FINA 307 - Exam 2 Study Set

Approximately how much must be saved for retirement in order to withdraw $100,000 per year for the next 25 years if the balance earns 8% annually, and the first payment occurs one year from now?

$1,067,477.62 Calculator: N=25, I=8, PMT= -100000, END Compute PV

Which of the following projects would you feel safest in accepting? Assume the opportunity cost of capital to be 12% for each project. "A" has a small, but negative, NPV. "B" has a positive NPV when discounted at 10%. "C's" cost of capital exceeds its rate of return. "D" has a zero NPV when discounted at 14%.

"D" has a zero NPV when discounted at 14%.

What is the present value of a five-period annuity of $3,000 if the interest rate per period is 12% and the first payment is made today?

$12,112.05 Calculator: N=5, I=12, PMT= -3000, BEGIN Compute PV

You have just retired with savings of $1.5 million. If you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.

$123,371.44 Calculator: N=30, I=8, PV= -1500000, BEGIN Calculate PMT

$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment?

$15,105.74 Payment = $50,000 / [1 / 0.1 − 1 / 0.1(1.1)^3] Payment = $20,105.74 Principal payment = $20,105.74 − ($50,000 × 0.1) Principal payment = $15,105.74 Ch5 part 2 #7

The $45.0 million lottery payment that you have just won actually pays $3.0 million per year for 15 years. The interest rate is 9%. a. If the first payment comes in 1 year, what is the present value of the winnings? b. What is the present value if the first payment comes immediately?

$24.18 $26.36

You believe you will spend $31,000 a year for 11 years once you retire in 22 years. If the interest rate is 7% per year, how much must you save each year until retirement to meet your retirement goal?

$4743.50 Calculator: N=11, I=7, PMT = -31000, Calculate PV = 232458.9045 Then N=22, I=7, PV=0, FV= - 232458.9045, Compute PMT

What will be the monthly payment on a $75,000 30-year home mortgage at 1% interest per month?

$771.46 Calculator: N=30x60, I=1, PV= -75000 Compute: PMT

Consider a 4-year amortizing loan. You borrow $3,000 initially and repay it in four equal annual year-end payments. a. If the interest rate is 10%, what is the annual payment? b. Prepare an amortization schedule.

$946.41 Using a financial calculator, enter PV = (−)3,000, FV = 0, i = 10%, n = 4; compute PMT = $946.41. see ch 5 part 2 #19

Rosita purchased a bond for $989 that had a 7% coupon and semiannual interest payments. She sold the bond after 6 months and earned a total return of 4.8% on this investment. At what price, did she sell the bond? $1,001.47 $974.28 $981.06 $1,003.18

.07*1000/2 = 35 PMT Using Holding Period Return Formula: (P1 - P0 + Interest) / P0 * 100 4.8% = [ (P1 - 989 ) + 35] / 989 P= $ 1001.472

A company with a return on equity of 15% and a plowback ratio of 60% would expect a constant-growth rate of: 4%. 9%. 21%. 25%.

.15*.6=9%

Professor's Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of $85,000 at age 65, the firm will pay the retiring professor $725 a month until death. a. If the professor's remaining life expectancy is 20 years, what is the monthly interest rate on this annuity? b. What is the effective annual interest rate? c. If the monthly interest rate is 1.00%, what monthly annuity payment can the firm offer to the retiring professor?

0.69% 8.60% $935.92 a. N= 20*12, PV= -85000, PMT= 725, Compute I b. (1+.0069)^12 - 1 c. N= 20*12, I=1, PV = -85000, Compute PMT

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

1 + real interest rate = (1 + nominal interest rate)/(1 + inflation) 1 + real interest rate = 1.12/1.06 (1.12/1.06) - 1 = 5.66%

In 1880 five aboriginal trackers were each promised the equivalent of 50 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1998 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the $50. However, the granddaughters also claimed that they were entitled to compound interest. a. How much was each granddaughter entitled to if the interest rate was 3%? b. How much was each entitled to if the interest rate was 6%?

1,635.92 Australian dollars 48,424.16 Australian dollars N=118 I=3 PV= -50 Compute FV N=118 I=6 PV= -50 Compute FV

If you earn 7% per year on your bank account, how long will it take an account with $115 to double to $230?

10.24 years I=7, PV= -115, FV=230 Compute N

I now have $19,000 in the bank earning interest of 1.00% per month. I need $29,000 to make a down payment on a house. I can save an additional $100 per month. How long will it take me to accumulate the $29,000?

29.77 months Calculator: I=1, PV= -19000, PMT= -100, FV=29000, Compute N

A local bank will pay you $299 at the end of each year for your lifetime if you deposit $4,600 in the bank today. If you plan to live forever, what interest rate is the bank paying?

6.5% 299/4600

Would you prefer a savings account that paid 7% interest compounded quarterly, 6.8% compounded monthly, 7.2% compounded weekly, or an account that paid 7.5% with annual compounding?

7.5% compounded annually Ch 5 part 3 #12

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment period?

7.64%1 + nominal rate = (1 + real rate)(1 + inflation rate) Nominal rate = (1.04 × 1.035) - 1 Nominal rate = 7.64%

Which one of the following changes will increase the NPV of a project? A decrease in the discount rate A decrease in the size of the cash inflows An increase in the initial cost of the project A decrease in the number of cash inflows

A decrease in the discount rate

BMM Industries pays a dividend of $3.00 per quarter. The dividend yield on its stock is reported at 5.80%. What is the stock price?

