final finance

date of record

the date by which a holder must be on record to be designated to receive a dividend

declaration date

the date on which the board of directors officially approves a dividend

date of payment

the date on which the dividend checks are mailed

ex-dividend date

the date two business days before the date of record, establishing those individuals entitled to a dividend

information content effect

the market's reaction to a change in corporate dividend payout

Clientele Effect

the observable fact that stocks attract particular groups based on dividend yield and the resulting tax effects

trading range

the price range between the highest and lowest prices at which a stock is traded

Cost of Equity

the return that equity investors require on their investment in the firm

taxation of mutual fund income

"Pass-through status" under the U.S. tax code •Taxes are paid only by the investor, not by the fund itself •Disadvantage is that fund investors do not control the timing of the sales of securities from the portfolio, reducing their ability to engage in tax management •High portfolio turnover rate can be particularly "tax inefficient" •Average turnover dropped to 30% in 2017

Rate of Return Formula

(NAV1-NAV0+ income and capital gain distributions)/NAV0

Other Investment Organizations

-Commingled funds partnerships of investors that pool funds -REITs similar to closed end fund equity versus mortgage trusts -Hedge Funds vehicles that allow private investors to pool assets to be invested by a fund manager

Cost of Debt

the return that lenders require on the firm's debt

Initial Public Offering (IPO)

A company's first equity issue made available to the public also called an unseasoned new issue

Seasoned Equity Offering (SEO)

A new equity issue of securities by a company that has previously issued securities to the public

nvestment Companies

An investment company pools and invests the funds of individual investors in securities or other assets •Record keeping and administration •Diversification and divisibility •Professional management •Lower transaction cost

chapter 7 Bond J has a coupon rate of 3 percent. Bond K has a coupon rate of 9 percent. Both bonds have 14 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?

Initially, at a YTM of 6 percent, the prices of the two bonds are: PJ = $15(PVIFA3%,28) + $1,000(PVIF3%,28) = $718.54PK = $45(PVIFA3%,28) + $1,000(PVIF3%,28) = $1,281.46 If the YTM rises from 6 percent to 8 percent: PJ = $15(PVIFA4%,28) + $1,000(PVIF4%,28) = $583.42PK = $45(PVIFA4%,28) + $1,000(PVIF4%,28) = $1,083.32 The percentage change in price is calculated as: Percentage change in price = (New price - Original price)/Original price ΔPJ% = ($583.42 - 718.54)/$718.54 = -.1880, or -18.80%ΔPK% = ($1,083.32 - 1,281.46)/$1,281.46 = -.1546, or -15.46% If the YTM declines from 6 percent to 4 percent: PJ = $15(PVIFA2%,28) + $1,000(PVIF2%,28) = $893.59PK = $45(PVIFA2%,28) + $1,000(PVIF2%,28) = $1,532.03 ΔPJ% = ($893.59 - 718.54)/$718.54 =.2436, or 24.36%ΔPK% = ($1,532.03 - 1,281.46)/$1,281.46 =.1955, or 19.55% All else the same, the lower the coupon rate on a bond, the greater is its price sensitivity to changes in interest rates. CALCULATOR for J and K calculate I/Y for 4%,6% and 8%, then find the difference in PV and divide by the PV at 6% ex. (Jat4%-Jat6%)/Jat6% SOLVE FOR PV AND REMEMBER TO LOOK IF IT'S SEMIANNUAL

to find Present value FORMULA

FV/(1+r)^t

chapter 7 A Japanese company has a bond outstanding that sells for 105.43 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?

Here we need to find the YTM of a bond. The equation for the bond price is: P = ¥105,430 = ¥3,400(PVIFAR%,16) + ¥100,000(PVIFR%,16) Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find: R = YTM = 2.97% CALCULATOR PART N=16 I/Y=? PV= -(100,000x 1.0543) PMT= (100,000x 0.034) FV=100,000

chapter 7 McConnell 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 $1,045. The bonds make semiannual payments. What must the coupon rate be on these bonds?

Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $1,045 = C(PVIFA2.65%,29) + $1,000(PVIF2.65%,29) Solving for the coupon payment, we get: C = $28.74 Since this is the semiannual payment, the annual coupon payment is: 2 × $28.74 = $57.49 And the coupon rate is the annual coupon payment divided by par value, so: Coupon rate = $57.49/$1,000Coupon rate = .0575, or 5.75% CALCULATOR N=29 I/Y=(5.3/2) PV= -1045 PMT=? FV= 1000

chapter 7 Gabriele Enterprises has bonds on the market making annual payments, with eight years to maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.1 percent. What must the coupon rate be on the bonds?

Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows: P = $948 = C(PVIFA5.10%,8) + $1,000(PVIF5.10%,8) Solving for the coupon payment, we get: C = $42.92 The coupon payment is the coupon rate times par value. Using this relationship, we get: Coupon rate = $42.92/$1,000Coupon rate = .0429, or 4.29% CALCULATOR N=9 I/Y= 5.1 PV= -948 PMT=? FV=1000

mutual funds: how funds are sold

How Funds Are Sold •Directly by the fund underwriter (i.e., direct-marketed funds) •Sold through the mail, various offices of the fund, over the phone,or over the Internet •Indirectly through brokers acting on behalf of the underwriter (i.e., sales-force distributed) •Broker or financial advisers receive a commission for selling shares •Potential conflict of interest •Financial supermarkets •Sell shares in funds of many complexes •Broker splits management fees with the mutual fund compa

mutual funds" investment policies

MONEY MARKET invest money market securities such as commercial paper, repurchase agreements or CDs EQUITY invest primarily in stock SECTOR concentrate on a particular industry or country BOND specialize in the fixed-income sector INTERNATIONAL global, international, regional and emerging market BALANCED designed to be candidates for an individual's entire investment portfolio, hold both equities and fixed-income securities in relatively stable proportions ASSET ALLOCATION AND FLEXIBLE FUNDS hold both stocks and bonds engaged in market timing; not designed to be low-risk INDEX tries to match the performance of a broad market index

CHAPTER 7 You find a zero coupon bond with a par value of $10,000 and 17 years to maturity. If the yield to maturity on this bond is 4.2 percent, what is the price of the bond? Assume semiannual compounding periods.

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation. To find the price of a zero coupon bond, we need to find the value of the future cash flows. With a zero coupon bond, the only cash flow is the par value at maturity. We find the present value assuming semiannual compounding to keep the YTM of a zero coupon bond equivalent to the YTM of a coupon bond, so: P = $10,000(PVIF2.10%,34) P = $4,933.16 CALCULATOR N= 17x2 I/Y=(4.2/2) PV= ? PMT=0 FV=-10,000

Managed Investment Companies

OPEN END stand ready to redeem or issue shared at the NAV priced at Net Asset Value (NAV) CLOSED END do not redeem or issue shared shares outstanding constant; investors cash out by selling to new investors priced at premium or discount to NAV

to find future value/par value FORMULA

PV(1+r)^t

CHAPTER 9 Bronco, Inc., imposes a payback cutoff of three years for its international investment projects. Year Cash Flow (A) Cash Flow (B) 0 -$ 35,000 -$ 45,000 1 12,000 11,000 2 17,000 13,000 3 14,000 16,000 4 9,000 255,000 What is the payback period for both projects? Which project should the company accept? project A or B?

Project A has total cash flows of $29,000 after Year 2, so the cash flows are short by $6,000 of recapturing the initial investment, so the payback for Project A is: Payback = 2 + ($6,000/$14,000)Payback = 2.43 years Project B has cash flows of: Cash flows = $11,000 + 13,000 + 16,000Cash flows = $40,000 during the first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is: Payback = 3 + ($5,000/$255,000)Payback = 3.02 years Using the payback criterion and a cutoff of three years, accept Project A and reject Project B because project A is within 3 years

CHAPTER 10 A proposed new investment has projected sales of $585,000. Variable costs are 44 percent of sales, and fixed costs are $187,000; depreciation is $51,000. Prepare a pro forma income statement assuming a tax rate of 21 percent. What is the projected net income?

Sales$585,000 Variable costs 257,400 Fixed costs 187,000 Depreciation 51,000 EBT$89,600 Taxes (21%) 18,816 Net income$70,784

CHAPTER 9 A firm evaluates all of its projects by applying the IRR rule. A project under consideration has the following cash flows: Year Cash Flow 0 -$ 34,000 1 15,000 2 17,000 3 13,000 If the required return is 14 percent, what is the IRR for this project? should the firm accept the project?

