2024 – 1 Compute the present value of a 130 cash flow for the following combinations of discount rates

1.     Compute the present value of a $130 cash flow for the following combinations of discount rates and times:(Do not round intermediate calculations. Round your answers to 2 decimal places.)

    Present Value

  a. r = 8%, t = 10 years

  b. r = 8%, t = 20 years

  c. r = 4%, t = 10 years

  d. r = 4%, t = 20 years

2.     Compute the future value of a $220 cash flow for the same combinations of rates and times: (Do not round intermediate calculations. Round your answers to 2 decimal places.)

     Future Value

  a. r = 8%, t = 10 years

  b. r = 8%, t = 20 years

  c. r = 4%, t = 10 years

  d. r = 4%, t = 20 years

3.     In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1999 the granddaughters of two of the trackers claimed that this reward had not been paid. The prime minister stated that if this was true, the government would be happy to pay the $100. However, the granddaughters also claimed that they were entitled to compound interest.

a.

How much was each entitled to if the interest rate was 3%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b.

How much was each entitled to if the interest rate was 6%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

4.     Investments in the stock market have increased at an average compound rate of about 5% since 1902. It is now 2012.

a.

If you invested $1,000 in the stock market in 1902, how much would that investment be worth today?(Do not round intermediate calculations. Round your answer to 2 decimal places.) 

b.

If your investment in 1902 has grown to $1 million, how much did you invest in 1902? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

5.     In mid-2010 a pound of apples cost $1.16, while oranges cost $1.00. Ten years earlier the price of apples was only $.87 a pound and that of oranges was $.65 a pound.

a.

What was the annual compound rate of growth in the price of the two fruits? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

b.

If the same rates of growth persist in the future, what will be the price of apples in 2030? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c.

What about the price of oranges? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

6.     a.

If you take out an $8,200 car loan that calls for 60 monthly payments starting after 1 month at an APR of 12%, what is your monthly payment? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b.

What is the effective annual interest rate on the loan? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

7.     You can buy property today for $2 million and sell it in 4 years for $3 million. (You earn no rental income on the property.)

a.

If the interest rate is 6%, what is the present value of the sales price? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.)

b.

Is the property investment attractive to you?

c-1.

What is the present value of the sales price, if you also could earn $100,000 per year rent on the property? (Do not round intermediate calculations. Enter your answer in millions rounded to 3 decimal places.)

c-2.

Is the property investment attractive to you?

8.     A factory costs $430,000. You forecast that it will produce cash inflows of $135,000 in year 1, $195,000 in year 2, and $330,000 in year 3. The discount rate is 12%.

a.

Calculate the PV of cash inflows. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

9.     If the interest rate this year is 7.2% and the interest rate next year will be 9.2%, what is the future value of $1 after 2 years? What is the present value of a payment of $1 to be received in 2 years? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

  Future value

$   

  Present value

$  

11.  A bond has 12 years until maturity, a coupon rate of 7.4%, and sells for $1,107.

a.

What is the current yield on the bond? (Round your answer to 2 decimal places.)

  Current yield

  %  

b.

What is the yield to maturity? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Yield to maturity

 %  

12.  General Matter’s outstanding bond issue has a coupon rate of 9.8%, and it sells at a yield to maturity of 8.20%. The firm wishes to issue additional bonds to the public at face value. What coupon rate must the new bonds offer in order to sell at face value? (Round your answer to 2 decimal places.)

  Coupon rate

  %  

13.  Refer the table below:

Maturity

Coupon

Bid Price

Asked Price

Asked Yield, %

2012 May 15

1.375       

101:05       

101:06       

0.78

2013 May 15

3.625       

106:31       

107:01       

1.23

2014 May 15

4.75       

111:22       

111:23       

1.70

2020 May 15

8.75       

144:17       

144:19       

3.44

2025 Aug 15

6.875       

133:07       

133:11       

3.94

2030 May 15

6.25       

128:25       

128:27       

4.12

2040 May 15

4.375       

100:28       

100:29       

4.32

What is the current yield of the 6.875% 2025 maturity bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Current yield

  %  

14.  One bond has a coupon rate of 7%, another coupon rate of 9%. Both bonds have 5-year maturities and sell at a yield to maturity of 8%.

a.

If their yields to maturity next year are still 8%, what is the rate of return on each bond? (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Rate of Return   

  Bond 1

 %

  Bond 2

 %

b.

Does the higher coupon bond give a higher rate of return?

15.  Sure Tea Co. has issued 6.3% annual coupon bonds that are now selling at a yield to maturity of 9.2% and current yield of 8.7770%. What is the remaining maturity of these bonds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Remaining period

 years  

16.  Consider three bonds with 6.0% coupon rates, all selling at face value. The short-term bond has a maturity of 4 years, the intermediate-term bond has maturity 8 years, and the long-term bond has maturity 30 years.

a.

What will be the price of each bond if their yields increase to 7.0%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

4 Years

8 Years

30 Years

  Bond price

$ 

$ 

$ 

b.

What will be the price of each bond if their yields decrease to 5.0%? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

4 Years

8 Years

30 Years

  Bond price

$ 

$ 

$ 

17.  A 2-year maturity bond with face value of $1,000 makes annual coupon payments of $102 and is selling at face value. What will be the rate of return on the bond if its yield to maturity at the end of the year is (Do not round intermediate calculations. Round your answers to 2 decimal places.)

   Rate of Return

a.

6%

%        

b.