Annual dividend =(Quarterly dividend)(4)=$3(4)=$12 Current stock price=(Annual dividend)/(Dividend yield)=$12/(5.8%)= $206.90

What is the present value of the following cash-flow stream if the interest rate is 4%? Year - Cash Flow 1 - $240 2 - $440 3 - $340

CF0=0 CO1=240 CO2=440 CO3=340 FO1 = 1 FO2 = 1 FO3 = 1 I = 4 CPT NPV = $939.83

A bond has a coupon rate of 8%, pays interest semiannually, sells for $960, and matures in 3 years. What is its yield to maturity? 4.78% 5.48% 9.57% 12.17%

Calculator: N = 3*2 PV = -960 FV = 1000 PMT = .08*1000/2 P/Y = 2 Compute I = 9.57%

You want to buy a new car, but you can make an initial payment of only $1,200 and can afford monthly payments of at most $850. a. If the APR on auto loans is 12% and you finance the purchase over 48 months, what is the maximum price you can pay for the car? b. How much can you afford if you finance the purchase over 60 months?

Calculator: N=48, I=12/12, PMT= -850, Compute PV then add 1200 = $33,477.87 Calculator: N=60, I=12/12, PMT= -850, Compute PV then add 1200 = $39,411.78

Which one of the following is fixed for the life of a given bond? Current price Current yield Yield to maturity Coupon rate

Coupon rate

A 10-year Treasury bond is issued with face value of $1,000, paying interest of $72 per year. If market yields increase shortly after the T-bond is issued, what is the bond's coupon rate?

Coupon rate=Annual interest / Face value $72 / $1,000 =0.072 or 7.2%

Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely. a. What price should the stock sell at if the discount rate is 15%. b. What price should the stock sell at if the discount rate is 12%.

D0(1+g)/(r-g) a. 3(1+.05)/(.15-.05) = 31.50 b. 3(1+.05)/(.12-.05) = 45

Which one of the following will increase the present value of an annuity, other things equal? Increasing the interest rate Decreasing the interest rate Decreasing the number of payments Decreasing the amount of the payment

Decreasing the interest rate

What should you pay for a stock if next year's annual dividend is forecast to be $5.25, the constant-growth rate is 2.85%, and you require a 15.5% rate of return? $31.25 $38.87 $41.50 $42.68

Dividend discount model CONTACT GROWTH = Payment for the year/(discount rate-constant rate) So... Price = $5.25/(0.155 − 0.0285) = $41.50

A stock currently sells for $50 per share, has an expected return of 15%, and an expected capital gain rate of 10%. What is the amount of the expected dividend? $2.50 $2.75 $3.00 $3.50

Dividend yield = 0.15 − 0.10 = 0.05 Expected dividend = 0.05 × $50 = $2.50

If the dividend yield for year 1 is expected to be 5% based on a stock price of $25, what will the year 4 dividend be if dividends grow annually at a constant rate of 6%? $1.33 $1.49 $1.58 $1.67

Dividend yield for year 1 = 25*5% i.e 1.25 Dividend yield for year 4 = 1.25(1.06^3) i.e 1.49

What dividend yield would be reported in the financial press for a stock that currently pays a $1 dividend per quarter and the most recent stock price was $40? 2.5% 4.0% 10.0% 5.0%

Dividend yield=Annual dividend/Current stock priceGiven that the company pays 1 dividend per quarter, so the annual dividend=1*4=4Recent stock price=40 So, dividend yield=4/40=0.1 or 10.00%

Dani's just paid an annual dividend of $6 per share. What is the dividend expected to be in five years if the growth rate is 4.2%? $7.07 $7.37 $7.14 $7.44

Expected dividend = Annual Dividend*(1+r)^n = $6*(1+0.042)^5 = $7.37

What will be the approximate population of the United States, if its current population of 300 million grows at a compound rate of 2% annually for 25 years? 413 million 430 million 488 million 492 million

FV = PV(1 + r)t FV = 300 million × (1.02)25 FV = 492.2 million ≈ 492 million

Given the future value, which of the following will contribute to a lower present value? Higher discount rate Fewer time periods Less frequent discounting Lower discount factor

Higher discount rate

How long will it take for $600 to grow to $3,000 at the following interest rates? 6% 10% 18%

I= 6 PV= -600 FV= 3000 Compute N = 27.62 I= 10 PV= -600 FV= 3000 Compute N = 16.87 I= 18 PV= -600 FV= 3000 Compute N = 9.72

What is the rate of return for an investor who pays $1,054.47 for a 3-year bond with an annual coupon payment of 6.5% and sells the bond 1 year later for $1,037.19? 4.53% 5.33% 5.16% 4.92%

Interest on bond = 1000 x 6.5% = $65 Loss on sale = 1054.47 - 1037.19 = 17.28 Rate of return on bond = (65 - 17.28) / 1054.47 = 4.53%

How much should you be prepared to pay for a 10-year bond with a 6% coupon, semiannual payments, and a semiannually compounded yield of 7.5%? $895.78 $897.04 $938.40 $1,312.66

N = 10*2 I = 7.5 PMT = .06*1000/2 FV = 1000 P/Y = 2 Compute PV = - 895.78 = $895.78

Find the interest rate implied by the following combinations of present and future values: Present Value - Years - Future Value $500 - 12 years - $1126 $233 - 5 years - $375 $400 - 8 years - $400

N=12 PV= -500 FV=1126 Compute I= 7% N=5 PV= -233 FV=375 Compute I=9.99% r=(FV / PV)1/t - 1 r=($400 / $400)1/8 - 1 = 0.0000, or 0%

A U.S. Treasury strip that will pay $1,000 in 9 years is selling today for $460.43. What interest rate does the bond offer?

