FIN3403 Ch 6-9 Review

capital gains yield formula

(ending price - beginning price) / beginning price

Good Decision Criteria

1. Does the decision rule adjust for the time value of money? 2. Does the decision rule adjust for risk? 3. Does the decision rule provide information on whether we are creating value for the firm?

payback period computation

1. Estimate CFs 2. Subtract future CFs from initial cost until initial investment has been recovered

NPV 3 Steps

1. Estimate the expected future cash flows 2. Estimate the required return 3. Calculate PV of CFs and subtract the initial investment

George Jefferson established a trust fund that will provide $212,500 per year in scholarships. The trust fund earns an annual return of 3.5 percent. How much money did Mr. Jefferson contribute to the fund assuming that only income is distributed?

212500/.035 = 6071428.57

Grateful Eight Co. is expected to maintain a constant 5.4 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 7.2 percent, what is the required return on the company's stock?

5.4+7.2=12.6%

discount bond

A bond that sells below its par value; if YTM > coupon rate

Treasury bills are currently paying 8 percent and the inflation rate is 2.8 percent. What is the approximate real rate of interest? What is the exact real rate?

Approximate Rate = 8-2.8 = 5.2% Exact Real Rate = [(1+.08)/(1+.028)] -1 = 5.058%

You're trying to determine whether to expand your business by building a new manufacturing plant. The plant has an installation cost of $12.6 million, which will be depreciated straight-line to zero over its four-year life. If the plant has projected net income of $1,914,300, $1,967,600, $1,936,000, and $1,389,500 over these four years, respectively, what is the project's average accounting return (AAR)?

Average Net Income/Average Book Value Average NI= 1914300+1967600+1936000+1389500=7207400 7207400/4 = 1801850 Average Book Value= 12600000-0/2=6300000 1801850/630000=0.286 AAR = 28.6%

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 -28200 1 12200 2 15200 3 11200 If the required return is 13 percent, what is the IRR for this project?

CF0= -28200 CF1= 12200 CF2= 15200 CF3= 11200 i/y = 13 IRR = 17.71 Since 17.71 > 13, they should accept the project

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 -28800 1 12800 2 15800 3 11800 What is the NPV for the project if the required return is 10 percent? At a required return of 10 percent, should the firm accept this project? What is the NPV for the project if the required return is 26 percent? At a required return of 26 percent, should the firm accept this project?

CF0= -28800 CF1= 12800 CF2= 15800 CF3= 11800 i/y = 10 NPV = 4759.73 Since 4759.73>0, they should accept CF0= -28800 CF1= 12800 CF2= 15800 CF3= 11800 i/y = 26 NPV = -2790.25 Since -2790.25<0, they should reject

What is the value of the cash flows today assuming an annual interest rate of 9.9 percent? Yr1 $1800 Yr2 $2,270 Yr3 $2,605 Yr4 $2,615

CF0= 0 CF1= 1800 CF2= 2270 CF3 = 2605 CF4 = 2615 I/y = 9.9% NPV = 7272.41 $7,272.41

Huggins Co. has identified an investment project with the following cash flows. Year1 $730 Year2 950 Year3 1,210 Year4 1,300 If the discount rate is 8 percent, what is the present value of these cash flows?

CF0=0 CF1=730 CF2=950 CF3= 1,210 CF4= 1,300 I/y= 8% NPV= 3406.4736

Discounted Payback Period

Calculates the time it takes to get back invested capital in present value terms; not a primary decision-making rule; ACCEPT if the project pays back on a discounted basis within a specified time

Bronco, Inc., imposes a payback cutoff of three years for its international investment projects. Cash Flow A Cash Flow B Year 0 -57000 -67000 Year 1 21500 13500 Year 2 25000 16500 Year 3 19500 23000 Year 4 6500 227000 What is the payback period for both projects? Which project should the company accept?

Cash Flow A Cash Flow B -57000+21500= -35500 -67000+13500=-53500 -35500+25000= -10500 -53500+16500=-37000 -10500/19500= -.54 -37000+23000=-14000 -14000/227000=-.06 Project A 2.54 years Project B 3.06 years The company should accept Project A because 2.54<3.06

Hudson Corporation will pay a dividend of $3.06 per share next year. The company pledges to increase its dividend by 6 percent per year indefinitely. If you require a return of 12 percent on your investment, how much will you pay for the company's stock today?