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is: 0 = -$34,000 + $15,000/(1 + IRR) + $17,000/(1 + IRR)2 + $13,000/(1 + IRR)3 Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that: IRR = 15.80% Since the IRR is greater than the required return, we would accept the project. Calculator Solution: CFo -$34,000 C01 $15,000 F01 1 C02 $17,000 F02 1 C03 $13,000 F03 1 IRR CPT 15.80%

CHAPTER 9 A project that provides annual cash flows of $11,700 for nine years costs $63,000 today. What is the NPV for the project if the required return is 8 percent? At a required return of 8 percent, should the firm accept this project? What is the NPV for the project if the required return is 20 percent? At a required return of 20 percent, should the firm accept this project? At what discount rate would you be indifferent between accepting the project and rejecting it?

The NPV of a project is the PV of the inflows minus the PV of the outflows. Since the cash inflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = -$63,000 + $11,700((PVIFA8%, 9)NPV = $10,088.59 At an 8 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 20 percent required return is: NPV = -$63,000 + $11,700(PVIFA20%, 9) NPV = -$15,837.69 At a 20 percent required return, the NPV is negative, so we would reject the project. We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is: 0 = -$63,000 + $11,700(PVIFAIRR, 9) IRR = 11.72%

homemade dividend policy

the tailored dividend policy created by individual investors who undo corporate dividend policy by reinvesting dividends or selling shares of stock

CHAPTER 9 A firm evaluates all of its projects by applying the NPV decision rule. A project under consideration has the following cash flows: Year Cash Flow 0 -$ 34,000 1 15,000 2 17,000 3 13,000 What is the NPV of the project if the required return is 11 percent? At a required return of 11 percent, should the firm accept this project? What is the NPV of the project if the required return is 24 percent? At a required return of 24 percent, should the firm accept this project?

The NPV of a project is the PV of the inflows minus the PV of the outflows. The equation for the NPV of this project at an 11 percent required return is: NPV = -$34,000 + $15,000/1.11 + $17,000/1.112 + $13,000/1.113 NPV = $2,816.58 At an 11 percent required return, the NPV is positive, so we would accept the project. The equation for the NPV of the project at a 24 percent required return is: NPV = -$34,000 + $15,000/1.24 + $17,000/1.242 + $13,000/1.243 NPV = -$4,028.70 At a 24 percent required return, the NPV is negative, so we would reject the project.

CHAPTER 17 Ginger, Inc., has declared a $5.60 per share dividend. Suppose capital gains are not taxed, but dividends are taxed at 15 percent. New IRS regulations require that taxes be withheld at the time the dividend is paid. The company's stock sells for $94.10 per share, and the stock is about to go ex dividend. What do you think the ex-dividend price will be?

The aftertax dividend is the pretax dividend times one minus the tax rate, so: Aftertax dividend = $5.60(1 - .15)Aftertax dividend = $4.76 The stock price should drop by the aftertax dividend amount, or: Ex-dividend price = $94.10 - 4.76Ex-dividend price = $89.34

CHAPTER 12 Returns Year X Y 1 12 % 25 % 2 28 34 3 9 13 4 - 7 - 27 5 10 14 Using the returns shown above, calculate the arithmetic average returns, the variances, and the standard deviations for X and Y.

The average return is the sum of the returns, divided by the number of returns. The average return for each stock was: X⎯⎯⎯=[Σi−1Nxi]/N=[.12+.28+.09−.07+.10]5=.1040,or10.40%X¯=[Σi−1Nxi]/N=[.12+.28+.09−.07+.10]5=.1040, or⁢ 10.40% Y⎯⎯⎯=[Σi−1Nyi]/N=[.25+.34+.13−.27+.14]5=.1180,or11.80%Y¯=[Σi−1Nyi]/N=[.25+.34+.13−.27+.14]5=.1180, or⁢ 11.80% Remembering back to "sadistics," we calculate the variance of each stock as: σX2=[Σi−1N(xi−x⎯⎯)2]/(N−1)σX2=[Σi−1N(xi−x¯)2]/(N−1) σX2=15−1{(.12−.104)2+(.28−.104)2+(.09−.104)2+(−.07−.104)2+(.10−.104)2}=.01543σX2=15−1{(.12−.104)2+(.28−.104)2+(.09−.104)2+(−.07−.104)2+(.10−.104)2}=.01543 σY2=15−1{(.25−.118)2+(.34−.118)2+(.13−.118)2+(−.27−.118)2+(.14−.118)2}=.05447σY2=15−1{(.25−.118)2+(.34−.118)2+(.13−.118)2+(−.27−.118)2+(.14−.118)2}=.05447 The standard deviation is the square root of the variance, so the standard deviation of each stock is: σX = .015431/2 = .1242, or 12.42% σY = .054471/2 = .2334, or 23.34%