N=9 PV= -460.43 FV=1000 Compute I= 9%

If investors are to earn a 3.7% real interest rate, what nominal interest rate must they earn if the inflation rate is: a. zero b. 4.7% c. 6.7%

Nominal rate=(1+Real interest rate)(1+inflation rate)-1 1. 3.7% 2.Nominal rate=(1.037*1.047)-1=8.5739% 3.Nominal rate=(1.037*1.067)-1=10.6479%

If a stock's P/E ratio is 13.5 at a time when earnings are $3 per year and the dividend payout ratio is 40%, what is the stock's current price? $24.30 $18.00 $22.22 $40.50

P/E Ratio = Market Price Per Share/ Earnings Per Share Market Price Per Share = P/E Ratio * Earnings Per Share = 13.5* $ 3 = $ 40.50 Answer = $ 40.50

Favorita Candy's stock is expected to earn $2.50 per share this year. Its P/E ratio is 19. What is the stock price?

P/E ratio = Price of stock/ EPS 19 = Price of stock/ 2.5 Price of the stock = 19*2.5 = $47.5

A stock is selling for $37.50 and is expected to pay a dividend of $3 at the end of the year. If investors expect a return of 14%, what must be the sustainable growth rate?

P0 = D1/(ke-g) 37.5 = 3/(14%-g) g = 6%

What should be the price for a common stock paying $3.50 annually in dividends if the growth rate is zero and the discount rate is 8%? $22.86 $28.00 $42.00 $43.75

P0=3.5/.08= $43.75

A perpetuity of $5,000 per year beginning today offers a 15% return. What is its present value?

PV = 5000+5000/.15 = $38,333.33

You will be receiving cash flows of: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5. What is the present value of these cash flows at an interest rate of 7%?

PV = FV/(1+r)^t PV = (1000) + (2000/1.07^1) + (4000/1.07^3) + (6000/1.07^5) = $10,412.27

You will require $650 in 5 years. If you earn 5% interest on your funds, how much will you need to invest today in order to reach your savings goal?

PV=FV / (1 + r)^t =$650 / 1.05^5 =$509.29

Wilt's has earnings per share of $2.98 and dividends per share of $0.35. What is the firm's sustainable rate of growth if its return on assets is 14.6% and its return on equity is 18.2%? 2.14% 1.71% 12.89% 16.06%

Sustainable growth rate = Return on equity x Retention rate = 18.20% x 0.88255 = 16.06% (Answer) Note: Retention ratio = 1 - Dividend / EPS = 1 - $0.35 / $2.98 = 1 - 0.117450 = 0.88255

What is the plowback ratio for a firm that has earnings per share of $2.68 and pays out $1.75 per share in dividends? 28.20% 34.70% 66.67% 71.80%

Pay back ratio = EPS - DPS / EPS*100 '=($2.68 - $1.75)/$2.68 * 100 = $ 34.70 So, the option with 34.70%

A stock is expected to pay dividends of $1.20 per share in Year 1 and $1.35 per share in Year 2. After that, the dividend is expected to increase by 2.5% annually. What is the current value of the stock at a discount rate of 14.5%? $11.29 $10.87 $12.07 $13.39

Price = $1.20/1.145 + $1.35/1.145^2 + [($1.35 × 1.025) /(0.145 − 0.025)] /1.145^2 = $10.87

ABC common stock is expected to have extraordinary growth in earnings and dividends of 20% per year for 2 years, after which the growth rate will settle into a constant 6%. If the discount rate is 15% and the most recent dividend was $2.50, what should be the approximate current share price? $31.16 $33.23 $37.39 $47.77

Price = ($2.50 × 1.2)/1.15 + ($2.50 × 1.2^2)/1.15^2 + [($2.50 × 1.2^2 ×1.06)/(0.15 − 0.06)]/1.15^2 = $37.39

What price would you pay today for a stock if you require a rate of return of 13%, the dividend growth rate is 3.6%, and the firm recently paid an annual dividend of $2.50? $27.55 $30.28 $26.60 $31.37

Price = D1/(r-g)where D1 = the next expected dividend = D0 (last dividend)*(1+g), r = required rate of return and g = growth rate in dividends. Therefore, Price = ($2.50 × 1.036)/(0.13 − 0.036) = $27.55

The following are the cash flows of two projects: Year Project A Project B 0 (280) (280) 1 160 180 2 160 180 3 160 180 4 160 What is the payback period of each project?

Project A: 280/160 = 1.8 years Project B: 280/180 = 1.6 years

The following are the cash flows of two projects: Year.....Project A.....Project B ...0............(210)................(210) ....1.............90....................110 ...2.............90....................110 ...3.............90....................110 ...4.............90 What are the internal rates of return on projects A and B?

Project A: irr(-210,{90},{4}) = 25.68% Project B: irr(-210,{110},{3}) = 26.51%

Which mutually exclusive project would you select, if both are priced at $1,000 and your required return is 15%: Project A with three annual cash flows of $1,000; or Project B, with 3 years of zero cash flow followed by 3 years of $1,500 annually? Project A Project B You are indifferent since the NPVs are equal. Neither project should be selected.

Project A: npv(15,-1000,{1000},{3}) = 1283.23 Project B: 1500/(1.15)^4+1500/(1.15)^5+1500/(1.15)^6 =$2251.89, Hence NPV=(2251.89-1000)=$1251.89 Project A is better.

