.62

Growing Annuities Mateo has received a job offer from a large investment bank as a clerk to an associate banker. His base salary will be $50,000. He will receive his first annual salary payment one year from the day he begins to work. In addition, he will get an immediate $10,000 bonus for joining the company. His salary will grow at 3 percent each year. Each year he will receive a bonus equal to 10 percent of his salary. He is expected to work for 25 years. What is the present value of the offer if the discount rate is 9 percent?

Calculation of present value of the offer; We will use present value of growing annuity formula; Preset value = B + A * (1 + b) * [1 - (1 + g)^n * (1 + r)^-n] / (r - g) Where; B = Initial bonus $10,000 A = First salary $50,000 b = Annual bonus rate 0.10 or 10% g = Annual growth rate 0.03 or 3% r = Discount rate 0.09 or 9% n = Period 25 years Now put values in the formula; Preset value = $10,000 + $50,000 * (1 + 0.10) * [1 - (1 + 0.03)^25 * (1 + 0.09)^-25] / (0.09 - 0.03) Preset value = $704,090.013252106 or $704,090.01 (Approx)

Calculating Perpetuity Values The Perpetual Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $20,000 per year forever. If the required return on this investment is 6.2 percent, how much will you pay for the policy? Suppose the Perpetual Life Insurance Co. told you the policy costs $285,000. At what discount rate would this be a fair deal?

Cash flow (CF) = $20,000 Rate (r) = 6.2% The present value (PV) is calculated as follows= PV=CF/r=$20,000/ 0.062=$322,580.65 You will pay $322,580.65 for your policy. If present value of perpetuity (PV) = $285,000 Cash flow (CF) = $20,000 The fair rate is calculated as follows= Fair rate=Cash flow/PV=20,000/ 285,000=0.0702 The fair interest rate would be 7.02%

Bond Example - I

Consider a U.S. government bond with as 6.375 percent coupon that expires in December 2025. •The par value of the bond is $1,000. •Coupon payments are made semiannually (June 30 and December 31 for this particular bond). •Since the coupon rate is 6.375 percent, the semiannual payment is $31.875. (1000 x 6.375%)/2 •On January 1, 2021, the size and timing of cash flows are: The time line has the following values. 1/1/21; 6/30/21 payout of $31.875; 21/31/21 payout of $31.875; 6/30/25 payout of $31.875; 12/311/25 F V of $1,031.875.

Yield to Maturity YTM with Annual Coupons

Consider a bond with a 10 percent annual coupon rate, 15 years to maturity, and a par value of $1,000. The current price is $928.09. •Will the yield be more or less than 10 percent? •N = 15; PV = −928.09; FV = 1,000; PMT = 100 CPT I/Y = 11%

Valuing Bonds Union Local School District has a bond outstanding with a coupon rate of 2.9 percent paid semiannually and 16 years to maturity. The yield to maturity on this bond is 2.7 percent, and the bond has a par value of $5,000. What is the dollar price of the bond?

Coupon Rate: 2.9 / 2 = 1.45 5000 x .029 = 145 /2 = 72.5 Years to Maturity 16 x 2 = 32 YTM I/Y: 2.7 / 2 = 1.35 Par FV: 5000 PV: 5,129.226

Nonconstant Growth and Quarterly Dividends Mitchell Mineral Water, Inc., will pay a quarterly dividend per share of $.95 at the end of each of the next 12 quarters. Thereafter, the dividend will grow at a quarterly rate of 1 percent, forever. The appropriate rate of return on the stock is 11 percent, compounded quarterly. What is the current stock price?

Current Stock Price = Present value of next 12 quarter dividend + Present value of all dividends after 12 quarters Quarterly rate of return = 12%/4 =3% Present value of next 12 quarter dividend = Quarterly Dividend * [{1 - (1 + r)^-n} / r] = $0.95 * [{1 - (1+0.03)^-12}/0.03] = $0.95 * [0.2986/0.03] = $0.95 * 9.9540 = $9.46 Present value of all dividends after 12 quarters = [{d(1+g)}/(ke-g)] * (1+ke)^-12 = [{$0.95*(1+0.013)}/{0.03-0.013)] * (1+0.03)^-12 = [$0.96/0.017] * 0.7014 = $56.61 * 0.7014 = $39.70 Current Stock Price = $9.46 + $39.70 = $49.16

Maturity of bond Shinoda Corp. has 6 percent coupon bonds making annual payments with a YTM of 5.2 percent. The current yield on these bonds is 5.55 percent.

Current yield = .0555 = $60 / P0 P0 = $60 / .0555 P0 = $1,081.08 Enter 5.2% ±$1,081.08 $60 $1,000 N: I/Y:5.2% PV: 1,081.08 PMT: 60 FV: 1,000 Solve for N 14.77

Current Yield versus Yield to Maturity

Current yield = annual coupon / price Yield to maturity = Current yield + Capital gains yield Example: 10 percent coupon bond, with semiannual coupons, face value of 1,000, 20 years to maturity, $1,197.93 price Current Yield = $100/$1197.3 = .0835 Price in one year, assuming no change in YTM = 1,193.68 Capital Gain Yield = (1193.68 - 1197.3) / 1197.3 = -.035 YTM = 8.35% − .35% = 8%, which is the same YTM computed earlier

Bond Yields Williams Software has 6.4 percent coupon bonds on the market with 18 years to maturity. The bonds make semiannual payments and currently sell for 106.32 percent of par. What is the current yield on the bonds? The YTM? The effective annual yield?

Current yield= Annual coupon/Price Coupon = 64 1000*6.4% Price= 1063.2 1000*106.32% Current yield= 64/1063.2 6.02% Ans= 6.02% Computation of YTM Put in calculator FV 1000 PMT=1000*6.4%/2 32.00 PV -1063.2 N=18*2 36 Compute I 2.91% YTM = 2.91%*2 5.83% Ans= 5.83% Effective annyal yield (1+2.91%)^2-1 5.91% Ans= 5.91%

Perpetual Cash Flows What is the value of an investment that pays $75,000 every other year forever, if the first payment occurs one year from today and the discount rate is a 7 percent APR compounded daily? What is the value today if the first payment occurs four years from today? Assume 365 days per year.

DISCOUNT RATE 7% COMPOUNDED DAILY Effective daily interest rate=7%/365=0.07/365=0.00019178=0.019178% Effective discount rate for one year=((1+0.00019178)^365)-1=0.07250098=7.250098% Effective discount rate for TWO Years(730 days)=((1+0.00019178)^730)-1=1.15025836-1=0.15025836=15.025836% Value of $75000 in every two years in perpetuity at the end of Year1 (time of occuring first payment: $75000+(75000/0.15025836)=$75000+$499,140.28=$574,140.28 Present Value of $75000 in every two years in perpetuity starting from Year1=574140.28/1.07250098=$535,328.45 ANSWER: $535328.45 IF THE FIRST PAYMENT OCCURS FOUR YEARS FROM TODAY: VALUE TWO YEARS FROM TODAY=75000/0.15025836=$499,140.28 PRESENT VALUE=$499,140.28/1.15025836=$433,937.54 ANSWER: $433,937.54

Calculating Discounted Payback An investment project has annual cash inflows of $2,800, $3,700, $5,100, and $4,300, for the next four years, respectively. The discount rate is 9 percent. What is the discounted payback period for these cash flows if the initial cost is $5,200? What if the initial cost is $6,400? What if it is $10,400?

Discounted cash flow = Cash flow /(1+rate)^n 2800 / (1+.09)^1 = 2568.81 3700 / (1+.09)^2 = 3114.22 Year Cash flow Discounted cash flowCumulative Discounted cash flow 1 2800 2568.81 2568.81 2 3700 3114.22 5683.02 3 5100 3938.14 9621.16 4 4300 3046.23 12667.39 Discounted payback year 1=1+5,200−2,568.81÷3,114.22=1.84 Discounted payback year 2=2+6,400−5,683.02÷3,938.14=2.18 Discounted payback year 3=3+10,400−9,621.16÷3,046.23=3.26

4. Stock Values Five Star Corporation will pay a dividend of $3.04 per share next year. The company pledges to increase its dividend by 3.75 percent per year indefinitely. If you require a return of 11 percent on your investment, how much will you pay for the company's stock today?

Dividend next year (D1) = $3.04 Growth rate (g) = 3.75% Required rate of return (Ke) = 11% Price of company's stock today = D1 / (Ke - g) = $3.04 / (0.11 - 0.0375) = $41.93 Stock price = $41.93

8. Valuing Preferred Stock Fegley, Inc., has an issue of preferred stock outstanding that pays a $3.80 dividend every year in perpetuity. If this issue currently sells for $93 per share, what is the required return?

Dividend per year = $3.80 Current selling price = $93 Required return = Dividend per year/Current selling price Required return = 4.09%

3. Stock Values For the company in the previous problem, what is the dividend yield? What is the expected capital gains yield?

Dividend yield = D1 / P0 = $1.89 / $38.00 = .0497, or 4.97% Required return = (D1 / P0) + g = ($1.89 / $38.00) + .05 = .0997, or 9.97% The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, So: Capital gains yield = Required return - Dividend Yield = 9.97% - 4.97% ==> 5.00% Note : Assuiming Price of stock (P0) be $38

Bond Yields A Japanese company has a bond outstanding that sells for 96.318 percent of its ¥100,000 par value. The bond has a coupon rate of 3.4 percent paid annually and matures in 16 years. What is the yield to maturity of this bond?

FV/Par: 100,000 PV: -96.318 Coupon Rate: 3.4% PMT: 3400 NPER/N: 16 CPT I/Y: 3.709 Yield to Maturity

Bond Yields Uliana Co. wants to issue new 20-year bonds for some much-needed expansion projects. The company currently has 6 percent coupon bonds on the market with a par value of $1,000 that sell for $967, make semiannual payments, and mature in 20 years. What coupon rate should the company set on its new bonds if it wants them to sell at par?

Face value= future value= $1,000 Present value= $967 Time= 20 years*2= 40 semi-annual periods Coupon rate= 6%/2= 3% Coupon payment= 0.03*1,000= $30 per semi-annual period FV= 1,000 PV= -967 PMT= 30 N= 40 Press the CPT key and I/Y to compute the yield to maturity. The value obtained is 3.15. Therefore, the yield to maturity of the current bond is 3.15%*2 = 6.29%.

Bond Example: Calculator

Find the present value (as of January 1, 2021) of a 6.375 percent coupon bond with semiannual payments and a maturity date of December 2025 if the YTM is 5 percent. N = 10 I/Y = 2.5 PV = negative 1,060.17 PMT = 31.875, equals 1,000 times 0.06375 all divided by 2 FV = 1,000

Real Cash Flows Paul Adams owns a health club in downtown Los Angeles. He charges his customers an annual fee of $500 and has an existing customer base of 720. Paul plans to raise the annual fee by 5 percent every year and expects the club membership to grow at a constant rate of 3 percent for the next five years. The overall expenses of running the health club are $145,000 a year and are expected to grow at the inflation rate of 2 percent annually. After five years, Paul plans to buy a luxury boat for $500,000, close the health club, and travel the world in his boat for the rest of his life. What is the annual amount that Paul can spend while on his world tour if he will have no money left in the bank when he dies? Assume Paul has a remaining life of 25 years after he retires and earns 9 percent on his savings.

Future Value of Health Club Membership Fees: Year 1: 550 × $640 × 1.05 = $369,600 Year 2: 550 × $640 × (1.05)2 = $388,080 Year 3: 550 × $640 × (1.05)3 = $407,484 Year 4: 550 × $640 × (1.05)4 = $427,858.40 Year 5: 550 × $640 × (1.05)5 = $449,245.32 Future Value of Investment Income: 120,000 × (1.04)^5 = $134,778.24 Total Future Value: $369,600 + $388,080 + $407,484 + $427,858.40 + $449,245.32 + $134,778.24 = $2,176,046.96 Future Value = Present Value * (1 + Rate)n, where n is no. of years. Calculate the Remaining Life Annuity Factor: Using the remaining life of 25 years and the interest rate of 10%, the annuity factor will be calculated. 1− [1 / (1.10)^25 ] ​= 16.0461 Determine Annual Spending: Annual Spending/ Withdrawal = $2,176,046.96 / 16.0461 = $135,661.89 Paul can spend approximately $135,661.89 annually during his world tour to exhaust his savings by the end of his life. Explanation: Annual Spending = Total Future Value / Annuity Factor

18. Finding the Dividend Matterhorn Corporation stock currently sells for $49 per share. The market requires a return of 11 percent on the firm's stock. If the company maintains a constant 3.5 percent growth rate in dividends, what was the most recent dividend per share paid on the stock?