CHAPTER 7 Chamberlain 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 that sell for $1,083, 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?

The company should set the coupon rate on its new bonds equal to the required return. The required return can be observed in the market by finding the YTM on the outstanding bonds of the company. So, the YTM on the bonds currently sold in the market is: P = $1,083 = $30(PVIFAR%,40) + $1,000(PVIFR%,40) Using a spreadsheet, financial calculator, or trial and error we find: R = 2.660% This is the semiannual interest rate, so the YTM is: YTM = 2 × 2.660% YTM = 5.32% CALCULATOR N=40 I/Y=? PV=-1083 PMT= (60/2) FV=1000 REMEMBER TO X2 THE I/Y BECAUSE ITS SEMIANNUAL

CHAPTER 8 Antiques R Us is a mature manufacturing firm. The company just paid a dividend of $9.80, but management expects to reduce the payout by 4 percent per year indefinitely. If you require a return of 9.5 percent on this stock, what will you pay for a share today?

The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0(1 + g)/(R − g)P0 = $9.80(1 - .04)/[(.095 - (-.04)]P0 = $69.69

CHAPTER 14 Holdup Bank has an issue of preferred stock with a stated dividend of $4.25 that just sold for $93 per share. What is the bank's cost of preferred stock?

The cost of preferred stock is the dividend payment divided by the price, so: RP = $4.25/$93RP = .0457, or 4.57%

CHAPTER 12 Suppose a stock had an initial price of $65 per share, paid a dividend of $1.45 per share during the year, and had an ending share price of $71. What was the dividend yield and the capital gains yield?

The dividend yield is the dividend divided by the beginning of the period price, so: Dividend yield = $1.45/$65Dividend yield = .0223, or 2.23% And the capital gains yield is the increase in price divided by the initial price, so: Capital gains yield = ($71 - 65)/$65Capital gains yield = .0923, or 9.23%

CHAPTER 14 Viserion, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 23 years to maturity that is quoted at 103 percent of face value. The issue makes semiannual payments and has an embedded cost of 6 percent annually. a. What is the company's pretax cost of debt? b.If the tax rate is 21 percent, what is the aftertax cost of debt?

The pretax cost of debt is the YTM of the company's bonds, so: P0 = $1,030 = $30(PVIFAR%,46) + $1,000(PVIFR%,46)R = 2.881%YTM = 2 × 2.881%YTM = 5.76% And the aftertax cost of debt is: RD = .0576(1 - .21)RD = .0455, or 4.55%

chapter 7 Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 23 years to maturity, and a coupon rate of 3.8 percent paid annually. If the yield to maturity is 4.7 percent, what is the current price of the bond?

The price of any bond is the PV of the interest payments, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be: P = €38({1 - [1/(1 + .04723)]}/.047) + €1,000[1/(1 + .047)23] CALCULATOR N=23 I/Y=4.7 PV=? PMT= 38 FV=1000

pure play approach

the use of a WACC that is unique to a particular project, based on companies in similar lines of business

The Sloan Corporation is trying to choose between the following two mutually exclusive design projects: Year Cash Flow (I) Cash Flow (II) 0 -$ 63,000 -$ 15,500 1 28,900 7,900 2 28,900 7,900 3 28,900 7,900 a-1. If the required return is 10 percent, what is the profitability index for both projects? If the company applies the profitability index decision rule, which project should the firm accept? What is the NPV for both projects? If the company applies the NPV decision rule, which project should it take?