You buy a 20-year bond with a coupon rate of 9.2% that has a yield to maturity of 10.2%. (Assume a face value of $1,000 and semiannual coupon payments.) Six months later, the yield to maturity is 11.2%. What is your return over the 6 months?

Step 1: Calculator: FV = 1000 N = 20*2 PMT = .092*1000/2 P/Y = 1 I = 5.1 Compute PV = -915.3665 Step 2: Calculator: FV = 1000 N = 40-1 PMT = .092*1000/2 P/Y = 1 I = 11.2/2 Compute PV = -842.7550 Step 3: (46+(842.7550-915.3665))/915.3665 = -2.91%

A stock paying $5 in annual dividends currently sells for $80 and has an expected return of 14%. What might investors expect to pay for the stock one year from now after the next dividend has been paid? $82.20 $86.20 $87.20 $91.20

Step 1: Return on stock = 80*.14=11.2 Step 2: Capital gains = 11.2-5=6.20 Step 3: 80+6.20=86.20

Arts and Crafts, Inc. will pay a dividend of $4 per share in 1 year. It sells at $80 a share, and firms in the same industry provide an expected rate of return of 15%. What must be the expected growth rate of the company's dividends?

Stock Price = D1 / ( r - g) , where r is the expected rate of return and g is the growth rate. 80 = 4 / ( 0.15 - g) or 80 ( 0.15 - g ) = 4 or 12 - 80g = 4 or g = 8 / 80 = 0.10 or 10 %

Which one of the following is most likely for a CCC-rated bond, compared to a BBB-rated bond? The CCC bond will have a variable-coupon rate. The CCC bond will have a shorter term. The CCC bond will offer a higher promised yield to maturity. The CCC bond will have a higher price for the same term.

The CCC bond will offer a higher promised yield to maturity.

A bond is priced at $1,100, has 10 years remaining until maturity, and has a 10% coupon, paid semiannually. What is the amount of the next interest payment? $50 $55 $100 $110

The par value of the bond = $1000 Yearly interest payment = Coupon Rate(Par Value) = 10%(1000) = $100 Semiannual interest payment = 100/2 =50$

Which one of the following bond values will change when interest rates change? The expected cash flows The present value The coupon payment The maturity value

The present value

Assume a bond is currently selling at par value. What will happen in the future if the yield on the bond is lower than the coupon rate? The price of the bond will increase. The coupon rate of the bond will increase. The par value of the bond will decrease. The coupon payments will be adjusted to the new discount rate.

The price of the bond will increase.

If a project's NPV is calculated to be negative what should a project manager do? The discount rate should be decreased. The profitability index should be calculated. The present value of the project cost should be determined. The project should be rejected.

The project should be rejected.

What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence? The real cost is constant. The real cost is increasing. The real cost is decreasing. The price index must be known to answer this question.

The real cost is decreasing.

If investors expect a 14% return on a $50 stock that pays a dividend of $2.50, what is the implied capital gain rate? 5% 7% 9% 14%

Total expected return = Dividend yield + Capital gains yield Dividend yield = $2.50/$50 = 5% 14% = 5% + Capital gains yield. So: Capital gains yield = 9%

If a bond with face value of $1,000 and a coupon rate of 6% is selling at a price of $950, is the bond's yield to maturity more or less than 6%?

When the bond is selling at a discount, $950 in this case, the yield to maturity is greater than 6%. We know that if the yield to maturity were 6%, the bond would sell at par. At a price below par, the yield to maturity exceeds the coupon rate.

The following are the cash flows of two projects: Year Project A Project B 0 (330) (330) 1 160 230 2 160 230 3 160 230 4 160 If the opportunity cost of capital is 12%, is the project with the shortest payback period also the one with the highest NPV?

Yes

You expect a share of stock to pay dividends of $1.50, $1.65, and $1.90 in each of the next 3 years. You believe the stock will sell for $23.00 at the end of the third year. a. What is the stock price if the discount rate for the stock is 10%? b. What is the dividend yield for year 1? c. What will be the dividend yield at the start of year 2?

a. (1.5/1.1)+(1.65/1.1^2)+(1.9+23)/1.1^3=$21.44 b. 1.5/21.4=7% c. (1.65/1.1^1)+ (1.9+23)/(1.1^2) = 22.07851 1.65/22.08=7.47%

The coupon rate of a bond equals: its yield to maturity. a defined percentage of its face value. the yield to maturity when the bond sells at a discount. the annual interest divided by the current market price.

a defined percentage of its face value.

A stream of equal cash payments lasting forever is termed

a perpetuity

The internal rate of return is most reliable when evaluating: a single project with alternating cash inflows and outflows over several years. mutually exclusive projects of differing sizes. a single project with only cash inflows following the initial cash outflow. a single project with cash outflows at time 0 and the final year and inflows in all other time periods.

a single project with only cash inflows following the initial cash outflow.