Gordon Model Price of Stock = Expected Dividend / (required rate - growth rate) 49 = Expected dividend / (11% - 3.5%) Expected dividend: 3.675 Expected dividend: current dividend + growth = 3.675 current dividend + 3.5% of current dividend = 3.675 Current dividend: 3.675/1.035 Current dividend: 3.55

9. Growth Rate The newspaper reported last week that Chen Enterprises earned $19.2 million this year. The report also stated that the firm's return on equity is 12 percent. The firm retains 80 percent of its earnings. What is the firm's earnings growth rate? What will next year's earnings be?

Growth rate = ROE*Retention Ratio = 12%*80% = 9.60% Next year's earnings = Current earnings*(1+growth rate) = 19.2*(1+9.60%) = $21,043,200

Calculating the Number of Periods Your Christmas ski vacation was great, but it unfortunately ran a bit over budget. All is not lost: You just received an offer in the mail to transfer your $15,000 balance from your current credit card, which charges an annual rate of 18.6 percent, to a new credit card charging a rate of 9.2 percent. How much faster could you pay the loan off by making your planned monthly payments of $275 with the new card? What if there was a fee of 2 percent charged on any balances transferred?

How to do it on the financial calculator: a) PMT = -$275 PV = $15,000 I/Y = 18.6/12 CPT N = 121.40 PMT = -$275 PV = $15,000 I/Y = 9.2/12 N = 70.91 Months quicker to pay off card = 121.40 − 70.91 = 50.49 months b) PMT = -$275 PV = $15,300 I/Y = 9.2/12 CPT N = 72.81 Months quicker to pay off card = 121.40 - 72.81 = 48.59 months

Calculating IRR A firm evaluates all projects by applying the IRR rule. If the required return is 14 percent, should the firm accept the following project? Year Cash Flows 0 −$41,000 1 20,000 2 23,000 3 14,000

IRR Calculator CF: -41,000 Enter, Down Arrow CO1: 20,000 Enter, Down CO2: 23,000 Enter, Down CO3: 14000 IRR button, CPT 19.5756

1. Stock Values The RLX Co. just paid a dividend of $3.20 per share on its stock. The dividends are expected to grow at a constant rate of 4 percent per year indefinitely. If investors require a return of 10.5 percent on the company's stock, what is the current price? What will the price be in three years? In 15 years?

Last Dividend, D0 = $3.20 Growth Rate, g = 4.00% Required Return, rs = 10.50% Expected Dividend, D1 = D0 * (1 + g) Expected Dividend, D1 = $3.20 * 1.04 Expected Dividend, D1 = $3.328 Current Price, P0 = D1 / (rs - g) Current Price, P0 = $3.328 / (0.105 - 0.040) Current Price, P0 = $3.328 / 0.065 Current Price, P0 = $51.20 Stock Price in 3 years, P3 = P0 * (1 + g)^3 Stock Price in 3 years, P3 = $51.20 * (1 + 0.040)^3 Stock Price in 3 years, P3 = $51.20 * 1.124864 Stock Price in 3 years, P3 = $57.59 Stock Price in 15 years, P15 = P0 * (1 + g)^15 Stock Price in 15 years, P15 = $51.20 * (1 + 0.040)^15 Stock Price in 15 years, P15 = $51.20 * 1.8009435 Stock Price in 15 years, P15 = $92.21

16. Differential Growth Orkazana Corp. is experiencing rapid growth. Dividends are expected to grow at 30 percent per year during the next three years, 20 percent over the following year, and then 5 percent per year indefinitely. The required return on this stock is 12 percent, and the stock currently sells for $92 per share. What is the projected dividend for the coming year?

Let current Dividend =D0D1=D0*(1+g1) =D0*1.30D2=D0*(1+g1)^2=D0*1.30^2D3=D0*(1+g1)^3 =D0*1.30^3D4=D0*(1+g1)^3*(1+g2) =D0*1.30^3*1.20D5=D0*(1+g1)^3*(1+g2)*(1+g3)=D0*1.30^3*1.20*1.05 Terminal Value =D5/(r-g3) =D0*1.30^3*1.20*1.05/(12%-5%) =39.546*D0Current Price of Stock =D1/(1+r)+D2/(1+r)^2+D3/(1+r)^3+D4/(1+r)^4+Terminal Value/(1+r)^4=D0*1.30/(1.12)+D0*1.30^2/(1.12)^2+D0*1.30^3/(1.12)^3+D0*1.30^3*1.20/1.12^4+39.546*D0/(1.12)^492 =D0*30.8794D0 =92/30.8794Projected Dividend =D0*1.30 =92/30.8794*1.30 =3.87

What are the major categories of financial ratios?

Liquidity Ratio(Current ratio, quick ratio, cash ratio) Activity Ratio(Inventory turnover, receivable turnover, payable turnover, asset turnover) Leverage Ratio(Debt ratio, Debt to equity ratio, interest coverage ratio) Performance Ratio(Profit margin, Return on assets, Return on equity) Valuation ratios( Price Earning,Price Earning Growth Rate, Market Value to Book Value)

Management Goals

Management goals may be different from shareholder goals. •Expensive perquisites. •Survival. •Independence. Increased growth and size are not necessarily equivalent to increased shareholder wealth.

Current Bond Price Sqeekers Co. issued 14-year bonds a year ago at a coupon rate of 8.6 percent. The bonds make semiannual payments and have a par value of $1,000. If the YTM on these bonds is 6.9 percent, what is the current bond price?

N: 26 I/Y: 6.9% / 2 PV: PMT: 86 / 2 FV: 1,000 PV 1,144.38

Coupon rate DMA Corporation has bonds on the market with 19.5 years to maturity, a YTM of 8 percent, and a current price of $1,069. The bonds make semiannual payments and have a par value of $1,000 What must the coupon rate be on these bonds?

N: 39 I/Y: 8.0% / 2 PV:1,069 PMT: FV: 1,000 solve for PMT 43.52(2) / $1,000 = 8.70%

Summary—Discounted Cash Flow

Net present value •Difference between market value and cost. •Accept the project if the N P V is positive. •Has no serious problems. •Preferred decision criterion. Internal rate of return •Discount rate that makes N P V = 0. •Take the project if the I R R is greater than the required return. •Same decision as N P V with conventional cash flows. •IRR is unreliable with nonconventional cash flows or mutually exclusive projects. Profitability Index •Benefit-cost ratio. •Take investment if PI > 1. •Cannot be used to rank mutually exclusive projects. •May be used to rank projects in the presence of capital rationing.

Problems with IRR Mako Corp. has a project with the following cash flows: Year Cash Flow 0 $25,000 1 −11,000 2 7,000 What is the IRR of the project?

No IRR is determined for the IRR application their must be a initial investment in t0 means There is no real IRR So IRR is 0

Nominal versus Real Returns Say you own an asset that had a total return last year of 14.1 percent. If the inflation rate last year was 2.83 percent, what was your real return?

Nominal return = 14.10% Inflation rate = 2.83% Real return =( 1+ nominal rate/1+inflation rate)−1 = (1+0.141/1+0.0283)−1 = 0.1095 or 10.96% Thus, the real return on asset would be 10.96%.

Coupon Rates Draiman Corporation has bonds on the market with 14.5 years to maturity, a YTM of 5.3 percent, a par value of $1,000, and a current price of $987. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Nper = 14.5 years *2 = 29 semi annual periods Rate = 5.30%/2 = 2.65% FV = 1000 PV = 987 Type = 0 (Depicting end of period payments) The PMT function of Excel is : = PMT(Rate, Nper, PV, FV, Type) =PMT(2.65%,29,-987,1000,0) = 25.85 The semi annual coupon amount is $25.85 Annual coupon = 25.85 * 2 = $51.70 Coupon rate = Annual coupon / Face value = $51.70/$1,000 = 5.17% Thus, the bonds pay an annual coupon rate of 5.17%

A Differential Growth Example A common stock just paid a dividend of $2. The dividend is expected to grow at 8 percent for 3 years, then it will grow at 4 percent in perpetuity. What is the stock worth? Assume the discount rate is 12 percent.

P=("$2" ×1.08)/(.12-.08) [1-(1.08^3)/(1.12^3 ) ]+ (((2(1.08)^3 (1.04))/(.12-.04)))/(1.12^3 ) P="$54"×[1-.8966]+"$32.75" /(1.12^3 ) P="$5.58"+23.31P="$28.89"

Pure Discount Bonds: Example Find the value of a 15-year zero-coupon bond with a $1,000 par value and a YTM of 12% (semi-annually compounded). PV = F / (1+r)^t

PAR/FV: 1000 YTM/I/Y: 12/2 = 6 N: 15 x 2 = 30 PMT: N/A P: 174.11

10. Stock Valuation and PE The Dahlia Flower Co. has earnings of $3.64 per share. The benchmark PE for the company is 18. What stock price would you consider appropriate? What if the benchmark PE were 21?

PE= price/EPS 18= price /3.64 Price = 18 ×3.64 Price = $ 65.52 And if PE is $ 21 Then PE = price / EPS 21 = price /3.64 Price = 21 × 3.64 Price = $76.44 When PE is $ 18 then stock price would be $65.52 And when PE is $21 then stick price would be $76.44

3. Accrued Interest You purchase a bond with a coupon rate of 6.4 percent, a par value of $1,000, and a clean price of $1,027. If the next semiannual coupon payment is due in two months, what is the invoice price?

Par value of bond = $1000 Semi-annual Coupon Payment = Par Value*Coupon rate*1/2 = $1000*6.40%*1/2 = $32 Clean price = $1027 - Invoice price includes Accrued Interest while clean price does not include accrued Interest. Accrued Interest earned for 4 months = Semi-annual Coupon Payment*4/6 = $32*4/6 = $21.33 Invoice Price = Clean Price + Accrued Interest = $1027 + $21.33 = 1048.33

Zero Coupon Bonds You find a zero coupon bond with a par value of $10,000 and 24 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the dollar price of the bond? Assume semiannual compounding periods.

Par/FV: 10,000 N/Maturity: 24 x 2 = 48 YTM/ I/Y: 4.2 / 2 = 2.1 Semi Annual PMT: 0 PV: -3687.77

Valuing Bonds Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.4 percent paid semiannually and 18 years to maturity. The yield to maturity on this bond is 4.7 percent. What is the price of the bond?

Par/FV: 2000 YTM I/Y: 4.7 / 2 = 2.35 Coupon rate: 4.4 / 2 = 2.2 Coupon PMT: 44 Years to Maturity: 18 x 2 = 36 1927.66

Stock Valuation and PE Meadow Dew Corp. currently has an EPS of $4.05, and the benchmark PE for the company is 21. Earnings are expected to grow at 4.9 percent per year. a. What is your estimate of the current stock price? b. What is the target stock price in one year? c. Assuming the company pays no dividends, what is the implied return on the company's stock over the next year? What does this tell you about the implicit stock return using PE valuation?

Part a: Price of stock today = EPS today * PE Ratio = $ 4.05 * 21 = $ 85.05 Price of Stock today is $ 85.05 Part b: Expected EPS = EPS Today ( 1 + Growth rate ) = $ 4.05 * ( 1 + 0.049 ) = $ 4.25 Expcted Price after 1 Years = Expected EPS * PE Ratio' = $ 4.25 * 21 = $ 89.22 Expected Price in One Year is $ 89.22 Part c: Ret over a year = [ Expected Price after 1 Year / Price Today ] - 1 = [ $ 89.22 / $ 85.05 ] - 1 = 0.049 Ret over a year is 0.049 or 4.9%

Summary—Payback Criteria

Payback period •Length of time until initial investment is recovered. •Take the project if it pays back in some specified period. •Does not account for time value of money, and there is an arbitrary cutoff period. Discounted payback period •Length of time until initial investment is recovered on a discounted basis. •Take the project if it pays back in some specified period. •There is an arbitrary cutoff period.

Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9 percent, and payback cutoff is 4 years. •What is the payback period? •What is the discounted payback period? •What is the N P V? only one that reliably gives correct answer •What is the I R R? •Should we accept the project?

Payback period = 4 years The project does not pay back on a discounted basis. NPV = -2758.72 IRR = 7.93% Accept the project if the IRR is greater than the discount rate. Reject the project if the IRR is less than the discount rate.

Interest Rate Risk Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 18 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

Percentage change in price of Bond J: N = 28 (14 x 2) I/Y = (6 / 4) PMT = ( 30 / 2) FV = (-1000) CPT - >PV = 718.54 Adding the YTM rise from 6 to 8 percent in Bond J: N = 28 (14 x 2) I/Y = (8% / 2) PMT = (30 / 2) FV = (-1000) CPT -> PV = 583.42 Now computing the percent change in Bond J: (583.42 - 718.54) / 718.54 = -18.80 %

FV of an uneven cash flow stream .At a rate of 8%, what is the future value of the following cash flow stream? $0 at Time 0; $100 at the end of Year 1; $300 at the end of Year 2; $0 at the end of Year 3; and $1000 at the end of Year 4?