The profitability index is the PV of the future cash flows divided by the initial investment. The cash flows for both projects are an annuity, so: PII = $28,900(PVIFA10%,3)/$63,000 PII = 1.141 PIII = $7,900(PVIFA10%,3)/$15,500 PIII = 1.267 The profitability index decision rule implies that we accept Project II, since PIII is greater than PII. b. The NPV of each project is: NPVI = -$63,000 + $28,900(PVIFA10%,3)NPVI = $8,870.02 NPVII = -$15,500 + $7,900(PVIFA10%,3)NPVII = $4,146.13 The NPV decision rule implies accepting Project I, since the NPVI is greater than the NPVII. PI = $71,870.02/$63,000 = 1.141 PI = $19,646.13/$15,500 = 1.267

stock repurchase

The purchase, by a corporation, of its own shares of stock; also known as a buyback

CHAPTER 12 Suppose a stock had an initial price of $65 per share, paid a dividend of $1.45 per share during the year, and had an ending share price of $71. Compute the percentage total return

The return of any asset is the increase in price, plus any dividends or cash flows, all divided by the initial price. The return of this stock is: R = [($71 - 65) + 1.45]/$65R = .1146, or 11.46%

chapter 5 First City Bank pays 9 percent simple interest on its savings account balances, whereas Second City Bank pays 9 percent interest compounded annually. If you made a deposit of $7,500 in each bank, how much more money would you earn from your Second City Bank account at the end of eight years? difference in accounts:

The simple interest per year is: $7,500 × .09 = $675 So after 8 years you will have: $675 × 8 = $5,400 in interest The total balance will be $7,500 + 5,400 = $12,900 With compound interest we use the future value formula: FV = PV(1 + r)tFV = $7,500(1.09)8 = $14,944.22 The difference is: $14,944.22 - 12,900 = $2,044.22 calculator set up n=8 I/y=9 pv= +/- 7500 PMT= 0 FV= ?

CHAPTER 17 The balance sheet for Sinking Ship Corp. is shown here in market value terms. There are 7,000 shares of stock outstanding. Market Value Balance Sheet Cash $ 44,100 Equity $ 394,100 Fixed assets 350,000 Total $ 394,100 Total $ 394,100 The company has declared a dividend of $1.80 per share. The stock goes ex dividend tomorrow. Ignoring any tax effects, what is the stock selling for today? Ignoring any tax effects, what will it sell for tomorrow? Ignoring any tax effects, what will the balance sheet look like after the dividends are paid?

The stock price is the total market value of equity divided by the shares outstanding, so: P0 = $394,100 equity/7,000 shares = $56.30 per share Ignoring tax effects, the stock price will drop by the amount of the dividend, so: PX = $56.30 - 1.80 = $54.50 The total dividends paid will be: $1.80 per share(7,000 shares) = $12,600 The equity and cash accounts will both decline by $12,600.

CHAPTER 12 Suppose you bought a bond with an annual coupon of 7 percent one year ago for $1,010. The bond sells for $985 today. a.Assuming a $1,000 face value, what was your total dollar return on this investment over the past year? b.What was your total nominal rate of return on this investment over the past year? c.If the inflation rate last year was 3 percent, what was your total real rate of return on this investment?

The total dollar return is the increase in price plus the coupon payment, so: Total dollar return = $985 - 1,010 + 70 Total dollar return = $45 The total percentage return of the bond is: R = [($985 - 1,010) + 70]/$1,010R = .0446, or 4.46% Notice here that we could have simply used the total dollar return of $45 in the numerator of this equation. Using the Fisher equation, the real return was: (1 + R) = (1 + r)(1 + h) r = (1.0446/1.03) - 1r = .0141, or 1.41%

CHAPTER 9 Year Cash Flow 0 -$ 8,300 1 2,100 2 3,000 3 2,300 4 1,700 What is the payback period for the set of cash flows given above?

To calculate the payback period, we need to find the time that the project requires to recover its initial investment. After three years, the project has created: $2,100 + 3,000 + 2,300 = $7,400 in cash flows. The project still needs to create another: $8,300 - 7,400 = $900 in cash flows. During the fourth year, the cash flows from the project will be $1,700. So, the payback period will be three years, plus what we still need to make divided by what we will make during the fourth year. The payback period is: Payback = 3 + ($900/$1,700)Payback = 3.53 years.