A bond with a face value of $1,000 has 12 years until maturity, has a coupon rate of 6.4%, and sells for $1,097. a. What is the current yield on the bond? b. What is the yield to maturity if interest is paid once a year? c. What is the yield to maturity if interest is paid semiannually?

a) 6.4% of 1000 = $64, 64/1097 = 5.83% b). Calculator: FV = 1000 PV = -1097 N = 12 PMT = 64 compute for I/Y = 5.29% c). If coupon is paid twice in a year, semiannual coupon payment = $64/2 = $32 Calculator: FV = 1000 PV = -1097 N = 12*2 = 24 PMT = 32 compute for I/Y = 2.65% CHECK CH6 #3

Your landscaping company can lease a truck for $7,100 a year (paid at year-end) for 7 years. It can instead buy the truck for $38,000. The truck will be valueless after 7 years. The interest rate your company can earn on its funds is 8%. a. What is the present value of the cost of leasing? b. Is it cheaper to buy or lease? c.What is the present value of the cost of leasing if the lease payments are an annuity due, so the first payment comes immediately? d. Is it now cheaper to buy or lease?

a. $36,965.23 b. lease c. $39,922.45 d. buy a. calculator as normal c. switch to BEGIN

a. Several years ago, Castles in the Sand Inc. issued bonds at face value of $1,000 at a yield to maturity of 8.6%. Now, with 7 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15%. What is the price of the bond now? (Assume semiannual coupon payments.) b. Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

a. $733.73 b. 12.60% CHECK CH6 #6

First National Bank pays 6.3% interest compounded semiannually. Second National Bank pays 6% interest compounded monthly. a. Calculate the effective annual rate for each bank. b. Which bank offers the higher effective annual interest rate?

a. (1+(.063/2))^2-1 = 6.40 (1+(.06/12))^12-1 = 6.17 b. The first bank

Suppose you can borrow money at 11.80% per year (APR) compounded semiannually or 9.36% per year (APR) compounded monthly. a. Calculate the effective annual rates. b. Which is the better deal?

a. (1+(.118/2))^2-1 = 12.15 (1+(.0936/12))^12-1 = 9.77 b. 9.36% per year (APR) compounded monthly

If a bond is priced at par value, then: it has a very low level of default risk. its coupon rate equals its yield to maturity. it must be a zero-coupon bond. the bond is quite close to maturity.

its coupon rate equals its yield to maturity.

You have just borrowed $130,000 to buy a condo. You will repay the loan in equal monthly payments of $1,046.01 over the next 30 years. a. What monthly interest rate are you paying on the loan? b. What is the APR? c. What is the effective annual rate on that loan? d. What rate is the lender more likely to quote on the loan?

a. 0.75% Calculator: N= 30*12, PV= 130000, PMT= -1046.01, Compute I b. 9.0% 0.0075*12 = 9 c. 9.38% (1+.0075)^12-1 d. APR

A proposed nuclear power plant will cost $2.1 billion to build and then will produce cash flows of $290 million a year for 15 years. After that period (in year 15), it must be decommissioned at a cost of $890 million. a. What is the NPV of the project if the discount rate is 3%? b. What is the NPV of the project if the discount rate is 18%?

a. 0.791 billion b. -0.698 billion Ch 8 #8

Here are data on two stocks, both of which have discount rates of 16%: Return on equity: 16%. 15% Earnings per share: $2.20. $1.80 Dividends per share: $1.10. $1.10 a. What are the dividend payout ratios for each firm? b. What are the expected dividend growth rates for each stock? c. What is the proper stock price for each firm?

a. 1.1/2.2 = 50% 1.1/1.8=61.11% b. 0.16*(1-0.5)=.08=8% 0.15*(1-.6111)=.0583=5.83% c. 1.1/(.16-.08)=$13.75 1.1/(.16-.0583)=$10.82

Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and dividends to continue for another 3 years. a. If the last dividend paid was $11, what will the next dividend be? b. If the discount rate is 23% and the steady growth rate after 3 years is 4%, what should the stock price be today?

a. 11(1+.20)=$13.20 b. 13.20(1+.20)=$15.84 15.84(1+.20)=$19.008 19.008(1+.20)=104.04 (13.20/(1+.23^1)) + (15.84/(1+.23^2)) + ((19.008+104.04)/ (1+.23^1)) = $87.326

Assume you take out a car loan of $7,000 that calls for 72 monthly payments of $140 each. a. What is the APR of the loan? b. What is the effective annual interest rate on the loan?

a. 12.84 Calculator: N=72, PV= -7000, PMT 140, FV=0, Compute I = 1.07 THEN 1.07*12=12.84 b. 13.64 (1.01071^12)-1 = 13.64

A famous quarterback just signed a $19.5 million contract providing $3.9 million a year for 5 years. A less famous receiver signed a $18.5 million 5-year contract providing $4 million now and $2.9 million a year for 5 years. The interest rate is 10%. a. What is the PV of the quarterback's contract? b. What is the PV of the receiver's contract?

a. 14.78 million b. 14.99 million calculator: N=5, I=10, PMT= -3900000, compute PV calculator: N=5, I=10, PMT= -2900000, compute PV, add 4,000,000

Consider two mutually exclusive projects A and B: .........C0...........C1.........C2.......NPV@10% A: -39000 28200 28200 +9942 B: -59000 42000 42000 +13893 a. Calculate IRRs for A and B. b. Which project does the IRR rule suggest is best? c. Which project is really best?

a. 28.55% & 27.17% b. Project A c. Project B Ch8

A project that costs $3,200 to install will provide annual cash flows of $670 for the next 6 years. The firm accepts projects with payback periods of less than 4 years. a. What is this project's payback period? b.Will the project be accepted? c-1. What is project NPV if the discount rate is 3%? c-2.Should this project be pursued? d-1. What is project NPV if the discount rate is 9%? d-2. Should this project be pursued? e. Will the firm's decision change as the discount rate changes?

a. 3200/670=4.776 years b. No c1. 429.52 c2. Yes d1. -194.43 d2. No e. Yes Ch 8 #12

You can buy property today for $2.7 million and sell it in 4 years for $3.7 million. (You earn no rental income on the property.) a. If the interest rate is 12%, what is the present value of the sales price? b. Is the property investment attractive to you? c-1.What is the present value of the future cash flows, if you also could earn $170,000 per year rent on the property? The rent is paid at the end of each year. c-2. Is the property investment attractive to you now?

a. 3700000/(1.12^4)=2.351 mil (N=4, I=12, FV= -3700000, END, compute PV) b. The investment is not attractive because the present value of the sales price is less than the purchase price of the property. c. 2.868 (N=4, I=12, PMT= -170000, FV= -3700000, END, compute PV) d. The investment is attractive now because the present value of the future cash flows exceeds the current purchase price of the property.