Present Value= CF1/(1+r)1+CF2/(1+r)^2+CF3/(1+r)^3+CF4/(1+r)^4=0+100/1.08+300/1.081^2+0/1.08^3+1,000/1.08^4=1,084.82

7. Stock Valuation Hailey Corp. pays a constant $9.45 dividend on its stock. The company will maintain this dividend for the next 13 years and will then cease paying dividends forever. If the required return on this stock is 10.7 percent, what is the current share price?

Present value of annuity = Annuity * ( 1 - (1 + rate)^-number of periods) / rate = 9.45 * ( 1 - (1 + 10.7%)⁻¹³) / 10.7% = 9.45 * 6.8529386295 = $64.76

Payback and NPV An investment under consideration has a payback of seven years and a cost of $745,000. If the required return is 11 percent, what is the worst-case NPV? The best-case NPV? Explain. Assume the cash flows are conventional

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period) =745,000/1.11^7 =$745,000*0.48165841 =$358,835.515 NPV=Present value of inflows-Present value of outflows =$$358,835.515-745,000 =(386,164.485) (Approx)(Negative)

Accrued Interest You purchase a bond with an invoice price of $1,053 and a par value of $1,000. The bond has a coupon rate of 5.3 percent, and there are four months to the next semiannual coupon date. What is the clean price of the bond?

Purchase Price: 1053 Accrued Interest = Par x (CR/100) x 2/12 1000 x (5.3/100) x 2/12 = 8.8333333 1053 - 8.83 = 1044.166667

The Fisher Effect: Example If we require a 10 percent real return and we expect inflation to be 8 percent, what is the nominal rate?

R = (1.1) × (1.08) − 1 = .188, or 18.8% Approximation: R = 10% + 8% = 18%

Nominal and Real Returns An investment offers a total return of 11.7 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 9 percent. What does Janice believe the inflation rate will be over the next year?

Real Rate of return = ((1+Nominal Rate)/(1+Inflation Rate))-1 Real Rate of return = 9% Nominal Rate = 11.7% Real Rate of return = ((1+Nominal Rate)/(1+Inflation Rate))-1 .09= ((1+.117)/(1+Inflation Rate))-1 .09 + 1 = (1.117)/(1+Inflation Rate) 1.09 = 1.117 / (1+Inflation Rate) 1+Inflation Rate = 1.117 / 1.09 1+Inflation Rate = 1.02477064220183 Inflation Rate = 1.02477064220183 - 1 Inflation Rate = 0.0248 Inflation Rate = 2.48%

Real Cash Flows You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $700 per month in a stock account in real dollars and $300 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 11 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an effective return of 9 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? What is the nominal dollar amount of your last withdrawal?

Real rate of return for the stock account: 11%−4%=7% Real rate of return for the bond account:7%−4%=3% To calculate the future value of the investments in the stock and bond accounts, we can use the following formula: FV = PV * (1 + r)^n Where: FV is the future value PV is the present value r is the real rate of return n is the number of periods Future value of the stock account: $700×(1+0.07)^30=$120,386.75 For the bond account, the present value is $300 per month, the real rate of return is 3%, and the number of periods is 30 years. Future value of the bond account: 300∗(1+0.03)^30=50,592.25 FV = PV * (1 + r)^n Combine the future values of the stock and bond accounts into a single account with an effective return of 9 percent. Future value of the combined account:$170,979×(1+0.09)^25=$688,024.75 Calculate the monthly withdrawal amount in real terms. The real rate of return is 4%, and the number of periods is 25 years. Monthly withdrawal amount in real terms:$688,024.75/(1+0.04)^25=$2,821.93 Calculate the nominal dollar amount of the last withdrawal. Nominal dollar amount of the last withdrawal: $2,821.93×(1+0.04)^25=$4,951.56

2. Stock Values The next dividend payment by Im, Inc., will be $1.87 per share. The dividends are anticipated to maintain a growth rate of 4.3 percent forever. If the stock currently sells for $37 per share, what is the required return?

Required return=(D1/Current price)+Growth rate =(1.87/37)+0.043 =0.0505405405+0.043 which is equal to =9.35%(Approx)

Stock Valuation and EV FFDP Corp. has yearly sales of $43 million and costs of $14 million. The company's balance sheet shows debt of $58 million and cash of $19 million. There are 1.85 million shares outstanding and the industry EV/EBITDA multiple is 6.4. What is the company's enterprise value? What is the stock price per share?

Sales = $ 43 M Costs = $ 14 M EBITDA=Sales − Costs=$43−14=$29 EV/EBITDA = 6.4 times Enterprise value=EV/EBITDA ∗EBITDA=6.4×$29=$185.60 Enterprise Value, EV = $185.60 Debt = $ 58 Cash = $ 19 M Market value of equity=EV−Debt+Cash=$185.60−58+19=$146.60 Number of shares o/s = 1.85 M Price per share =Market value of equity/ Number of shares o/s=$146.60/1.85=$79.24 Enterprise value of company = $185.60 Million Stock price per share =$ 79.24

What is the price of the bond? Par Value =1,000Settlement date 1/1/2000Maturity date 1/1/2015Annual coupon rate =7.00%Coupons per year =2Yield to maturity =7%

Semi annual coupon = (7%/2)*1000 = 35 Semi annual Yield to maturity = 7%/2 = 0.035 Time = (2015-2000)*2 = 30 The price of the bond = Coupon*((1-(1+r)^-n)/r + F/(1+r)^n The price of the bond = ((35*((1-1.035^-30)/0.035) + 1000/1.035^30 The price of the bond =643.72 + 356.28 The price of the bond = $1000

Valuing Bonds Air Taxi, Inc. has issued a bond with the following characteristics:Par Value 1,000Settlement date 1/1/2000Maturity date 1/1/2015Annual coupon rate 7.00%Coupons per year 2Yield to maturity 9%What is the price of the bond?

Semi annual coupon = (7%/2)*1000 = 35 Semi annual Yield to maturity = 9%/2 = 0.045 Time = (2015-2000)*2 = 30 The price of the bond = Coupon*((1-(1+r)^-n)/r + F/(1+r)^n The price of the bond = ((35*((1-1.045^-30)/0.045) + 1000/1.045^30 The price of the bond =570.11 + 267.00 The price of the bond = $837.11

19. Valuing Preferred Stock E-Eyes.com just issued some new 20/20 preferred stock. The issue will pay an annual dividend of $20 in perpetuity, beginning 20 years from now. If the market requires a return of 5.4 percent on this investment, how much does a share of preferred stock cost today?

Stock price=Dividend/Rate(1+rate)n= ($20)/5.4%/(1+0.054)^19=$136.53

Constant Growth Example

Suppose Big D, Inc., just paid a dividend of $.50. It is expected to increase its dividend by 2 percent per year. If the market requires a return of 15 percent on assets of this risk level, how much should the stock be selling for? .5(1.02) / (.15 - .02) = 3.92

YTM with Semiannual Coupons

Suppose a bond with a 10 percent coupon rate and semiannual coupons has a face value of $1,000, 20 years to maturity, and is selling for $1,197.93. •Is the YTM more or less than 10 percent? •What is the semiannual coupon payment? •How many periods are there? •N = 40; P V = −1,197.93; P M T = 50; F V = 1,000; C P T I/Y = 4% YTM = 4% x 2 = 8%

Treasury bill rate Suppose the real rate is 3.1 percent and the inflation rate is 4.7 percent.What rate would you expect to see on a Treasury bill?

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h) R = (1 + .031)(1 + .047) - 1 R = .0795, or 7.95%

Real return Say you own an asset that had a total return last year of 10.8 percent. If the inflation rate last year was 5.1 percent, what was your real return?

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is: (1 + R) = (1 + r)(1 + h) r = [(1 + .108) / (1 + .051)] - 1 r = .0542, or 5.42%

MIRR Chamberlain Corp. is evaluating a project with the following cash flows:Year Cash Flow0 -$ 19,5001 7,9302 9,4903 8,9704 7,2105 - 3,980Required:The company uses an interest rate of 10 percent on all of its projects. Calculate the MIRR of the project using all three methods.

The MIRR for the project with all three approaches is: Discounting approach: In the discounting approach, we find the value of all cash outflows at time 0, while any cash inflows remain at the time at which they occur. So, discounting the cash outflows at time 0, we find: Time 0 cash flow = -$19,500 - $3,980 / 1.105 Time 0 cash flow = -$21,971.27 So, the MIRR using the discounting approach is: 0 = -$21,971.27 + $7,930 / (1 + MIRR) + $9,490 / (1 + MIRR)2 + $8,970 / (1 + MIRR)3 + $7,210 / (1 + MIRR)4 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: MIRR = 19.75% Reinvestment approach: In the reinvestment approach, we find the future value of all cash except the initial cash flow at the end of the project. So, reinvesting the cash flows to Time 5, we find: Time 5 cash flow = $7,930(1.104) + $9,490(1.103) + $8,970(1.102) + $7,210(1.10) - $3,980 Time 5 cash flow = $39,046.20 So, the MIRR using the reinvestment approach is: 0 = -$19,500 + $39,046.20/(1+MIRR)5 $39,046.20 / $19,500 = (1+MIRR)5 MIRR = ($39,046.20 / $19,500)1/5 - 1 MIRR = .1490, or 14.90% Combination approach: In the combination approach, we find the value of all cash outflows at Time 0, and the value of all cash inflows at the end of the project. So, the value of the cash flows is: Time 0 cash flow = -$19,500 - $3,980 / 1.105 Time 0 cash flow = -$21,971.27 Time 5 cash flow = $7,930(1.104) + $9,490(1.103) + $8,970(1.102) + $7,210(1.10) Time 5 cash flow = $43,026.20 So, the MIRR using the discounting approach is: 0 = -$21,971.27 + $43,026.20 / (1 + MIRR)5 $43,026.20 / $21,971.27 = (1 + MIRR)5 MIRR = ($43,026.20 / $21,971.27)1/5 - 1 MIRR = .1439, or 14.39%

Suppose the following bond quotes for IOU Corporation appear in the financial page of today's newspaper. Assume the bond has a face value of $2,000 and the current date is April 19, 2015.Company (Ticker) Coupon Maturity Last Price Last Yield EST Vol (000s)IOU (IOU) 6.4 Apr 19, 2028 103.96 ?? 1,838

The current yield is the annual coupon payment divided by the bond price, so: Current yield = $128 / $2,079.20 Current yield = .0616, or 6.16% Calculator Solution: Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. Enter N: 26 I/Y: X PV: $2,079.20 PMT: 128 / 2 FV: 2,000 2.979% × 2 = 5.96%

11. Stock Valuation Quinoa Farms just paid a dividend of $2.95 on its stock. The growth rate in dividends is expected to be a constant 3.4 percent per year indefinitely. Investors require a return of 15 percent for the first three years, a return of 13 percent for the next three years, and a return of 11 percent thereafter. What is the current share price?

The dividends for the years are: Year 1: = 2.95 x ( 1 + 0.034) = $3.0503 Year 2: = 3.0503 x ( 1 + 0.034) = $3.1540 Year 3: = 3.154 x 1.034 = $3.2612 Year 4: = 3.2612 x 1.034 = $3.3721 Year 5: = 3.3721 x 1.034 = $3.4868 Year 6: = 3.4868 x 1.034 = $3.6053 Year 7: = 3.6053 x 1.034 = $3.7279 This allows us to calculate the terminal value at year 6: = 3.7279 / (11% - 3.4%) = $49.05 The current price is: = 3.0503 / 1.15 + 3.1540 / 1.15² + 3.2612 / 1.15³ + 3.3721 / (1.15³ x 1.13) + 3.4868 / (1.15³ x 1.13²) + 3.6053 / (1.15³ x 1.13³) + 49.05 / (1.15³ x 1.13³) = $34.93

How does inflation affect interest rates?

The higher the inflation rate, the more interest rates are likely to rise.

Calculating Payback Period and NPV Janina, Inc., has the following mutually exclusive projects. Project A CF Year 0 =−$ 20,000 CF Year 1= 15,200 CF Year 2=5,900 CF Year 3= 2,100 Project B CF Year 0 =−$ 23,000 CF Year 1= 14,300 CF Year 2 =8,100 CF Year 3= 7,100 a. Suppose the company's payback period cutoff is two years. Which of these two projects should be chosen? b. Suppose the company uses the NPV rule to rank these two projects. Which project should be chosen if the appropriate discount rate is 15 percent?