10.2%

%        

c.

12.2%

%        

18.  A bond’s credit rating provides a guide to its risk. Long-term bonds rated Aa currently offer yields to maturity of 7.6%. A-rated bonds sell at yields of 7.9%. Assume a 10-year bond with a coupon rate of 7.1% is downgraded by Moody’s from Aa to A rating.

a.

Calculate the initial price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Initial price

$ 

b.

Calculate the new price. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  New price

$   

19.  Favored stock will pay a dividend this year of $2.16 per share. Its dividend yield is 9%. At what price is the stock selling? (Do not round intermediate calculations.)

  Current price

$    

20.  Preferred Products has issued preferred stock with an $7.32 annual dividend that will be paid in perpetuity.

a.

If the discount rate is 12%, at what price should the preferred sell?

  Current price

$    

b.

At what price should the stock sell 1 year from now?

  Future price

$   

c.

What is the dividend yield, the capital gains yield, and the expected rate of return of the stock? (Leave no cells blank – be certain to enter “0” wherever required.)

  Dividend yield

 %  

  Capital gains yield

 %  

  Expected rate of return

  %  

21.  Waterworks has a dividend yield of 10.50%. If its dividend is expected to grow at a constant rate of 7.50%, what must be the expected rate of return on the company’s stock? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Expected rate of return

 %  

22.  Steady As She Goes, Inc., will pay a year-end dividend of $3.20 per share. Investors expect the dividend to grow at a rate of 6% indefinitely.

a.

If the stock currently sells for $32 per share, what is the expected rate of return on the stock? (Do not round intermediate calculations.)

  Expected rate of return

  %  

b.

If the expected rate of return on the stock is 18.5%, what is the stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Stock price

$   

23.  Integrated Potato Chips paid a $2.00 per share dividend yesterday. You expect the dividend to grow steadily at a rate of 5% per year.

a.

What is the expected dividend in each of the next 3 years? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected Dividend

  Year 1

$ 

  Year 2

  Year 3

b.

If the discount rate for the stock is 11%, at what price will the stock sell? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Current price

$   

c.

What is the expected stock price 3 years from now? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Future price

$   

d.

If you buy the stock and plan to hold it for 3 years, what payments will you receive? What is the present value of those payments? (Leave no cells blank – be certain to enter “0” wherever required. Do not round intermediate calculations. Round your answers to 2 decimal places.)

    Year 1

    Year 2

    Year 3

  DIV

$ 

$   

$ 

  Selling price

  Total cash flow

  PV of cash flow

24.  Arts and Crafts, Inc., will pay a dividend of $2 per share in 1 year. It sells at $40 a share and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company’s dividends? (Do not round intermediate calculations.)

  Expected growth rate

 %  

25.  Horse and Buggy Inc. is in a declining industry. Sales, earnings, and dividends are all shrinking at a rate of 6% per year.

a.

If r = 10% and DIV₁ = $4, what is the value of a share? (Do not round intermediate calculations.)

  Value of a share

$    

b.

What price do you forecast for the stock next year? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Stock price

$    

c.

What is the expected rate of return on the stock? (Do not round intermediate calculations.)

  Expected rate of return

  %  

26.  You expect a share of stock to pay dividends of $1.10, $1.35, and $2.00 in each of the next 3 years. You believe the stock will sell for $10 at the end of the third year.

a.

What is the stock price if the discount rate for the stock is 10%? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Stock price

$    

b.

What is the dividend yield? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Dividend yield

  %  

27.  No-Growth Industries pays out all of its earnings as dividends. It will pay its next $4 per share dividend in a year. The discount rate is 21%.

a.

What is the price-earnings ratio of the company? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  P/E ratio

b.

What would the P/E ratio be if the discount rate were 5%? (Round your answer to 2 decimal places.)

  P/E ratio

28.  Assume that market and book values are equal for current assets, current liabilities, and debt and other long-term liabilities.

SIMPLIFIED BALANCE SHEET OF GOOD FORTUNES, INC. FOR MAY 31, 2010
(Millions of dollars)

  Current assets

$

7,288

  Current liabilities

$

4,649  

  Plant, equipment and other long-term assets

17,626

  Debt and other long-term liabilities

6,450  

  Shareholders’ equity

13,815  

   Total assets

$

24,914

   Total liabilities and equity

$

24,914  

Note: Shares of stock outstanding: 318 million. Book value of equity (per share): 13,815/318 = $43.44. The stock price is $75.70.

a.

Construct a market-value balance sheet from the above data. (Be sure to list the assets and liabilities in order of their liquidity. Enter your answers in millions rounded to 2 decimal places.)

SIMPLIFIED BALANCE SHEET OF GOOD FORTUNES, INC. FOR MAY 31, 2010
(Millions of dollars)

  Total liabilities and equity

b.

How much extra value shows up on the asset side of the balance sheet? (Enter your answer in millions rounded to 2 decimal places.)

  Extra value on the asset side

$ million  

29.  Grandiose Growth has a dividend growth rate of 10%. The discount rate is 9%. The end-of-year dividend will be $2 per share.

a.

What is the present value of the dividend to be paid in year 1? Year 2? Year 3? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

              Present Value

  Year 1

$ 

  Year 2

  Year 3

30.  Computer Corp. reinvests 70% of its earnings in the firm. The stock sells for $50, and the next dividend will be $2.50 per share. The discount rate is 15%. What is the rate of return on the company’s reinvested funds? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

  Rate of return

%