CHAPTER 10 An asset used in a four-year project falls in the five-year MACRS class for tax purposes. The asset has an acquisition cost of $5,100,000 and will be sold for $1,600,000 at the end of the project. If the tax rate is 21 percent, what is the aftertax salvage value of the asset? Refer to Table 10.7.

To find the BV at the end of four years, we need to find the accumulated depreciation for the first four years. The easiest way is to add the MACRS depreciation amounts for each of the first four years and multiply this percentage times the cost of the asset. We can then subtract this from the asset cost. Doing so, we get: BV4 = $5,100,000 - 5,100,000(.2000 + .3200 + .1920 + .1152)BV4 = $881,280 The asset is sold at a gain to book value, so this gain is taxable. Aftertax salvage value = $1,600,000 + ($881,280 - 1,600,000)(.21)Aftertax salvage value = $1,449,069

Weighted Average Cost of Capital (WACC)

the weighted average of the cost of equity and the aftertax cost of debt

zero coupon bonds

they make no payments

CHAPTER 17 Simmons Mineral Operations, Inc., (SMO) currently has 450,000 shares of stock outstanding that sell for $90 per share. Assuming no market imperfections or tax effects exist, what will the share price be after: a. SMO has a four-for-three stock split? b. SMO has a 10 percent stock dividend? c.SMO has a 47.5 percent stock dividend? e.Determine the new number of shares outstanding in parts (a) through (d)

To find the new stock price, we multiply the current stock price by the ratio of old shares to new shares, so: a.$90(3/4) = $67.50b.$90(1/1.10) = $81.82c.$90(1/1.475) = $61.02d.$90(7/4) = $157.50 e. To find the new shares outstanding, we multiply the current shares outstanding times the ratio of new shares to old shares, so: a:450,000(4/3) = 600,000 b:450,000(1.10) = 495,000 c:450,000(1.475) = 663,750 d:450,000(4/7) = 257,143

CHAPTER 7 Excey 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?

To find the number of years to maturity for the bond, we need to find the price of the bond. Since we already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P0 P0 = $80/.0755 = $1,059.60 Now that we have the price of the bond, the bond price equation is: P0 = $1,059.60 = $80[(1- (1/1.072t))/.072] + $1,000/1.072t We can solve this equation for t as follows: $1,059.60(1.072)t = $1,111.11(1.072)t - 1,111.11 + 1,000 111.11 = 51.51(1.072)t 2.1571 = 1.072t t = ln2.1571/ln1.072 = 11.06 The bond has 11.06 years to maturity. CALCULATOR N=? I/Y=7.2 PV=-1059.60 PMT=80 FV=1000 TO FIND THE PV TAKE THE PMT AND DIVIDE BY THE CURRENT YIELD %

CHAPTER 14 Suppose Stark, Ltd., just issued a dividend of $2.51 per share on its common stock. The company paid dividends of $2.01, $2.17, $2.25, and $2.36 per share in the last four years. a.If the stock currently sells for $43, what is your best estimate of the company's cost of equity capital using the arithmetic average growth rate in dividends? b.What if you use the geometric average growth rate?

To use the dividend growth model, we first need to find the growth rate in dividends. So, the increase in dividends each year was: g1 = ($2.17 - 2.01)/$2.01 = .0796, or 7.96%g2 = ($2.25 - 2.17)/$2.17 = .0369, or 3.69%g3 = ($2.36 - 2.25)/$2.25 = .0489, or 4.89%g4 = ($2.51 - 2.36)/$2.36 = .0636, or 6.36% So, the average arithmetic growth rate in dividends was: g = (.0796 + .0369 + .0489 + .0636)/4g = .05723, or 5.723% Using this growth rate in the dividend growth model, we find the cost of equity is: RE = [$2.51(1.05723)/$43] + .05723 RE = .1189, or 11.89% Calculating the geometric growth rate in dividends, we find: $2.51 = $2.01(1 + g)4g = .05711, or 5.711% The cost of equity using the geometric dividend growth rate is: RE = [$2.51(1.05711)/$43] + .05711RE = .1188, or 11.88%

CHAPTER 12 Suppose a stock had an initial price of $65 per share, paid a dividend of $1.45 per share during the year, and had an ending share price of $58. a, Compute the percentage total return. b.What was the dividend yield and the capital gains yield?