Preferred Products has issued preferred stock with an annual dividend of $5.60 that will be paid in perpetuity. a. If the discount rate is 10%, at what price should the preferred sell? b. At what price should the stock sell 1 year from now? c. What are the (i) the dividend yield; (ii) the capital gains yield; (iii) the expected rate of return of the stock?

a. 5.6/.10=56 b. 56 c. 5.6/56 = 10%, 0, 10%

British government 4.9% perpetuities pay £4.9 interest at the end of each year forever. Another bond, 3.4% perpetuities, pays £3.40 a year forever. a. What is the value of 4.9% perpetuities if the long-term interest rate is 6.9%? b. What is the value of 3.4% perpetuities?

a. 71.01 b. 49.28 4.9/.069 3.4/.069

Your consulting firm will produce cash flows of $170,000 this year, and you expect cash flow thereafter to keep pace with any increase in the general level of prices. The interest rate currently is 5.6%, and you anticipate inflation of about 1.6%. a. What is the present value of your firm's cash flows for years 1 through 6? b. How would your answer to (a) change if you anticipated no growth in cash flow?

a. 892,985.28 (1.056/1.016) -1 = 0.0393 170,000 * [(1/0.0393) - 1/(0.0393*1.0393^6)] b. 846,547.60 170,000 * [(1/0.056) - 1/(0.056*1.056^6)]

A couple will retire in 40 years; they plan to spend about $25,000 a year in retirement, which should last about 20 years. They believe that they can earn 8% interest on retirement savings. a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. b. How would the answer to part (a) change if the couple also realize that in 15 years they will need to spend $55,000 on their child's college education?

a. 947.49 Calculator: N=20, I=8, PMT= -25000, Compute PV N=40, I=8, FV= -245453.69, Compute PMT b. Ch 5 Part 3 # 17

A 30-year maturity bond with face value of $1,000 makes semiannual coupon payments and has a coupon rate of 7.60%. a. What is the yield to maturity if the bond is selling for $990? b. What is the yield to maturity if the bond is selling for $1,000?

a. Calculator: FV = 1000 PV = -990 N = 30*2 PMT = .076*1000/2 P/Y = 2 compute for I = 7.6858% b. Calculator: FV = 1000 PV = -1000 N = 30*2 PMT = .076*1000/2 P/Y = 2 compute for I = 7.6000%

The following are the cash flows of two independent projects: Year.....Project A.....Project B ...0............(220)..............(220) ...1..............100..................120 ...2.............100..................120 ...3.............100..................120 ...4.............100 a. If the opportunity cost of capital is 10%, calculate the NPV for both projects. b. Which of these projects is worth pursuing?

a. Calculator: npv(10,-220,{100},{4}) = $96.97 Project A npv(10,-220,{120},{3}) = $78.42 Project B b. Both

The following are the cash flows of two projects: Year.....Project A.....Project B ...0............(330)..............(330) ...1..............160..................230 ...2.............160..................230 ...3.............160..................230 ...4.............160 a. Calculate the NPV for both projects if the discount rate is 12%. b. Suppose that you can choose only one of these projects. Which would you choose?

a. Calculator: npv(12,-330,{160},{4}) = $155.98 Project A npv(12,-330,{230},{3}) = $222.42 Project B b. Project B

The following are the cash flows of two projects: Year Project A Project B 0 (350) (350) 1 180 250 2 180 250 3 180 250 4 180 a. Calculate the NPV for both projects if the opportunity cost of capital is 16%. b. Suppose that you can choose only one of these projects. Which would you choose?

a. Calculator: npv(16,-350,{180},{4}) = $153.67 Project A npv(16,-350,{250},{3}) = $211.47 Project B b. Project B

Compute the future value of a $200 cash flow for the following combinations of rates and times. (Do not round intermediate calculations. Round your answers to 2 decimal places.) a. r = 8%; t = 10 years b. r = 8%; t = 20 years c. r = 4%; t = 10 years d. r = 4%; t = 20 years

a. FV = $200 × (1.08)10 = $431.78 b. FV = $200 × (1.08)20 = $932.19 c. FV = $200 × (1.04)10 = $296.05 d. FV = $200 × (1.04)20 = $438.22 OR calculator a. N= 20. I= 8 PV = -200

Compute the present value of a $230 cash flow for the following combinations of discount rates and times. a. r = 10%; t = 9 years b. r = 10%; t = 18 years c. r = 5%; t = 9 years d. r = 5%; t = 18 years

a. N=9 I=10 FV= -230 Compute PV $97.54 b. PV = $230 / (1.10)^18 = $41.37 c. PV = $230 / (1.05)^9 = $148.26 d. PV = $230 / (1.05)^18 = $95.57

If you insulate your office for $17,000, you will save $1,700 a year in heating expenses. These savings will last forever. a. What is the NPV of the investment when the cost of capital is 8%? 10%? b. What is the IRR of the investment? c. What is the payback period on this investment?