The initial cost of project A is 20,000, the cash flow in year 1 is 15200, and the cash flow in year 2 is 5900. Therefore, break-even will happen between years 1 and 2. Payback period − Project A =Year before Break even + unrecovered amount / cash flow in recovery year =(1+20,000−15,200/5,900.000)=1.814years Therefore, the payback period of project A is 1.814 years. The initial cost of project B is 23,000; the cash flow in year 1 is 14,300; the cash flow in year 2 is 8,100; and the cash flow in year 3 is 7,100. Therefore, break-even will happen between years 2 and 3. Payback period − Project B=Year before Break even + unrecovered amount / cash flow in recovery year=2.000+23,000−(14,300+8,100)/7,100=2.085years Therefore, the payback period of project B is 2.085 year Therefore, only project A will be selected. NPV − Project A =CF 0 + CF1/(1+r)^1+ CF2/(1+r)^2+ CF3/(1+r)^3 =−$20,000+(15,200÷(1+15%)^1)+(5,900÷(1+15%)^2)++(2,100÷(1+15%)^3)=$−940.58 Therefore, the NPV of Project A is $ -940.58 NPV − Project B=CF 0 + CF1/(1+r)^1+ CF2/(1+r)^2+ CF3/(1+r)^3=−$23,000+(14,300÷(1+15%)^1)+(8,100÷(1+15%)^2)+(7,100÷(1+15%)^3)=$227.91 Therefore, the NPV of Project B is $ 227.91 Therefore, Project B alone should be chosen.

Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the inflation rate is 2.7 percent. What rate would you expect to see on a Treasury bill?

The rate of return on Treasury Bills can be calculated as follows: Nominal rate of return = (1+ Real rate of return)(1+ Inflation rate) - 1 Nominal rate of return = (1 +0.018)(1+0.027) - 1 Answer: The Rate of return that one would expect to see on Treasury Bills is 4.55%

Bond Yields Heginbotham Corp. issued 15-year bonds two years ago at a coupon rate of 8.5 percent. The bonds make semiannual payments. If these bonds currently sell for 106 percent of par value, what is the YTM?

The yield to maturity is given by rate function in excel as =rate(nper,pmt,pv,fv) where nper = 15 * 2 = 30 semiannual periods pmt = 0.085 *1000 = 85/2 = 42.5 pv = 1060 FV =1000 Hence semiannual yield = rate(30,42.5,-1060,1000) = 3.9069% Hence annual yield = 3.9069*2 = 7.8139% = 7.81%

8.2 Government and Corporate Bonds

Treasury Securities: •Federal government debt. If the US government owes me, the money is promising the full faith and credit of the US government. we're thinking about Treasuries, we're thinking about typically what we call the risk free rate for a Treasury bond, because the government can always pay back their debt. •T-bills—pure discount bonds with original maturity less than one year. municipal securities, which are state or local securities that they may issue to build roads •T-notes—coupon debt with original maturity between one and ten years. •T-bonds—coupon debt with original maturity greater than ten years.

Zero Coupon Bonds You buy a zero coupon bond at the beginning of the year that has a face value of $1,000, a YTM of 5.3 percent, and 25 years to maturity. If you hold the bond for the entire year, how much in interest income will you have to declare on your tax return? Assume semiannual compounding.

Value of the zero−coupon bond =Par value / (1+Rate)^Period =$1,000÷(1+0.0265)^50=$270.43 =$1,000÷(1+0.0265)^48=$284.95 The calculated value of the zero-coupon bond is $284.95. Interest income =Value of the zero coupon bond after 1 year− Value of the zero coupon bond =$284.95−$270.43=$14.52 The interest income is $14.52.

Calculating Annuities Due You want to lease a set of golf clubs from Pings Ltd. The lease contract is in the form of 24 equal monthly payments at an APR of 10.4 percent compounded monthly. Because the clubs cost $3,850 retail, the company wants the value today of the lease payments to equal $3,850. Suppose that your first payment is due immediately. What will your monthly lease payments be?

We can solve for PMT as follows: 2800 = PMT x (1-(1+.093/12)^(-12x2))/(.093/12) $2,800=PMT×[1−(1+0.09312)−12×20.09312] $2,800=PMT×0.1691308458/0.00775 $2,800=PMT×21.8233349419 PMT=$2,800/21.8233349419=$128.30 Explanation: In this case, PV = $2,800, r = 0.093 (9.3%), n = 12 (compounded monthly), and t = 2 (24 months / 12). Therefore, your monthly lease payments would be $128.30

Valuing Bonds Valuing Bonds What is the price of a 20-year, zero coupon bond paying $1,000 at maturity, assuming semiannual compounding, if the YTM is: a.6 percent? b.8 percent?

a) YTM = 6 percent = 0.06 P=1,000(1+0.062)^2×20 =1,000(1.03)^40 =1,0003.262 =$306.56 Explanation: We got the YTM = 6% is $306.56 b) YTM = 8 percent = 0.08 P=1,000(1+0.082)^2×20 =1,000(1.04)^40 =1,0004.801 =$208.28 = YTM

Finding the Maturity You found a 10 percent coupon bond on the market that sells for par value. What is the maturity on this bond?

hence the maturity of bond can be any number of periods

Finding the Dividend Sorenson, Inc., is expected to pay equal dividends at the end of each of the next two years. Thereafter, the dividend will grow at a constant annual rate of 5.3 percent, forever. The current stock price is $58. What is next year's dividend payment if the required rate of return is 13 percent?

idend Year 2 =D D3=D×(1+g) TerminalValue=D3r−g TerminalValue=D×1+gr−g P0=D1+r+D1+r+D×1+gr−g×1(1+r)^2 58=D1+13%+D(1+13%)^2+D×1+5.3%13%−5.3%×1(1+13%)^2 58=D×(11.13+11.13^2+1.05313%−5.3%×11.13^2 58=D×12.3778875991265 D=58/12.3778875991265 D=4.69 Explanation for step 2

What determines the price of a share of stock?

if you know the dividends and you know the dividend stream and you know the growth rate and, you know, the discount rate or the risk adjusted rate of return, you can actually calculate the price of a stock

Nonconstant Dividends McCabe Corporation is expected to pay the following dividends over the next four years: $15, $11, $9, and $2.95. Afterward, the company pledges to maintain a constant 4 percent growth rate in dividends forever. If the required return on the stock is 10.3 percent, what is the current share price?

of Share Price in Year 4 Required Return (ke) = 12% or 0.12 Share Price in Year 4= Dividend in Year 5 / (Ke − g)=6.825/0.12−0.05=97.500 Share Price in Year 4 = $97.50 Share Price in Year 4 is needed to calculate Current Share Price. Calculation of Current Share Price Current Share Price=(Dividend in Year 1 / (1 + Ke)^Year) + (Dividend in Year 2 / (1 + Ke)^Year) + (Dividend in Year 3 / (1 + Ke)^Year) + (Dividend in Year 4 / (1 + Ke)^Year) + (Share Price in Year 4 / (1 + Ke)Year)=(15/(1+0.12)^1)+(11/(1+0.12)^2)+(10/(1+0.12)^3)+(6.50/(1+0.12)^4)+(97.50/(1+0.12)^4)=95.37 Current Share Price = $95.37

Real Cash Flows When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. The week after she died in 1962, a bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $7. Based on actuarial tables, "Joltin' Joe" could expect to live for 30 years after the actress died. Assume that the EAR is 6.8 percent. Also, assume that the price of the flowers will increase at 3.5 percent per year, when expressed as an EAR. Assuming that each year has exactly 52 weeks, what is the present value of this commitment? Joe began purchasing flowers the week after Marilyn died.

rate compounded weekly=((1+10.9%)^(1/52)-1)*52=10.356% price rise compounded weekly=((1+4.2%)^(1/52)-1)*52=4.116% Present value of the commitment=4/(1+10.356%/52)*(1-((1+4.116%/52)/(1+10.356%/52))^(52*39))/(1-((1+4.116%/52)/(1+10.356%/52)))=$3,039.94

5. Stock Valuation Caccamise Co. is expected to maintain a constant 3.4 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 5.3 percent, what is the required return on the company's stock?

required return=dividend yield+growth rate=5.3%+3.4%=8.7000%

Calculating Real Rates of Return If Treasury bills are currently paying 4.6 percent and the inflation rate is 1.9 percent, what is the approximate real rate of interest? The exact real rate?

s the inflation rate is 1.9% for the period, Approximate real rate of return=4.6%−1.9%=0.027 Exact real rate of return=(1+4.6%) / (1+1.9%−1)=0.0265 Real rate of return is the difference or the ratio between the nominal rate and inflation rate

what factors determine the required return on the bonds?

that has to do with what the what the alternative investments in the market are available or that are available to you. So if you know what the alternate investment's available to your yielding for a similar risk,

What is the term structure of interest rates?

that tells you for a risk free bond for a our fixed risk bond Usually we think about term structure in terms of US treasuries. What's the yield maturity for a risky bond Of different maturities. And generally that's upward sloping but it could be downward sloping in the

What are some of the major characteristics of N Y S E and Nasdaq?

the NASDAQ, the New York Stock Exchange is an auction market. got one logical location, one one book that every every New York Stock Exchange trade trades over Nasdaq is a distributed market over the counter trades Each broker is going to trade It's going to trade that stock separately in their own in their own marketplace.

What are bond ratings, and why are they important?

they kind of give you an assessment of likelihood of at least one company's assessment of the likelihood of default on a particular bond.

Discuss the importance of valuation ratios.

valuation ratios are important checks you can actually look for in general. The p e ratio is going to be higher if people think a stock is going to be growing faster. So there's. So the higher G is, the higher the P ratio tends to be.

What determines g and R in the D G M?

when you're calculating that terminal value of the stock

Suppose you buy a bond with a 12 percent annual coupon, payable semiannually; you pay $1,080; and the next coupon is due in four months

•$1,080 is the dirty, or invoice, price. •The next coupon will be $60. Accrued interest = (2/6)($60) = $20 Clean Price = $1080 - 20 = $1,060

What are some of the problems associated with financial statement analysis?

•There is no underlying theory, so there is no way to know which ratios are most relevant •Benchmarking is difficult for diversified firms •Globalization and international competition makes comparison more difficult because of differences in accounting regulations •Firms have different fiscal years •Extraordinary, or one-time, events

CALCULATING TOTAL CASH FLOWS Nightwish Corp. shows the following information on its 2021 income statement: Sales = $336,000; Costs = $194,700; Other expenses = $9,800; Depreciation expense = $20,600; Interest expense = $14,200; Taxes = $21,275; Dividends = $21,450. In addition, you're told that the firm issued $7,100 in new equity during 2021 and redeemed $5,400 in outstanding long-term debt. a. What is the 2021 operating cash flow? b. What is the 2021 cash flow to creditors? c. What is the 2021 cash flow to stockholders? d. If net fixed assets increased by $53,200 during the year, what was the addition to net working capital (NWC)?

(a) Operating cash flow =EBIT -Taxes +Depreciation 336000 - 194,700 - 9800 - 26000 + 26000 - 21275 =110900-21275+20600 =110225 (b) Cash flow to creditors =Interest paid +Debt redeemed =14200+5400 =19600 (c) Cash flow to stockholders =Dividend -new equity raise =21450-7100 =14350 (d) Net capital spending =Net fixed assets increased +Depreciation =53200+20600 =73800 Addition to NWC =Operating cash flow -net capital spending-cash flow to shareholders-cash flow to creditors =110225-73800-19600-14350 =2475

Present Value and Discount Rates What is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought an annuity with 13 annual payments of $10,000 per year at a discount rate of 10 percent per year. What happens to the value of your investment if the discount rate suddenly drops to 5 percent?

(i) Calculation of Present Value of Annuity Rate (R) = 10% or 0.10 Annuity Payment (P) = $10,000 Period (n) = 13 years Present Value of Annuity = P * [{1 - (1 + R)^-n} / R] = 10,000 * [{1 - (1 + 0.10)^-13} / 0.10] = 10,000 * [{1 - (1.10)^-13} / 0.10] = 10,000 * [{1 - 0.28966438} / 0.10] = 10,000 * [0.7103356 / 0.10] = 10,000 * 7.103356 = $71,033.56 (ii) Calculation of Present Value of Annuity Rate (R) = 5% or 0.05 Annuity Payment (P) = $10,000 Period (n) = 13 years Present Value of Annuity = P * [{1 - (1 + R)^-n} / R] = 10,000 * [{1 - (1 + 0.05)^-13} / 0.05] = 10,000 * [{1 - (1.05)^-13} / 0.05] = 10,000 * [{1 - 0.53032135} / 0.05] = 10,000 * [0.46967865 / 0.05] = 10,000 * 9.393573 = $93,935.73

Sustainable Growth Rate The Iron River Company has an ROE of 11.05 percent and a payout ratio of 25 percent. a. What is the company's sustainable growth rate?