Using the equation for total return, we find: R = [($58 - 65) + 1.45]/$65R = -.0854, or -8.54% And the dividend yield and capital gains yield are: Dividend yield = $1.45/$65Dividend yield = .0223, or 2.23% Capital gains yield = ($58 - 65)/$65Capital gains yield = -.1077, or -10.77% Here's a question for you: Can the dividend yield ever be negative? No, that would mean you were paying the company for the privilege of owning the stock. However, this has happened on bonds.

CHAPTER 14 Stock in Daenerys Industries has a beta of 1.05. The market risk premium is 7 percent, and T-bills are currently yielding 3.4 percent. The company's most recent dividend was $2.35 per share, and dividends are expected to grow at an annual rate of 4.1 percent indefinitely. If the stock sells for $43 per share, what is your best estimate of the company's cost of equity?

We have the information available to calculate the cost of equity using the CAPM and the dividend growth model. Using the CAPM, we find: RE = .034 + 1.05(.07)RE = .1075, or 10.75% And using the dividend growth model, the cost of equity is RE = [$2.35(1.041)/$43] + .041RE = .0979, or 9.79% Both estimates of the cost of equity seem reasonable. If we remember the historical return on large capitalization stocks, the estimate from the CAPM model is about one percent lower than the historical average, and the estimate from the dividend growth model is about two percent lower than the historical average, so we cannot definitively say one of the estimates is incorrect. Given this, we will use the average of the two, so: RE = (.1075 + .0979)/2RE = .1027, or 10.27%

CHAPTER 9 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 11 percent. a. What is the discounted payback period for these cash flows if the initial cost is $5,200? b. What is the discounted payback period for these cash flows if the initial cost is $6,400? c. What is the discounted payback period for these cash flows if the initial cost is $10,400?

When we use discounted payback, we need to find the value of all cash flows today. The value today of the project cash flows for the first four years is: Value today of Year 1 cash flow = $2,800/1.11 = $2,522.52Value today of Year 2 cash flow = $3,700/1.112 = $3,003.00Value today of Year 3 cash flow = $5,100/1.113 = $3,729.08Value today of Year 4 cash flow = $4,300/1.114 = $2,832.54 To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $2,522.52, so the discounted payback for a $5,200 initial cost is: Discounted payback = 1 + ($5,200 - 2,522.52)/$3,003.00Discounted payback = 1.89 years For an initial cost of $6,400, the discounted payback is: Discounted payback = 2 + ($6,400 - 2,522.52 - 3,003.00)/$3,729.08Discounted payback = 2.23 years Notice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback. If the initial cost is $10,400, the discounted payback is: Discounted payback = 3 + ($10,400 - 2,522.52 - 3,003.00 - 3,729.08)/$2,832.54Discounted payback = 3.40 years

CHAPTER 14 The Drogon Co. just issued a dividend of $2.80 per share on its common stock. The company is expected to maintain a constant 4.5 percent growth rate in its dividends indefinitely. If the stock sells for $58 a share, what is the company's cost of equity?

With the information given, we can find the cost of equity using the dividend growth model. Using this model, the cost of equity is: RE = [$2.80(1.045)/$58] + .045RE = .0954, or 9.54%

regular cash dividend

a cash payment made by a firm to its owners in the normal course of business, usually paid four times a year

syndicate

a group of underwriters formed to share the risk and to help sell an issue

prospectus

a legal document describing details of the issuing corporation and the proposed offering to potential investors

Distribution

a payment made by a firm to its owners from sources other than current or accumulated retained earnings

stock dividend

a payment made by a firm to its owners in the form of stock, diluting the value of each share outstanding

dividend

a payment made out of a firm's earnings to its owners, in the form of either cash or stock

Red Herring

a preliminary prospectus distributed to prospective investors in a new issue of securities

rights offer

a public issue of securities in which securities are first offered to existing shareholders

registration statement

a statement filed with the SEC that discloses all material information concerning the corporation making a public offering

reverse split

a stock split in which a firm's number of shares outstanding is reduced

Unit Investment Trusts

pools of money invested in a portfolio that is fixed for the life of the fund unmanaged declined from 105 billion (1990) to 85 billion (2017)

to find interest rate (r) FORMULA

r = (FV/PV)^(1/t) - 1

CHAPTER 14 Jiminy's Cricket Farm issued a 30-year, 6 percent semiannual bond three years ago. The bond currently sells for 93 percent of its face value. The company's tax rate is 22 percent. a.What is the pretax cost of debt? b.What is the aftertax cost of debt?