D1/R-g 3.06/(.12-.06) = $51

Find the EAR in each of the following cases: Stated Rate (APR) Number of Times 8.7 % Quarterly 17.7 Monthly 13.7 Daily 10.7 Infinite

EAR= [1+(APR/m)]^m -1 Quarterly = [1+(.087/4]^4 -1 = 8.99% Monthly = [1+(.177/12)]^12 -1 = 19.21% Daily = [1+(.137/365)]^365 -1 = 14.68% Infinite = EAR=e^q-1 e^.107 - 1 = 11.29%

Annuity Formula for Future Value

FV = C[(1+r)^t-1/r]

Cannonier, Inc., has identified an investment project with the following cash flows. Year1 $1,060 Year2 1,290 Year3 1,510 Year4 2,250 If the discount rate is 6 percent, what is the future value of these cash flows in Year 4?

FV=PV(1+r)^t FV = 1060(1.06)^3 + 1290(1.06)^2 + 1510(1.06) + 2250 6562.52

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 = 13 x 2 = 26 FV = 1000 I/y= 6.9/2= 3.45% PMT= (.086x1000)/2 = 43 PV = 1144.3752

McConnell Corporation has bonds on the market with 18 years to maturity, a YTM of 10.0 percent, a par value of $1,000, and a current price of $1,196.50. The bonds make semiannual payments. What must the coupon rate be on these bonds?

N = 18 x 2 (semi) = 36 I/y= 10/2 (semi) = 5% FV= 1000 PV = 1196.50 PMT= 61.88 x 2 (semi) = 123.75 Coupon rate = annual coupon/FV 123.75/1000 = 12.38% 12.38%

Wine and Roses, Inc., offers a bond with a coupon of 6.5 percent with semiannual payments and a yield to maturity of 6.99 percent. The bonds mature in 8 years. What is the market price of a $1,000 face value bond?

N = 8 x 2 (semi) = 16 I/y= 6.99/2 (semi) = 3.495% PMT= (.065 x 1000)/2 (semi) = 32.50 FV = 1000 PV = 970.36 $970.36

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, 10 years to maturity, and a coupon rate of 7.6 percent paid annually. If the yield to maturity is 8.7 percent, what is the current price of the bond?

N= 10 FV = 1000 I/y=8.7% PMT = .076 x 1000 = 76 PV = $928.46

NPV vs. IRR

NPV and IRR will generally give us the same decision 2 Exceptions: 1. Nonconventional cash flows - cash flow signs change more than once 2. Mutually exclusive projects ALWAYS DEFAULT TO NPV

NYSE

New York Stock Exchange, secondary market, centralized trading venue (largest in the world)

The common stock of Eddie's Engines, Inc., has a market rate of return of 9.64%. The stock is expected to pay a dividend of $2.30 per share next year. Eddie's has established a pattern of increasing their dividends by 4.4 percent annually and expects to continue doing so. What is the price of shares today?

P0 = D1/(R-g) 2.30/(.0964-.044) P0= $43.88

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.80 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely. Investors require a return of 11 percent on the company's stock. What is the current stock price? What will the stock price be in 3 years? What will the stock price be in 16 years?

P0= (D0(1+.g))/(R-g) P0=(1.80(1.06))/(.11-.06) = $38.16 P3= (D0(1+g)^4)/(R-g) (1.80(1.06)^4)/(.11-.06) = $45.45 P16= (D0(1.06)^17)/(.11-.06)= $96.94

2 Stage Dividend Growth Model

P0= (D0(1+g))/R-g ~or~ P0= D1/R-g

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 $14 per share 10 years from today and will increase the dividend by 8 percent per year thereafter. If the required return on this stock is 14 percent, what is the current share price?

P9=D10/(R-g) =$14/(.14-.08) =233.33 P0= P9/(1.14)^9 P0=233.33/(1.14)^9 P0=$71.75

Annuity Formula for Present Value

PV = C [1-(1/(1+r)^t)/r]

If you put up $44,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be?

PV = C [1-(1/(1+r)^t)/r] 44000=C[1-(1/1+.0675)^14)/.0657 44000=C(8.878) 44000/8.878= C 4956.07=C

An investment offers $5,700 per year for 10 years, with the first payment occurring one year from now. If the required return is 5 percent, what is the value of the investment

PV = C [1-(1/(1+r)^t)/r] PV= 5700[1-(1/1+.05)^10)/.05] 5700(7.7217) 44013.69

Perpetuity Formula

PV = C/r

An investment project has annual cash inflows of $4,300, $4,000, $5,200, and $4,400, for the next four years, respectively. The discount rate is 13 percent. What is the discounted payback period for these cash flows if the initial cost is $5,800? What is the discounted payback period for these cash flows if the initial cost is $7,900? What is the discounted payback period for these cash flows if the initial cost is $10,900