- Return on Equity(ROE) = 11.05% - Payout Ratio = 25% − Retention ratio(b) =1 − Payout Ratio=1−0.25=0.75 - Calculating the company's Sustainable Growth Rate:- Sustainable Growth Rate=ROE×b ÷1−(ROE×b) Sustainable Growth Rate=0.1105×0.75÷1−(0.1105×0.75) Sustainable Growth Rate=0.082875÷ 1−0.082875 Sustainable Growth Rate=0.082875÷0.917125 Sustainable Growth Rate=0.090364 So, the company's Sustainable Growth Rate is 9.04%

1. You buy a CD (certificate of deposit) with $10,000 today. Interest rate is 8%, compounding monthly. How much you can get in two years? (keep the integer, 135.67 => 135); 2. You buy a CD with $10,000 today. Interest rate is 8%, compounding annually. How much you can get in two years? (keep the integer, 135.67 => 135) 3. You are saving money to buy a CD with $10,000 in 6 months. Interest rate is 8%, compounding monthly. You already have $7,000. How much more you still need for now? (keep the integer, 135.67 => 135)

1) Compound = Monthly = 12 Present Value = pv = $10,000 Interest Rate = r = 8 / 12 = .666667% Time = t = 2 (2 years) * 12 (monthly) = 24 FV = pv x (1xr)^2 10000 x (1 + .0066666)^24 = 11728 2) PV: 10000 I/Y: 8/1 = 8 N: 2 x 1 = 2 PMT: 0 10000 x (1+ .08)^2 = 11664 FV = 11664 3) I/Y: 8÷12 = .666666 N: 6 month compounding monthly = 6 FV: 10000 PMT: 0 FV: 9609 9609 - 7000 = 2609 PV: 7000 I/Y: 8÷12 = .666666 N: 6 month compounding monthly = 6 FV: N/A PMT: 0 PV: 7,284.71 10000 - 7284.71 = 2715.29 FV: 2715.19 PMT: 0 N: 6 I/Y: 8 ÷ 12 = .66666 PV: 2609

1) You need $50,000 to buy a car in three year. If interest rate (required return) is 20%, compounding annually. How much you need to have now? (keep the integer, 135.67 => 135); 2) You need $50,000 to buy a car in three year. If interest rate (required return) is 20%, compounding continuously. How much you need to have now? (keep the integer, 135.67 => 135);

1) FV: 50,000 I/Y: 20% N: 3 years PMT: 0 Present value = future value÷(1+ interest rate)^n PV: 28935 Compounding continuously 2) Present value = future value ÷ e^​​​​​(interest rate x n) 50000 ÷ e ^ (20% x 3) = 27440

1) An investment offers $4,000 every quarter for 20 years, with the first payment occurring 1 quarter from now. If the required return is 8 percent, what is the value of the investment? 2) An investment offers $4,000 every quarter for 20 years, with the first payment just occurred. If the required return is 8 percent, what is the value of the investment? 3) An investment offers $4,000 every quarter forever. If the required return is 8 percent, what is the value of the investment?

1) PMT: 4000 N: 20 year x quarterly = 80 I/Y: 8% ÷ 4 = 2 FV: 0 PV: 158,978 2) 158,978 x 1.02 = 162,157.56 3) FOREVER 4000 ÷ .02 = 200,000

You are expecting to get $3000 in five years (5 years from now). Assume interest rate is 10% and continuously compounding. (Answer format: keep the integer, 135.67 => 135) 1) What is the value now? 2) What will be the value in year 7?

1) PV = FV ÷ e^(r x n) PV = 3000 ÷ e^(.1 x 5) = 1819.59 2) FV = CF5 x e^(r x n) FV = 3,000 x e^(.1 x 2) = $3,664

You are expecting to get $3000 in five years (5 years from now). Assume interest rate is 8% and quarterly compounding. (Answer format: keep the integer, 135.67 => 135) 1) What will be the value in year 2? 2) What will be the value in year 8?

1) PV: FV: 3000 N: 3 x 4 = 12 I/Y: 8% ÷ = 2% Present value = future value÷(1+ interest rate)^n 3000 ÷ *(1 + 0.08/4)^(3 x 4) = 2366 2) PV: 3000 PMT: 0 I/Y: 8% ÷ 4 quarterly = 2% N: 3 years x 4 quarterly = 12 FV: 3804 A = 3000*(1 + 0.08/4)^(3 x 4) = 3804

What are the three major forms of business organization?

1) The Sole Proprietorship. One person to running a business 2) The Partnership: General Partnership > Limited Partnership. 3) The Corporation: separated the ownership from control

Days' Sales in Receivables A company has net income of $213,700, a profit margin of 7.1 percent, and an accounts receivable balance of $126,385. Assuming 65 percent of sales are on credit, what is the company's days' sales in receivables

1. Calculation of the total sales :- Total sales=Net income / Profit margin=$213,700÷ 7.1%=$3,009,859.15 2. Calculation of credit sales :- Credit sales=Total sales ∗ 65% =$3,009,859.15×65% =$1,956,408.45 3. Calculation of receivable turnover :- Receivable turnover=Credit sales / Accounts receivable $1,956,408.45 ÷ $126,385=15.48 Accounts receivable Days′ sales in receivable =365 ÷ Accounts receivable turnover =365 ÷ 15.48 = 23.58days

Chapter 3 Using the DuPont Identity Y3K, Inc., has sales of $5,987, total assets of $2,532, and a debt-equity ratio of .57. If its return on equity is 11 percent, what is its net income?

1. Equity Amount = Total Assets * 1 / (1 + DE Ratio) Equity Amount = 2532 * 1 / 1.57 Equity Amount = $1612.74 2. Net Income = Equity * ROE Net Income = 1612.74 * 11% Net Income = $177.40

Calculating Taxes Timmy Tappan is single and had $189,000 in taxable income. Using the rates from Table 2.3 in the chapter, calculate his income taxes. What is the average tax rate? What is the marginal tax rate? 0-9875 10% 9875-40,125 12% 40,125-85,525 22% 85,525-163,300 24% 163,300-207,350 32%

10($9,875) + .12($40,125 - 9,875) + .22($85,525 - 40,125) + .24($163,300 - 85,525) + .32($189,000 - 163,300) = 41,495.50Avg tax rate = tax paid / taxable income41,495.50 / 189,000 = 21.96% Marginal Tax Rate: 32%

13. The tax rates are as shown. Your firm currently has taxable income of $95000. Taxable Income Tax Rate (%) $0 - 50,000 15% 50,001 -75,000 25% 75,001 -100,000 35% 100,001 -335,000 39% What is the average tax rate?

= (50000*.15)+(75000-50000)*.25)+(95000-75000)*.35) = (7500+6250+7000) =20750. Average tax rate= (total tax payable/total taxable income) = (20750/95000)= 21.8% = 21.8%(Approximately). What is the marginal tax rate? 35% What shall be the taxable income used to determine the marginal tax rate? A or B A. $95000 B. $95001 so B

Financial Cash Flows The Stancil Corporation provided the following current information: Determine the total cash flows spent on fixed assets and NWC. What are the cash flows to investors of the firm? Proceeds from long-term borrowing $ 18,300 Proceeds from the sale of common stock 5,300 Purchases of fixed assets 22,300 Purchases of inventories 3,200 Payment of dividends 15,800

=-Purchases of fixed assets- Purchases of inventories =-22300-3200 =-25500 the cash flows to investors of the firm=15800-18300-5300=-7800

There are two financial products. A will offer $120,000 in five years. B will offer $5000 every quarter from now for five years. Assuming quarterly compounding and your required return is 10%. Which product should you invest today? What is the present value of product A? What is the present value of product B? Which product is more valuable today, A or B?

A) FV: 120,000 N: 5 x 4 (Quarterly) = 20 I/Y: 10%/4 = 2.5 PMT: 0 PV: 73232 B) N: 5 x 4 = 20 PMT: 5000 I/Y: 10%/4 = 2.5 FV: N/A PV: 77,945.81 Accelerate 77945.81 x 1.025 = 79894

Comparing Cash Flow Streams You have your choice of two investment accounts. Investment A is a 13-year annuity that features end-of-month $1,600 payments and has an APR of 7.8 percent compounded monthly. Investment B is a 7 percent continuously compounded lump sum investment, also good for 13 years. How much money would you need to invest in Investment B today for it to be worth as much as Investment A 13 years from now?

A) No. of years=13Monthly annuity (A)=$1,100Annual interest rate=6.7% Monthly interest rate (r)=Annual interest rate÷12 =0.067/ 12 No. of monthly paymens (n) =No. of years ∗ 12=13×12 =156 Future value of annuity=A×(1+r)^n−1r Future value of annuity=$1,100(×((1+0.067/12)^156) −1)/(0.067/12) =$272,573.66 B Future value of Investment A (FV)=$272,573.66Annual interest rate (r)=6.2% (continuous compounding)No. of years (n)=13 Investment or Present value=FV/ (e^ n×r) Investment or Present value=$272,573.66e^(0.062×13)=$121,742.59 Final answer: The lump sum amount you need to invest in B today is: $121,742.59, to be worth as much as investment A 13 years from now.

BUILDING AN INCOME STATEMENT During the year, the Senbet Discount Tire Company had gross sales of $1.07 million. The firm's cost of goods sold and selling expenses were $526,000 and $216,000, respectively. The firm also had notes payable of $810,000. These notes carried an interest rate of 6 percent. Depreciation was $131,000. The firm's tax rate was 30 percent. What is net income? What is operating cash flow?

A) Sales = $1,070,000 B) Cost of goods sold = $526,000 C) Selling Expenses = $216,000 D) Depreciation = $131,000 E) $1,070,000 - $526,000 - $216,000 - $131,000 = EBIT = $197,000 Less: Interest = $48,600 ($810,000 *6%) Taxable Income = 197,000- 48,600 = $148,400 Less: Income tax = $44,520 (148,400 *30%) 148,400 - 44,520 = Net Income = $103,880 Operating Cash Flow = EBIT + Depreciation - taxes Operating Cash Flow = $197,000 + $131,000 - $44,520 Operating Cash Flow = $283,480

Calculating Present Values A five-year annuity of ten $5,900 semiannual payments will begin 9 years from now, with the first payment coming 9.5 years from now. The discount rate is 8 percent compounded monthly. what is the value of this annuity five years from now? What is the value three years from now? What is the current value of the annuity?

APR r = 8% or 0.08 n = 12 (compounded monthly, which is 12months/1month) Now effective annual rate EAR = ((1+(r/n))^n)-1 EAR = ((1+(0.08/12))^12)-1 EAR = 0.083 Now effective semi annual rate ESAR = (1+r)^(1/2) - 1 ESAR = (1+0.083)^(1/2) - 1 ESAR = 0.04067 or 4.067% Payment amount A = 5,900 Number of payment n = 10 Period N = 4 (year 9 less year 5) Rate semi annual r = 0.04067 or 4.067% EAR = 0.083 PV(5) = [A×Annuity(r,n)] /(1+EAR)^N) PV(5) = A× [(1-((1+r)^-n))/r] /(1+EAR)^N)] PV(5) = 5,900 × [(1-((1+0.04067)^-10))/0.04067] /(1+0.083)^4 PV(5) = 34,670.07 Now present value will be PV(3) = PV(5)/(1+EAR)^N PV(3) = 34,670.07/(1+0.083)^2 PV(3) = 29,559.57 Step 4 present value today PV(3) = 29,559.57 Period N = 3 EAR = 0.083 Now present value will be PV = PV(3)/(1+EAR)^N PV = 29,559.57/(1+0.1268)^3 PV = 23,270.91

What is the difference between accounting income and cash flow? Which do we need to use when making decisions?

Accounting income has non cash items so cash flow does look at the actual cash balances

Perpetuities An investor purchasing a British consol is entitled to receive annual payments from the British government forever. What is the price of a consol that pays $210 annually if the next payment occurs one year from today? The market interest rate is 4 percent.

Amount Paid Annually(CF) = $210 Interest rate (r) = 4% Price of Consol=Annual Payment / Interest Rate Price of Consol=$2100.04 Price of Consol=$5,250 The Formula of Present value of perpetuity is used.

Annuity Present Values What is the value today of a 15-year annuity that pays $550 per year? The annuity's first payment occurs six years from today. The annual interest rate is 10 percent for Years 1 through 5, and 12 percent thereafter.

