Applications of TVM to capital asset pricing

 

  1. A project has the following returns (in $000)

 

Year

Return

0

-100

1

50

2

60

3

20

 

  1. Find the NPV of the project discounted at 10 percent.
  2. Find the IRR.

 

  1. You plan to raise $30 million in capital through a bond issue. 
    1. Find the market price of each of the $100,000, 10%, 20-year bonds, if investors require 11.5% on their investment.
    2. How large a bond issue will be required to raise the $30 million?

 

  1. What is the implied discount rate for 10-year, 8%, $1000 bonds selling for $1080 each?

 

  1. [From Gallagher and Andrew] An investor must decide between developing a mine and planting a vineyard on a parcel of land she owns.  The initial investment in both projects is $736,369.  The annual returns on the investment are given in the table below.

 

Year

Mine

Vineyard

0

-736,369

-736,369

1

500,000

0

2

300,000

0

3

100,000

0

4

20,000

50,000

5

5000

200,000

6

5000

500,000

7

5000

500,000

8

5000

500,000

 

    1. Find the IRR for each project.
    2. Calculate the NPV and return on investment for each project if the discount rate is 10%.
    3. Which project should be undertaken?
    4. Find the discounted rate at which an investor is indifferent between the two projects.

 

  1. Use the discounted dividend method to determine the current price of each of the three stocks given in the table below if the discount rate is 10% for all three.

 

Expected cash flows

Stock 1

Stock 2

Stock 3

Dividend, end of year 1

5

10

1

Dividend, end of year 2

5

4

2

Dividend, end of year 3

5

4

3

Dividend, end of year 4

5

5

4

Price at end of year 4

50

100

10

Current price

 

 

 

 

6.     An investor needs 25 million dollars in new capital next year.  Currently annual sales are ten million dollars and he is sole  owner of ten million shares of the stock, currently valued at five dollars a share.  He can debt finance the $25 million at 12 percent per year or issue stock.  Assuming the price of the stock is unchanged, EBIT is 20 percent of sales and the average tax rate is 30 percent, calculate and graph EPS vs. Sales for the following three sales levels: $10 million, $30 million and $50 million.