a. NPV at 8% = 1700/0.08 - 17,000 = 4,250 NPV at 10% = 1700/0.10 - 17,000 = 0 b. IRR = 1700/17000 = 10% c. payback = 17,000/1,700 = 10 years

Eastern Electric currently pays a dividend of $1.78 per share and sells for $36 a share. a. If investors believe the growth rate of dividends is 3% per year, what rate of return do they expect to earn on the stock? b. If investors' required rate of return is 12%, what must be the growth rate they expect of the firm? c. If the sustainable growth rate is 5% and the plowback ratio is 0.4, what must be the rate of return earned by the firm on its new investments?

a. Price of stock = [Current dividend * (1 + Growth rate)] / [Return on stock(ROS) - Growth rate] $36 = [$1.78 * (1 + 3%)] / [ROS - 3%] ROS = 8.09% b. Price of stock = [Current dividend * (1 + Growth rate(g))] / [Required return on stock - Growth rate] $36 = [$1.78 * (1 + g)] / [12% - g] g = 6.72% c. Sustainable growth rate = Plow back ratio * Rate of return 5% = 0.4 * Rate of return Rate of return = 5% / 0.4 = 12.50%

You deposit $1,100 in your bank account. a. If the bank pays 3% simple interest, how much will you accumulate in your account after 9 years? b. How much will you accumulate if the bank pays compound interest?

a. With simple interest, you earn 3% of $1,100, or $33 each year. There is no interest on interest. After 9 years, you earn total interest of $297, and your account accumulates to $1,397. FV Simple Interest= PV + PV × (r × t) = $1,100 + $1,100 × (0.03 × 9) = $1,397 b. FV= PV × (1 + r)t = $1,100 × 1.039 = $1,435.25

Integrated Potato Chips just paid a $1.3 per share dividend. You expect the dividend to grow steadily at a rate of 4% per year. a. What is the expected dividend in each of the next 3 years? b. If the discount rate for the stock is 12%, at what price will the stock sell today? c. What is the expected stock price 3 years from now? d. If you buy the stock and plan to sell it 3 years from now, what are your expected cash flows in (i) year 1; (ii) year 2; (iii) year 3? e. What is the present value of the stream of payments you found in part (d)?

a. Year 1: 1.3*1.04 = 1.35 Year 2: 1.35*1.04 = 1.41 Year 3: 1.41*1.04 = 1.46 b. Current price=D1/(Discount Rate-Growth rate) =(1.3*1.04)/(0.12-0.04) = $16.9 c.Price expected =Current price*(1+Growth rate)^3 =16.9*(1.04)^3 = $19.01 d. 1.35, 1.41, 1.46, 1.46+19.01=20.47 for year 3 e. 1.35/1.12^1=1.21 1.41/1.12^2=1.12 20.47/1.12^3=14.57

A factory costs $420,000. You forecast that it will produce cash inflows of $130,000 in year 1, $190,000 in year 2, and $320,000 in year 3. The discount rate is 10%. a. What is the value of the factory? b. Is the factory a good investment?

a. calculator: N=1, I=10, PMT = -130000, compute PV N=2, I=10, PMT = -190000, compute PV N=3, I=10, PMT = -320000, compute PV add together, then subtract 420,000 $95,627.35 b. yes

A project that costs $5,200 to install will provide annual cash flows of $1,750 for each of the next 6 years. a. What is NPV if the discount rate is 10%? b. How high can the discount rate be before you would reject the project?

a. npv(10,-5200,{1750},{6}) = $2421.71 b. irr(-5200,{1750},{6}) = 24.71%

You are offered the chance to participate in a project that produces the following cash flows: C0.........C1..........C2 7000....5000....-15,000 The internal rate of return is 15.0%. a. If the opportunity cost of capital is 13%, what is the net present value of the project? b. Will you accept the offer?

a. npv(13,7000,{5000,-15000}) = -322.42 b. No

Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowback ratio of 0.30. Its earnings this year will be $5 per share. Investors expect a rate of return of 12% on the stock. a. Find the price and P/E ratio of the firm. b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to 0.20.

a. step 1: 1-0.3 = 0.7 step 2: 5*0.7 = $3.5 step 3: 3.5/(12%-6%) = $58.33 per share step 4: 58.33/5= 11.67 times b. step 1: 1-0.2 = 0.8 step 2: 5*0.8 = $4 step 3: 0.2*20% = 4% step 4: 4/(12%-4%) = $50 per share step 4: 50/5= 10 times

Here are the cash-flow forecasts for two mutually exclusive projects: Year.....Project A.........Project B 0............-120.....................-120 1...............50........................69 2..............70........................69 3..............90........................69 a-1. What is the NPV of each project if the opportunity cost of capital is 2%? a-2. Which project would you choose? b-1. What is the NPV of each project if the opportunity cost of capital is 14%? b-2. Which would you choose?

a1. npv=(2,-120,{50,70,90}) = 81.11 npv=(2,-120,{69,69,69}) = 78.99 a2. Project A b1. npv=(14,-120,{50,70,90}) = 38.47 npv=(14,-120,{69,69,69}) = 40.19 b2. Project B

The decision rule for net present value is to: accept all projects with cash inflows exceeding the initial cost. reject all projects with rates of return exceeding the opportunity cost of capital. accept all projects with positive net present values. reject all projects lasting longer than 10 years.

accept all projects with positive net present values.

If interest is paid m times per year, then the per-period interest rate equals the: effective annual rate divided by m. compound interest rate times m. effective annual rate. annual percentage rate (APR) divided by m.

annual percentage rate (APR) divided by m.