Annual Payment = $550 Interest Rate for Year 1 - Year 5 = 10% Interest Rate for Year 6 - Year 20 = 12% Value of Annuity at the end of Year 5 = $550/1.12 + $550/1.12^2 + $550/1.12^3 + ... + $550/1.12^15 Value of Annuity at the end of Year 5 = $550 * (1 - (1/1.12)^15) / 0.12 Value of Annuity at the end of Year 5 = $550 * 6.81086 Value of Annuity at the end of Year 5 = $3,745.973 Present Value of Annuity = $3,745.973/1.10^5 Present Value of Annuity = $2,325.95 So, current value of the annuity is $2,325.95

How do you standardize balance sheets and income statements?

Balance Sheet: compute all accounts as a percent of total assets Income Statement: compute all line items as a percent of sales the case of balance sheets, divided by total assets in the case of income statement, divide by total sales.

What is the difference between book value and market value? Which should we use for decision-making purposes?

Book value is where it's held on the books of the firm. The controllers legally obligated to follow gap accounting, which means things have to be held at the lower of cost or market value. So if you buy an asset and the market value goes up, it still gets recorded at that lower cost, the difference being accounting income and cash flow.

Calculating Interest Rates Solve for the unknown interest rate in each of the following: Present Value Years Interest Rate Future Value $ 181 8 $ 317 335 13 1,080 48,000 11 185,382

CALCULATOR PV: -181 PMT: 0 FV: 317 N: 8 CPT I/Y: 7.256 A=P(1+r/100)^nwhereA=future valueP=present valuer=rate of interestn=time period. a.317=181*(1+r/100)^8 (317/181)^(1/8)=(1+r/100) (1+r/100)=1.07256244 r=1.07256244-1 =7.26%(Approx) b.1080=335*(1+r/100)^13 (1080/335)^(1/13)=(1+r/100) (1+r/100)=1.09422359 r=1.09422359-1 =9.42%(Approx) c.185382=48000*(1+r/100)^11 (185382/48000)^(1/11)=(1+r/100) (1+r/100)=1.13070119 r=1.13070119-1 =13.07%(Approx)

15.Firm UUU earns $0.1 in profit on every $1 of sales, has $1.2 in assets for every $1 of sales and for has for $1 debt, issue $1.5 equity. The firm pays out 30 percent of its profits to its shareholders. What are the values for ROE and ROA ? .1389 .0833 What is the value of b, i.e., retention ratio? .7 What is the internal growth rate? .0619 What is the sustainable growth rate? .1077

Calculating the Debt-Equity ratio:- debt - equity ratio = debt/equity 1/1.5 = .6666 Equity multiplier 1 + D - E 1 + .6666 = 1.666 First, we will calculate the Net Profit Margin:- net profit / sales .1/1 = .1 Total Asset Turnover sales / total assets 1/ 1.2 = .8333 Return on Equity(ROE) Net profit x Total asset turnover x equity multiplier .1 x .8333 x 1.6666 = .1389 Return on Assets(ROA) Net profit margin x total asset turnover .1 x .8333 = .0833 SGR: (ROE*b)/(1-ROE*b) = (0.1388*0.7)/(1-0.1388*0.7) = 0.1077 IGR: SG(ROA*b)/(1-ROA*b) = (0.0833*0.7)/(1-0.0833*0.7) = 0.0619

_____ analysis is popular because it is difficult to manipulate.

Cash flow The cash from the firm must EXCEED the cash from the financial markets

Growing Annuity Southern California Publishing Company is trying to decide whether to revise its popular textbook Financial Psychoanalysis Made Simple. The company has estimated that the revision will cost $325,000. Cash flows from increased sales will be $94,000 the first year. These cash flows will increase by 4 percent per year. The book will go out of print five years from now. Assume that the initial cost is paid now and revenues are received at the end of each year. If the company requires a return of 10 percent for such an investment, should it undertake the revision?

Cash inflows=$94,000 Growthrate=g=4% Requiredrate=r=10% Period of cash flow=n=5years Find out present value of cash inflows. Explanation: Present value is the equivalent value today based on time and interest rate. Step 2/2 Present value of cash inflows=Cash inflows/(r−g) x (1−((1+g)/(1+r))^n) =94,000/ 0.1−0.04×(1−(1.041.1)^5)=$383,135.02 Present value of cash inflow=$383,135.02

Corporation vs Partnership

Corp Liquidity: Shares can be easily exchanged Voting rights: Usually each share gets one vote Taxation: Double Reinvestment and dividend payout: Broad latitude Liability: Limited liability Continuity: Perpetual life Partnership Liquidity: Subject to substantial restrictions Voting rights: General partner is in charge; limited partners may have some voting rights Taxation: Partners pay personal taxes on partnership profits Reinvestment and dividend payout: All net cash flow is distributed to partners Liability: General partners may have unlimited liability; limited partners enjoy limited liability Continuity: Limited life

Market Values and Book Values Klingon Widgets, Inc., purchased new cloaking machinery three years ago for $6 million. The machinery can be sold to the Romulans today for $5.4 million. Klingon's current balance sheet shows net fixed assets of $3.5 million, current liabilities of $945,000, and net working capital of $275,000. If the current assets and current liabilities were liquidated today, the company would receive a total of $1.25 million cash. What is the book value of Klingon's total assets today

Current assets = Net working capital + Current liabilities = 275,000 + 945,000 = $1,220,000 Book value of total assets = Current asset + Net fixed assets = $1,220,000 + 3,500,000 = $4,720,000 Book value of total assets = $4,720,000 Sum of market value of NWC and market value of fixed assets = $1,250,000 + 5,400,000 = $6,650,000 Sum of market value NWC and market value of fixed assets = $6,650,000

Ratios and Fixed Assets The Mikado Company has a ratio of long-term debt to longterm debt plus equity of .35 and a current ratio of 1.45. Current liabilities are $1,140, sales are $8,370, profit margin is 8.3 percent, and ROE is 16.5 percent. What is the amount of the firm's net fixed assets?

Current ratio=Current assets/Current liabilities Current assets=1,140*1.45 =$1653 Profit margin=Net income/Sales Net income=8,370*8.3% =$694.71 ROE=Net income/Equity Equity=694.71/0.165 =$4210.36364 Long term debt ratio=Long term debt/(Long term debt+equity) 0.35=Long term debt/(Long term debt+4210.36364) 0.35*(Long term debt+4210.36364)=Long term debt 0.35*Long term debt+1473.62727=Long term debt Long term debt*(1-0.35)=1473.62727 Long term debt*0.65=1473.62727 Long term debt=(1473.62727/0.65) =$2267.11888 (Approx) Total liabilities+Total equity=Current liabilities+Long term debt+Equity =1,140+2267.11888+4210.36364 =$7617.48252(Approx) Total assets=Total liabilities+Total equity =$7617.48252(Approx) Total assets=Current assets+Net fixed assets Hence net fixed assets=$7617.48252-$1653 =$5964.48 (Approx)

Cash Flow Management

Earnings can be manipulated using subjective decisions required under G A A P. Total cash flow is more objective, but the underlying components may also be "managed" Moving cash flow from the investing section to the operating section may make the firm's business appear more stable.

Assume APR = 10%, fill the following table where m is compounding frequency and compute EAR (4 digits after decimal NOT %, e.g., 0.12367 -> 0.1234) Annual compounding m = 1 EAR = APR = 0.1000

Effective annual rate = (1 + r/m)^m − 1 Semi-annual compounding m = 2 EAR = (1+ .1÷ 2)^2 - 1 = .1025 Quarterly compounding m = 4 EAR = (1+ .1÷4)^4 - 1 = .1038 Monthly compounding m = 12 EAR = (1+ .1÷12)^12 - 1 = .1047 Daily compounding m = 365 EAR = (1+ .1÷365)^365 - 1 = .1052 Continuous compounding m = ∞ EAR = =e^. 1 -1 = .1052

Constraints on Growth Tinsley, Inc., wishes to maintain a growth rate of 12 percent per year and a debt-equity ratio of .55. The profit margin is 6.2 percent, and the ratio of total assets to sales is constant at 1.05. Is this growth rate possible? To answer, determine what the dividend payout ratio must be.

Equity Multiplier = 1 + Debt-Equity Ratio Equity Multiplier = 1 + 0.55 Equity Multiplier = 1.55 Profit Margin = 6.20% Total Asset Turnover = 1 / Ratio of Total Assets to Sales Total Asset Turnover = 1 / 1.05 Total Asset Turnover = 0.95238 Return on Equity = Profit Margin * Total Asset Turnover * Equity Multiplier Return on Equity = 6.20% * 0.95238 * 1.55 Return on Equity = 9.15237% Growth Rate = [Return on Equity * Retention Ratio] / [1 - Return on Equity * Retention Ratio] 0.1200 = [0.0915237 * Retention Ratio] / [1 - 0.0915237 * Retention Ratio] 0.1200 - 0.0109828 * Retention Ratio = 0.0915237 * Retention Ratio 0.1200 = 0.1025065 * Retention Ratio Retention Ratio = 1.1707 or 117.07% Payout Ratio = 100% - Retention Ratio Payout Ratio = 100% - 117.07% Payout Ratio = -17.07% No, this growth rate is not possible. Retention Ratio = 100% - Payout Ratio Retention Ratio = 100% - 0% Retention Ratio = 100% Growth Rate = [Return on Equity * Retention Ratio] / [1 - Return on Equity * Retention Ratio] Growth Rate = [0.0915237 * 1] / [1 - 0.0915237 * 1] Growth Rate = 0.0915237 / 0.9084763 Growth Rate = 0.1007 or 10.07%

Return on Equity Firm A and Firm B have debt-total asset ratios of 60 percent and 35 percent, respectively, and returns on total assets of 4.5 percent and 8 percent, respectively. Which firm has a greater return on equity?

Firm A:- 0.045 Total Assets= PAT Frim B:- 0.08 Total Assets =PAT Firm A: 0.6 Total Assets=Total liab Equity = assets-Liab Equity=Assets-0.6 Assets =0.4 Assets Frim B : 0.35 Total Assets=Total - liab Equity=0.65 Assets Return on Equity(ROE)=PAT/shareholding equity Firm A:- ROE =0.045 Total Assets/0.4 Total Assets =0.1125 =11.25% Firm B:- Roe=0.08 Total Assets/0.65 Total Assets =0.1231 = 12.31%

Simple Interest versus Compound Interest First Simple Bank pays 6.4 percent simple interest on its investment accounts. If First Complex Bank pays interest on its accounts compounded annually, what rate should the bank set if it wants to match First Simple Bank over an investment horizon of 10 years?

First Simple Bank: Interest Rate = 6.4 %, Investment Horizon = 10 years, Let the initial investment amount be $ 100 Therefore, Interest Accumulated = (100 x 6.4 x 10) / 100 = $ 64 Total Amount = 100 + 64 = $ 164 First Complex Bank: Let the annually compounded interest rate be Y Therore, 100 x (1+Y)^(10) = 164 Y = [(164/100)^(1/10)] - 1 = 0.050714 or 5.0714 % ~ 5.07 %

Calculating Rates of Return You're trying to choose between two different investments, both of which have up-front costs of $65,000. Investment G returns $125,000 in 6 years. Investment H returns $205,000 in 10 years. Which of these investments has the higher return?

Investment G rate of return: =RATE(nper,pmt,pv,fv) =RATE(6,,-30000,65000) =13.75% Investment H rate of return: =RATE(9,,-30000,98000) =14.06%

Simple Interest versus Compound Interest First City Bank pays 7.5 percent simple interest on its savings account balances, whereas Second City Bank pays 7.5 percent interest compounded annually. If you made a $7,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years?

First city bank investment amount = $7000 Interest rate = 7.50% p.a. simple interest Future value after 10 years using simple interest rate is: Future value=Investment x (1+ interest rate x number of years)=$7,000×(1+0.0750×10)=$12,250.00 Explanation: The money will be worth $12250 in 10 years in first city bank. Second city bank: Investment = $7000 Interest rate - 7.50% p.a. compounding annually Number of years = 10 Future value of investment after 10 years using compounding interest rate: Future value=Investment x (1+Interest rate)number of years=$7,000×(1+0.0750)10=$14,427.22 Hence excess interest earned with second city bank is: Extra interest with second city bank=future value with second city bank −future value with first city bank=$14,427.22−$12,250=$2,177.22 The money will be worth $14427.22 in 10 years in second city bank. Hence with second city bank a total of $2,177.22 can be earned more as compared to first city bank in 10 years.

Full-Capacity Sales Blue Sky Mfg., Inc., is currently operating at 90 percent of fixed asset capacity. Current sales are $720,000. How much can sales increase before any new fixed assets are needed? Fixed Assets and Capacity Usage For the company in the previous problem, suppose fixed assets are $720,000 and sales are projected to grow to $665,000. How much in new fixed assets are required to support this growth in sales?