a. The pretax cost of debt is the YTM of the company's bonds, so: P0 = $930 = $30(PVIFAR%,54) + $1,000(PVIFR%,54)R = 3.278%YTM = 2 × 3.278%YTM = 6.56% b. The aftertax cost of debt is: RD = .0656(1 - .22)RD = .0511, or 5.11% c. The aftertax rate is more relevant because that is the actual cost to the company.

CHAPTER 12 You've observed the following returns on Crash-n-Burn Computer's stock over the past five years: 8 percent, −15 percent, 19 percent, 31 percent, and 21 percent. a.What was the arithmetic average return on the company's stock over this five-year period? What was the variance of the company's returns over this period? What was the standard deviation of the company's returns over this period?

a. To find the average return, we sum all the returns and divide by the number of returns, so: Average return = (.08 - .15 + .19 +.31 +.21)/5 Average return = .1280, or 12.80% b. Using the equation to calculate variance, we find: Variance = 1/4[(.08 - .128)2 + (-.15 - .128)2 + (.19 - .128)2 + (.31 - .128)2 + (.21 - .128)2] Variance = .03082 So, the standard deviation is: Standard deviation = .030821/2Standard deviation = .1756, or 17.56%

CHAPTER 14 Targaryen Corporation has a target capital structure of 70 percent common stock, 5 percent preferred stock, and 25 percent debt. Its cost of equity is 10 percent, the cost of preferred stock is 5 percent, and the pretax cost of debt is 6 percent. The relevant tax rate is 23 percent. a.What is the company's WACC? b.What is the aftertax cost of debt?

a. Using the equation to calculate the WACC, we find: WACC = .70(.10) + .05(.05) + .25(.06)(1 - .23) WACC = .0841, or 8.41% b. Since interest is tax deductible and dividends are not, we must look at the aftertax cost of debt, which is: RD = .06(1 - .23)RD = .0462, or 4.62% Hence, on an aftertax basis, debt is cheaper than the preferred stock.

Current price

aka present value and market value

regulation A

an SEC regulation that exempts public issues of less than $5 million from most registration requirements

tombstone

an advertisement announcing a public offering

stock split

an increase in a firm's shares outstanding without any change in owner's equity

general cash offer

an issue of securities offered for sale to the general public on a cash basis

mutual funds

common name for open end investment companies dominant investment company today accounts for 87% of investment company assets

gross spread

compensation to the underwriter, determined by the difference between the underwriter's buying price and offering price

Costs of Investing in Mutual Funds

fee structure 1. operating expenses 2. front end load 3 back end load 4 12 b-1 charges fees must be disclosed in the prospectus share classes with different fee combinations

venture capital (VC)

financing for new, often high risk, ventures

underwriters

investment firms that act as intermediaries between a company selling securities and the investing public

exchange traded funds (ETFs)

•ETFs are offshoots of mutual funds that allow investors to trade index portfolios just as they do shares of stock •Examples: "spiders," "diamonds," "cubes," and "WEBS" •Potential advantages •Trade continuously like stocks •Can be sold short or purchased on margin •Cheaper than mutual funds •Tax efficient •Potential disadvantages •Prices can depart from NAV •Must be purchased from a broker (for a fee)

Net Asset Value (NAV)

•Investment companies pool assets of individual investors, but also need to divide claims to those assets among investors •Calculation of NAV: (Market Value of Assets - Liabilities)/Shares Outstandin

Mutual Fund Investment Performance

•Performance of actively managed funds •Wilshire 5000 index used as a benchmark for the performance of equity fund managers •Wilshire 5000 outperformed average return on diversified equity funds in 29 of the 48 years from 1971 to 2018

Information on Mutual Funds

•Prospectus •Statement of Investment Objectives •Describes investment objectives and policies •Description of fund's investment adviser and portfolio manager •Presents fees and costs •Statement of Additional Information (SAI) •Fund's annual repor