Occasionally projects may have positive initial cash flows. Such projects: are like lending money. are like borrowing money. have no IRR. their IRR increases as the cost of capital increases.

are like borrowing money.

Real interest rates: always exceed inflation rates. can decline to zero but no lower. can be negative, zero, or positive. traditionally exceed nominal rates.

can be negative, zero, or positive.

A project can have as many different internal rates of return as it has: cash inflows. cash outflows. periods of cash flow. changes in the sign of the cash flows.

changes in the sign of the cash flows.

The APR on a loan must be equal to the effective annual rate when: compounding occurs monthly. compounding occurs annually. the loan is for less than one year. the loan is for more than one year.

compounding occurs annually.

Periodic receipts of interest by the bondholder are known as: the coupon rate. principal payments. coupon payments. the default premium.

coupon payments.

The present value of a perpetuity can be determined by:

dividing the payment by the interest rate.

What is the effective annual rate of interest on a deposit that pays interest of 10% continuously compounded?

e^.1 - 1 = 0.10517*100= 10.517%

An interest rate that has been annualized using compound interest is termed the: discount factor. annual percentage rate. discounted interest rate. effective annual interest rate.

effective annual interest rate.

A stock sells for $25. The next dividend will be $3 per share. If the rate of return earned on reinvested funds is a constant 10% and the company reinvests a constant 30% of earnings in the firm, what must be the discount rate?

g = 0.3*0.1 = 0.03 = 3% r=(3/25)+.03 Discount rate = 15%

It is possible to ignore cash dividends that occur very far into the future when using a dividend discount model because those dividends: will most likely be paid to a different investor. will most likely not be paid. have an insignificant present value. have a minimal, if any, potential rate of growth.

have an insignificant present value.

Investors who purchase bonds having lower credit ratings should expect: lower yields to maturity. higher default possibilities. lower coupon payments. higher purchase prices.

higher default possibilities.

Other things being equal, the more frequent the compounding period, the: higher the annual percentage rate. lower the annual percentage rate. higher the effective annual interest rate. lower the effective annual interest rate.

higher the effective annual interest rate.

When projects are mutually exclusive, you should choose the project with the: longer life. larger initial size. highest IRR. highest NPV.

highest NPV.

Many investors may be drawn to municipal bonds because of the bonds': speculative grade ratings. high coupon payments. long periods until maturity. income exemption from federal taxes.

income exemption from federal taxes.

Assume you are making $989 monthly payments on your amortized mortgage. The amount of each payment that is applied to the principal balance: decreases with each succeeding payment. increases with each succeeding payment. is constant throughout the loan term. fluctuates monthly with changes in market interest rates.

increases with each succeeding payment.

Other things equal, a firm's sustainable growth rate could increase as a result of: increasing the plowback ratio. increasing the payout ratio. decreasing the return on equity. increasing total assets.

increasing the plowback ratio.

The sustainable growth rate represents the ________ rate at which a firm can grow: maximum; while maintaining a constant debt-equity ratio. maximum; based solely on internal financing. minimum; while maintaining a constant debt-equity ratio. minimum; based solely on internal financing.

maximum; while maintaining a constant debt-equity ratio.

A project requires an initial outlay of $10 million. If the cost of capital exceeds the project IRR, then the project has a(n): positive NPV. negative NPV. acceptable payback period. positive profitability index.

negative NPV.

When calculating a project's payback period, cash flows are: discounted at the opportunity cost of capital. discounted at the internal rate of return. discounted at the risk-free rate of return. not discounted at all.

not discounted at all.

The concept of compound interest refers to: earning interest on the original investment. payment of interest on previously earned interest. investing for a multiyear period of time. determining the APR of the investment.

payment of interest on previously earned interest.

If the net present value of a project that costs $20,000 is $5,000 when the discount rate is 10%, then the: project's IRR equals 10%. project's rate of return is greater than 10%. net present value of the cash inflows is $4,500. project's cash inflows total $25,000.

project's rate of return is greater than 10%.

What constant-growth rate in dividends is expected for a stock valued at $32.40 if next year's dividend is forecast at $2.20 and the appropriate discount rate is 13.6%? 7.02% 6.59% 6.81% 7.38%

r=(D1/P0)+g g= r-(D1/P0) g=0.136-(2.2/32.4) = 6.81%

As long as the NPV of a project declines smoothly with increases in the discount rate, the project is acceptable if its: internal rate of return is positive. payback period is greater than one. rate of return exceeds the cost of capital. cash inflows equal the initial cost.

rate of return exceeds the cost of capital.

The growth of mature companies is primarily funded by: issuing new shares of stock. issuing new debt securities. reinvesting company earnings. increasing accounts payable.

reinvesting company earnings.

When market interest rates exceed a bond's coupon rate, the bond will: sell for less than par value. sell for more than par value. decrease its coupon rate. increase its coupon rate.

sell for less than par value.

Cash flows occurring in different periods should not be compared unless: interest rates are expected to be stable. the flows occur no more than one year from each other. high rates of interest can be earned on the flows. the flows have been discounted to a common date.

the flows have been discounted to a common date.

An amortizing loan is one in which:

the principal balance is reduced with each payment.

Firms that make investment decisions based on the payback rule may be biased toward rejecting projects: with short lives. with long lives. with late cash inflows. that have negative NPVs.

with long lives.

The discount rate that makes the present value of a bond's payments equal to its price is termed the: dividend yield. yield to maturity. current yield. coupon rate.

yield to maturity.