Full Cpaacity Sales = $575,000 / 0.90 = $638,889 Sales must grow by: $638,889 - $575,000 = $63,889 % of Growth in Sales: $63,889 / $575,000 = 0.1111 (11.11%) 575,000 x 1.1 = 638889 720,000/638889 = 112.695652 665,000 x 112.695652 = 749426.09 749426.09 - 720000 = 29426

Calculating the Number of Payments You're prepared to make monthly payments of $225, beginning at the end of this month, into an account that pays an APR of 6.5 percent compounded monthly. How many payments will you have made when your account balance reaches $15,000?

Future Value = $15,000 FV = C x ((1+r)^n - 1) / r) Monthly Payment at the end of each month = $225 r = Periodic Interest rate = 6.50%/12 = 0.5416666% n= no of periods 15,000 = 225 x (1+.005416666)^n -1)/ .005416666 0.36111106666 = (1.005416666)^n - 1 1.36111106666 = (1.005416666)^n Taking Log on both sides, Log(1.36111106666) = n*Log(1.005416666) 0.13389356507 = n*0.0023460799 n = 57.07 So, the Number of Payments is 57.07

Short run vs long Run Costs

In the short run, certain equipment, resources, and commitments of the firm are fixed, but the firm can vary such inputs as labor and raw materials. In the long run, all inputs of production (and hence costs) are variable. Financial accountants do not distinguish between variable costs and fixed costs. Instead, accounting costs usually fit into a classification that distinguishes product costs from period costs.

Calculating EAR First National Bank charges 13.8 percent compounded monthly on its business loans. First United Bank charges 14.1 percent compounded semiannually. As a potential borrower, to which bank would you go for a new loan?

Interest rate(r) = 13.8% compounded monthly Number of compounding periods in a year(m) = 12 For First United Bank Interest rate(r) = 14.1% compounded semi-annually Number of compounding periods in a year(m) = 2 Effective Annual Interest Rate=(1+rm)^m−1 Effective Annual Interest Rate=(1+0.13812)^12−1 Effective Annual Interest Rate=0.1470719115389 or 14.71% =Effective Annual Interest Rate=(1+0.1412)^2 −1 Effective Annual Interest Rate=0.14597025 or 14.60% The Formula of Effective Annual Interest rate is used. First United Bank is less than First National Bank (i.e. 14.6%<14.71%), hence the borrower should opt for loan from First United Bank

Managing Managers

Managerial compensation. •Incentives can be used to align management and stockholder interests. like paying a senior manage part cash and part stock •The incentives need to be structured carefully to make sure that they achieve their intended goal. For example, tying bonuses to profits might encourage management to pursue short-run profits and forgo projects that require a large initial outlay. Stock options may work, but there may be an optimal level of insider ownership. Corporate control. •The threat of a takeover may result in better management.

Residual Claims Polska, Inc., is obligated to pay its creditors $10,300 very soon. a. What is the market value of the shareholders' equity if assets have a market value of $11,600? b. What if assets equal $9,400?

Market value of equity = Market value of assets - Obligations towards creditors A. 11,600 - 10,300 = 1,300 (Market value of equity) B. 9,400 - 10,300 = -900 (Market value of equity)

The Income Statement

Measures financial performance over a specific period of time. What happens between balance sheets The accounting definition of income is: revenue - expenses = income There are three things to keep in mind: 1.Generally Accepted Accounting Principles (G A A P), controller responsible for maintaining gaap statements 2.Noncash Items. depreciation and deferred taxes 3.Time and Costs.

Cash Flow to Creditors The 2020 balance sheet of Osaka's Tennis Shop, Inc., showed long-term debt of $2.25 million, and the 2021 balance sheet showed long-term debt of $2.66 million. The 2021 income statement showed an interest expense of $305,000. What was the firm's cash flow to creditors during 2021? Cash Flow to Stockholders The 2020 balance sheet of Osaka's Tennis Shop, Inc., showed $780,000 in the common stock account and $4.78 million in the additional paid-in surplus account. The 2021 balance sheet showed $965,000 and $5.04 million in the same two accounts, respectively. If the company paid out $654,000 in cash dividends during 2021, what was the cash flow to stockholders for the year?

Net New Long-term Debt = Long-term Debt, 2021 - Long-term Debt, 2020 Net New Long-term Debt = $2,660,000 - $2,250,000 Net New Long-term Debt = $410,000 Cash Flow to Creditors = Interest Expense - Net New Long-term Debt Cash Flow to Creditors = $305,000 - $410,000 Cash Flow to Creditors = -$105,000 Net New Equity = Common Stock, 2021 + Additional Paid-in Surplus, 2021 - Common Stock, 2020 - Additional Paid-in Surplus, 2020 Net New Equity = $965,000 + $5,040,000 - $780,000 - $4,780,000 Net New Equity = $445,000 Cash Flow to Stockholders = Dividends - Net New Equity Cash Flow to Stockholders = $654,000 - $445,000 Cash Flow to Stockholders = $209,000 Cash Flow from Assets = Cash Flow to Creditors + Cash Flow to Stockholders Cash Flow from Assets = -$105,000 + $209,000 Cash Flow from Assets = $104,000 Cash Flow from Assets = Operating Cash Flow - Net Capital Spending - Net Increase in NWC $104,000 = Operating Cash Flow - $1,500,000 - (-$55,000) Operating Cash Flow = $1,549,000

Calculating Net Capital Spending Wallace Driving School's 2020 balance sheet showed net fixed assets of $2.3 million, and the 2021 balance sheet showed net fixed assets of $3.1 million. The company's 2021 income statement showed a depreciation expense of $327,000. What was net capital spending for 2021?

Net capital spending = ending value of fixed asset - beginning value of fixed asset + depreciation 3,100,000 - 2,300,000 + 327,000 = 1,127,000

Pop Evil Inc.'s net income for the most recent year was $16,481. The tax rate was 21 percent. The firm paid $3,681 in total interest expense and deducted $4,385 in depreciation expense. What was the cash coverage ratio for the year?

Net income = $16,481 Tax rate = 21 % interest expense = $3,681 Depreciation expense = $4,385 Cash Coverage ratio = EBIT + Non - cash expense ((16,481 / 1 - .21) + 4,385 + 3,681) / 3,681 = 7.86

Net Income and OCF During 2021, Raines Umbrella Corp. had sales of $865,000. Cost of goods sold, administrative and selling expenses, and depreciation expenses were $535,000, $125,000, and $170,000, respectively. In addition, the company had an interest expense of $90,000 and a tax rate of 25 percent. (Ignore any tax loss carryforward provisions and assume interest expense is fully deductible.) a. What is the company's net income for 2021? b. What is its operating cash flow?

Operating Cashflow = EBIT + Depreciation - Taxes = 35,000+170,000 -0 = $205,000 Cashflow from assets = Operating Cashflow - net working capital - net capital spending Cashflow from assets = $205,000 - 0 -0 = $205,000 Cahsflow to stock holders = Dividend - new Stock issued Cashflow to Stock holders = 128,000 - 0 = $128,000 Cashflow from assets = Cashflow to stock holders + Cashflow to creditors $205,000 = 128,000 + Cashflow to creditors Cash flow to creditors = 205,000 - 128,000 = 77,000 Cash flow to creditors = Interest expense - Net new long term debt = 77,000 = 90,000 - net new Long term debt Net new Long term debt = 90,000 - 77,000 = $13,000 Net new long term debt = $13,000

Calculating OCF Graff, Inc., has sales of $49,800, costs of $23,700, depreciation expense of $2,300, and interest expense of $1,800. If the tax rate is 22 percent, what is the operating cash flow, or OCF?

Operating cash flow = Operating income + Depreciation - Taxes Operating income = (Sales - Costs - Depreciation) = $49,800 - $23,700 - $2300 = $23,800 Depreciation = $2300 Taxes = (Sales - Costs - Depreciation - Interest) * Tax = ($49,800 - $23,700 - $2300 - $1800) * 0.22 = $22000 * 0.22 = $4840 Operating cash flow = $23,800 + $2300 - $4840 Operating cash flow = $21,260

Using Income Statements Given the following information for Troiano Pizza Co., calculate the depreciation expense: Sales = $76,800; Costs = $36,900; Addition to retained earnings = $6,800; Dividends paid = $2,370; Interest expense = $5,300; Tax rate = 22 percent.

PAT = Retained earnings + Dividend = $6,800 + $2,370 = $9,170 PBT = PAT/( 1 - Tax) = $9170/ ( 1-22%) = $11,756.41 EBITDA = Sales - Cost = $76800 - $36900 = $39,900 Depreciation = EBITDA - Interest - PBT = 39,900 - 5300 - 11756.41 = $22,843.59

Calculating Number of Periods One of your customers is delinquent on his accounts payable balance. You've mutually agreed to a repayment schedule of $500 per month. You will charge 1.65 percent per month interest on the overdue balance. If the current balance is $15,500, how long will it take for the account to be paid off?

PVA = C({1 - [1/(1 + r)^t]}/r) $15,500 = $500{[1 - (1/1.0165)t]/.0165} Now we solve for t: 1/1.0165^t = 1 − {[($15,500)/($500)](.0165)} 1/1.0165^t = .4885 1.0165t = 1/.4885 = 2.047 t = ln(2.047)/ln(1.0165) t = 43.78 months

Calculating Future Values Compute the future value of $1640 compounded annually for: a. 10 years at 5 percent. b. 10 years at 10 percent. c. 20 years at 5 percent.

Part a Future Value=1,640×(1+5%)10=2,671.39 The formula for Future Value is, Future Value = Present Value*(1+Rate)^time Part b Future Value =1,640×(1+10%)10=4,253.74 Part c Future Value =1,640×(1+5%)20=4,351.41

Calculating EFN The most recent financial statements for Hu, Inc., are shown Income Statement Balance Sheet Sales $9,400 Assets $20,300 Debt $ 8,400 Costs 6,730 Equity 11,900 Net income $2,670 Total $20,300 Assets and costs are proportional to sales; debt and equity are not. No dividends are paid. Next year's sales are projected to be $11,092. What is the external financing needed?

Percentage increase in sales = (Next year sales / Current year sales) - 1 = ($11,092 / $9,400) - 1 = 1.18 - 1 = 18% Increase in assets = Total assets * percentage increase in sales = $20,300 * 18% = $3,654 Addition to retained earnings = $2,670 * (1+18%) = $3,150.60 External financing needed = Increase in assets - Addition to retained earnings = $3,654 - $3,150.60 = $503.40 or $503 External financing needed = $503

16. A firm has sales of $800,000 for the year. The profit margin is 10 percent and the retention ratio is 70 percent. What is value of dividend payment in $? (format: no comma and no dollar sign. For example 10000)

Sales= $800,000 Net profit margin= 10% Therefore, 800,000 x 10%= 80,000 80,000 x (1-.7) 24,000

Present and Future Values The present value of the following cash flow stream is $8,200 when discounted at 9 percent annually. What is the value of the missing cash flow? Year Cash Flow 1 $2,100 2 ? 3 2,740 4 3,270

Present value of cashflow=CF1/(1+r)+CF3/(1+r)3+CF4/(1+r)4 =$2,100/ 1+0.09 + $2,740/ (1+0.09)^3+$3,270/(1+0.09)^4=6,358.94 Present value of cashflow = $6,358.94 Present value of year 2 cashflow=$8,200−$6,358.94=$1,841.06 Present value of year 2 cashflow = $1,841.06 Value of the missing cash flow=$1,841.06×(1+0.09)2=$2,187.36 Value of the missing cash flow = $2,187.36

There are two financial products. A will offer $100,000 in five years. B will offer $1,500 every month from now for five years. Product A is (single or multiple) cash flow(s)? $100,000 is (present or future) value? Product B is (single or multiple) cash flow(s)? How many cash flow(s) in total?

Product A is single $100,000 is (present or future) value? future Product B is multiple How many cash flow(s) in total? 60

Sustainable Growth Assuming the following ratios are constant, what is the sustainable growth rate? Total asset turnover = 2.20 Profit margin = 7.4% Equity multiplier = 1.40 Payout ratio = 40 %

ROA = 2.20*7.4 = 16.28 ROE = 16.28*1.40 = 22.792 Sustainable growth rate = .22792*(1-.40)/(1-.22792*.60) = 15.84%

Chapter 3 DuPont Identity If Rogers, Inc., has an equity multiplier of 1.43, total asset turnover of 1.87, and a profit margin of 6.05 percent, what is its ROE?

ROE = (Profit Margin) (Total Assets Turnover) (Equity Multiplier) ROE = (0.0605) (1.87) (1.43) = ROE = 16.18%

return on equity

ROE = Profit margin × Total asset turnover × Equity multiplier

Sustainable Growth If the Premier Corp. has an ROE of 14.1 percent and a payout ratio of 25 percent, what is its sustainable growth rate?