PV of CF1 = 4300/1.13 = 3805.31 PV of CF2= 4000/1.13^2 = 3132.59 PV of CF3= 5200/1.13^3 = 3603.86 PV of CF4= 4400/1.13^4= 2698.60 For initial cost of $5800 1+(5800-3805.31)/3132.59 = 1.64 years For initial cost of $7900 2+(7900-3805.31-3132.59)/3603.86 = 2.27 years For initial cost of $10900 3+(10900-3805.31-3132.59-3603.86)/2698.60= 3.13 years

A project that provides annual cash flows of $16,800 for nine years costs $74,000 today. At what discount rate would you be indifferent between accepting the project and rejecting it?

PV= -74000 PMT= 16800 N= 9 i/y= ? 17.3

The Perfect Rose Co. has earnings of $1.40 per share. The benchmark PE for the company is 15. What stock price would you consider appropriate? What if the benchmark PE were 18?

Pt= Benchmark PE Ratio x EPS 15x1.40= $21 18x1.40=$25.20

The common stock of Eddie's Engines, Inc., sells for $43.88 a share. The stock is expected to pay a dividend of $2.30 per share next year. Eddie's has established a pattern of increasing their dividends by 4.4 percent annually and expects to continue doing so. What is the market rate of return on this stock?

R = (D1/P0) +g (2.30/43.88) + .044 R= 9.64%

The next dividend payment by Savitz, Inc., will be $3.95 per share. The dividends are anticipated to maintain a growth rate of 3 percent forever.If the stock currently sells for $52 per share, what is the required return?

R = (D1/P0) +g (3.95/52) + .03 R= 10.60%

2 Stage Dividend Growth Model to find R

R = D1/P0 + g Return= dividend yield + capital gains yield

The next dividend payment by Savitz, Inc., will be $1.60 per share. The dividends are anticipated to maintain a growth rate of 6 percent forever. The stock currently sells for $30 per share. What is the dividend yield? What is the expected capital gains yield?

R=D1/P0 + g D1/P0= dividend yield g = capital gains yield 1.60/30 = 5.33% .06= 6%

coupon rate

The percentage of the face value that the bondholder receives each year until the bond matures. AKA interest rate

Annual Percentage Rate (APR)

The periodic rate times the number of periods per year **period rate = APR/# of periods per year

Yield to Maturity (YTM)

The required rate of return on a bond

constant growth model

Used to find the value of a constant growth stock

Bedeker, Inc., has an issue of preferred stock outstanding that pays a $5.35 dividend every year in perpetuity. If this issue currently sells for $93 per share, what is the required return?

Zero Growth Formula P0=D/R 93=5.35/R 93/5.35=R 5.75%=R

premium bond

a bond that is selling above its par value; if YTM < coupon rate

primary market

a market in which new issues of securities are offered to the public

coupon payment

an interest payment on a bond

coupon rate formula

annual coupon/par value

Current Yield Formula

annual coupon/price

ask-bid spread

ask price - bid price

Average Accounting Return (AAR)

average net income/average book value; not a primary decision-making rule; ACCEPT if AAR is greater than a preset rate

callable bonds

bonds that the issuing company can redeem (buy back) at a stated dollar amount prior to maturity

NASDAQ

computer based quotation system, American market for OTC securities, not a physical place

Dealers

hold inventory and stand ready to buy and sell, buy at bid prices, sells at ask prices

perpetuity

infinite series of equal payments

Broker

matches buyers and sellers for a fee, hold no inventory

secondary market

previously issued securities are traded among investors Ex. NYSE, Nasdaq

Effective Annual Rate (EAR)

the actual rate paid (or received) after accounting for compounding that occurs during the year EAR= [1+(APR/m)]^m-1 m= # of compounding periods per year

Net Present Value (NPV)

the difference between an investment's market value and its cost; primary decision-making rule; ACCEPT if NPV > 0

Internal Rate of Return (IRR)

the discount rate that makes the NPV of an investment zero; secondary decision-making rule; ACCEPT if IRR is greater than the required return

capital gains yield

the dividend growth rate, or the rate at which the value of an investment grows

face value

the dollar value printed on a bond

Payback Period

the length of time it takes to get the initial cost back in a nominal sense; not a primary decision-making rule; ACCEPT if the payback period is less than the preset limit

maturity

the time at which payment to a bondholder is due