Retention ratio=1-payout ratio =(1-0.25) =0.75 Sustainable growth rate=(ROE*Retention ratio)/[1-(ROE*Retention ratio)] =(0.141*0.75)/[1-(0.141*0.75)] =0.10575/[1-0.10575] =0.10575/0.89425 =11.83%(Approx)

Building an Income Statement Gia, Inc., has sales of $497,000, costs of $276,000, depreciation expense of $43,000, interest expense of $24,000, and a tax rate of 21 percent. What is the net income for the firm? Suppose the company paid out $30,000 in cash dividends. What is the addition to retained earnings?

Sales = $497,000 COGS = $276,000 Depreciation expense = $43,000 Interest expense = $24,000 Tax rate = 21% $497,000 - $276,000 - $43,000 - $24,000 =EBT $154,000 Tax@21% x 154,000 = $32,340 154,000 - $32,340 = $121,660 Net income = $121,660 Now we will calculate Addition to retained earnings, 121,660 - 30,000 = 91660

What major regulations impact public firms?

The Securities Act of 1933 and the Securities Exchange Act of 1934. •Issuance of Securities (1933) •Creation of S E C and reporting requirements (1934) Can't just sell, they have to be approved Sarbanes-Oxley ("S O X") •Increased reporting requirements and responsibility of corporate directors. Requires senior manager to be responsible for reports put out

Firm PM has total assets of $600,000, long term debt of $200,000, total equity of $300,000, fixed assets of $400,000, and sales of $700,000. The profit margin is 10 percent. What is the current ratio? What is the debt-equity ratio?

The current ratio = Current Assets/ Current liabilities = ( Total assets - fixed assets) / (total assets- total equity - long term debt) = ( $ 600,000 - $ 400,000) / ( $ 600,000 - $ 300,000 - $ 200,000) = 2:1 Hence the correct answer is 2:1 The firm's short-term solvency good because as per the general accounting principles a current ratio of 2 or above Debt equity ratio = Total liabilities / total equity = (Total Assets - Total Equity) / Total Equity = ($ 600,000 - $ 300,000) /$ 300,000 = 1

Variable Discount Rates A 15-year annuity pays $1,750 per month, and payments are made at the end of each month. If the APR is 9 percent compounded monthly for the first seven years, and APR of 6 percent compounded monthly thereafter, what is the value of the annuity today?

The value of the annuity today is $22,781.27. To calculate the value of the annuity today, we need to discount each payment back to the present. We can use the formula for the present value of an annuity: PV = PMT * ((1 - (1 + r)^-n) / r) where PV is the present value, PMT is the payment, r is the interest rate, and n is the number of payments. For the first seven years, we have: n = 7 * 12 = 84 r = 9% / 12 = 0.75% PMT = $1,750 So, the present value of the first 84 payments can be calculated as follows: PV = $1,750 * ((1 - (1 + 0.0075)^-84) / 0.0075) = $12,242.66 For the next 8 years, we have: n = 8 * 12 = 96 r = 6% / 12 = 0.5% So, the present value of the next 96 payments can be calculated as follows: PV = $1,750 * ((1 - (1 + 0.005)^-96) / 0.005) = $10,538.61 Adding the present value of both parts, we have: PV = $12,242.66 + $10,538.61 = $22,781.27 The value of the annuity today is $22,781.27.

Calculating Present Values Imprudential, Inc., has an unfunded pension liability of $450 million that must be paid in 20 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is 5.2 percent, what is the present value of this liability?

To find the PV of the pension liability, we use: PV = FV / (1 + r)t Substituting the values, we get PV = $450,000,000 / (1.052)20 = $ 163266738.60 PMT: 0 FV: 450 mil N: 20 PV: 163266738.60

Present Value and Multiple Cash Flows McCann Co. has identified an investment project with the following cash flows.Year | Cash Flow 1 $760 2 1,010 3 1,270 4 1,375a If the discount rate is 11 percent, what is the present value of these cash flows? What is the present value at 18 percent? What is the present value at 24 percent?

To solve this problem, we must find the PV of each cash flow and add them. To find the PV of a lump sum, we use: PV = FV/(1 + r)^t PV@11% = $760/1.11 + $1,010/1.11^2 + $1,270/1.11^3 + $1,375/1.11^4 = $3,338.79 PV@18% = $760/1.18 + $1,010/1.18^2 + $1,270/1.18^3 + $1,375/1.18^4 = $2,851.60 PV@24% = $760/1.24 + $1,010/1.24^2 + $1,270/1.24^3 + $1,375/1.24^4 = $2,517.46

Balance Sheet Analysis

When analyzing a balance sheet, the financial manager should be aware of three concerns: 1.Liquidity. how easily can they turn the asset to cash and how soon do they need to pay off the liability 2.Debt versus equity. debt has first claim over equity 3.Value of asset versus cost. An accountant's snapshot of the firm's accounting value at a specific point in time Assets = liabilities + stockholder equity

Calculating Annuity Present Value An investment offers $3,850 per year for 15 years, with the first payment occurring one year from now. If the required return is 6 percent, what is the value of the investment? What would the value be if the payments occurred for 40 years? Forever?

a) Present value = Cashflow * (1 - (1 + interest rate)-no of years) / interest rate Present value = $3850 * (1 - (1 + 6%)^-15) / 6%) Present value = $37,392.16 b) Present value = Cashflow * (1 - (1 + interest rate)-no of years) / interest rate Present value = $3850 * (1 - (1 + 6%)^-40) / 6%) Present value = $57,928.24 d) Present value = Cashflow / interest rate Present value = $3850 / 6% Present value = $64,166.67

What are the three basic questions financial managers must answer?

a. Capital budgeting: What long-term investments should the firm take? b. Capital structure: Where will the firm get the long-term financing to pay for its investments? Also, what mixture of debt and equity should it use to fund operations? c. Working capital management: How should the firm manage its everyday financial activities?

Cash Flow of the Firm

a. Cash flow from operations. b. Cash flow from changes in fixed assets. c. Cash flow from changes in working capital. CF (A) = CF(B) + CF(S)

Continuous Compounding Compute the future value of $1900 continuously compounded for: a. 7 years at an APR of 10 percent. b. 5 years at an APR of 8 percent. c. 10 years at an APR of 7 percent. d. 8 years at an APR of 9 percent

a. Future Value = (1,900)e^(0.10*7) = $3,826.13 b. Future Value = (1,900)e^(0.08*5) = $2,834.47 c. Future Value = (1,900)e^(0.07*10) = $3,826.13 d. Future Value = (1,900)e^(0.09*8) = $3,903.42

Present Value and Multiple Cash Flows Investment X offers to pay you $5,300 per year for eight years, whereas Investment Y offers to pay you $7,300 per year for five years. Which of these cash flow streams has the higher present value if the discount rate is 5 percent?

a. Present Value of Investment X Present Value of Annuity = Periodic Payment*[{1-(1+rate of Interest)^(-time)} / rate of interest] = $5,300*[{1-(1+5%)^(-8)} / 5%] = $ 5,300*6.463212759 = $ 34,255.03 Answer = $ 34,255.03 PMT: 5300 FV: 0 I/Y: 5 N: 8 PV: 34,255.03 b. Present Value of Investment Y Present Value of Annuity = Periodic Payment*[{1-(1+rate of Interest)^(-time)} / rate of interest] = $7,300*[{1-(1+5%)^(-5)} / 5%] = $ 7,300*4.329476671 = $ 31,605.18 Answer = $ 31,605.18

Building a Balance Sheet Bing, Inc., has current assets of $5,400, net fixed assets of $28,100, current liabilities of $4,100, and long-term debt of $10,600. What is the value of the shareholders' equity account for this firm? How much is net working capital?

a. Shareholder's Equity = Total Assets - Total Liabilities = (Current Assets + Fixed Assets) - (Current Liabilities + LT Debt) = (5,400 + 28,100) - (4,100 + 10,600) = 33,500 - 14,700 = $18,800 b. Net Working Capital = Current Assets - Current Liabilities = 5,400 - 4,100 = 1,300

A _____ between the stockholders and management of a firm is referred to as the agency problem.

conflict of interest A common example of an agency relationship is a real estate broker—in particular if you break it down between a buyer's agent and a seller's agent. A classic conflict of interest is when the agent is paid on commission, so they may be less willing to let the buyer know that a lower price might be accepted, or they may elect to only show the buyer homes that are listed at the high end of the buyer's price range.

Which form of business structure faces the greatest agency problems?

corporation

Which one of the following business types is best suited to raising large amounts of capital?

corporation

Short-Term Asset Management

current assets always have to be bigger than liabilities, current assets minus liabilities are networking capital which has to be positive to make sure they do their payments like for rent. If a company is below working capital for too long the business fails

Net working capital is defined as:

current assets minus current liabilities NWC = Current Assets - Current Liabilities if there is none, the company will fail to pay for electricity or employees

Chapter 3 Equity Multiplier and Return on Equity Kodi Company has a debt-equity ratio of .63. Return on assets is 8.4 percent, and total equity is $645,000. What is the equity multiplier? Return on equity? Net income?

debt to equity ratio = 0.63 return on assets = 8.4% total equity = 645,000 a) calculating the equity multiplier equity multiplier =1 + debt equity ratio =1+0.63=1.63 therefore the equity multiplier = 1.63 b) calculating the return on equity (ROE) ROE =return on assets∗equity multiplier=8.4%×1.63=0.1369 the return on equity is = 13.69% c) calculating the net income net income =ROE∗total equity= 13.69%×645,000 =$88,300.50 the net income is = $88,300.50

Present Value and Break-Even Rate Consider a firm with a contract to sell an asset for $175,000 four years from now. The asset costs $104,600 to produce today. Given a relevant discount rate of 11 percent per year, will the firm make a profit on this asset? At what rate does the firm just break even?

given , assets cost = $104600 fv = $175000 we know fv = pv(1+r)^n pv = fv/(1+r)^n a) discount rate = 11% years = 4 pv = 175000/(1+11%)^4 = 115277.92 pv of = 115277.92 firms profit on this asset = 115277.92 - 104600 = 10677.92 profit = $10677.92 b) rate at frim break even = 13.83%

A business formed by _____ individuals is referred to as partnership; the partnership who each have _____ personal liability for all of the firm's debts is called general partnership.

two or more, unlimited partnership in which partners share equally in both responsibility and liability

Ritter Corporation's accountants prepared the following financial statements for year-end 2021: a. Explain the change in cash during 2021. b. Determine the change in net working capital in 2021. c. Determine the cash flow generated by the firm's assets during 2021. Revenue $ 860 Expenses 620 Depreciation 101 Net income $ 139 Dividends $ 119 2020 2021 Assets Cash $ 66 $ 87 Other current assets 176 192 Net fixed assets 381 401 Total assets $ 623 $ 680 Liabilities and Equity Accounts payable $ 126 $ 147 Long-term debt 151 167 Stockholders' equity 346 366 Total liabilities and equity $ 623 $ 680

in cash : Change in cash =Ending cash balance − beginning cash balance=87−66=21 Answer a : 21 Net working capital = current assets - current liabilities Net working capital 2020=(66+176)−126=116 Net working capital 2021=(87+192)−147=132 Change in net working capital = Net working capital 2021 - Net working capital 2020 Change in Net working capital =132−116=16 Answer b : 16 Cash flow from assets =OCF - capital spending - change in net working capital OCF = Operating cash flow : OCF = Net income + depreciation OCF=139+101=240 capital spending = change in net fixed assets + depreciation capital spending=(401−381)+101=121 change in net working capital in step 2 = 16 NOW: Cash flow from assets Cash flow from assets =240−121−16=103 Answer c : cash flow from assets = 103

What is the goal of financial management? The goal of financial management is _______.

maximizing the value of existing owner's equity The goal of financial management is to maximize the current value per share of the existing stock

EAR versus APR You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2.6 million purchase price. The monthly payment on this loan will be $14,200. What is the APR on this loan? The EAR?

nper ( number of payment periods) 360 pmt (payment amount) $14200 pv (initial amount) $2080000 Periodic rate (monthly) 0.60% RATE (360, -14200, 2080000,,) RATE (nper, -pmt, pv,) Annual interest rate (APR) 7.26% periodic rate *12 (0.6*12) Effective annual interest (EAR) 7.50% (1+(r/n)^n-1 (1+(0.0726/12)^12-1the annual percentage rate on the mortgage loan is found to be 7.26 % while the effective annual rate is found to be 7.50%

A firm starts its year with a positive net working capital. During the year, the firm acquires more short-term debt than it does short-term assets. This means that:

the ending net working capital can be positive, negative, or equal to zero