Capital Budgeting and Other Topics: Problem Set

(Due before section, Monday, October 28)

B.A. 130


1. "If the efficient market hypothesis is true, then a portfolio manager might just as well select his or her portfolio by throwing darts at an open Wall Street Journal." Is this statement correct? Why or why not?

2. Suppose a company announces that it is going to split its stock two for one. Would you expect its stock to rise? Why or why not?

3. Consider an asset with the following cash flows:

   Year Zero Year One Year Two Year Three
 Cash Flows: -$60 +$26 +$24 +$22

The discount rate is 10% per year. Suppose that the firm uses straight-line book-value depreciation. Calculate the book rate of return in each year. Calculate economic depreciation. Calculate the true profitability of the asset. Account for any difference between book returns and economic profitability.

4. What is "economic depreciation"? Why would accountants do a better job if they used depreciation schedules that matched expected economic depreciation?

5. For what kinds of capital investment projects are Monte Carlo analyses most useful?

6. For what kinds of capital investment projects are decision tree analyses most useful?

7. Suppose that the Amalgamated Chemical Company is engaged in a highly competitive segment of the world chemical industry--a segment so risky that the required rate of return is 20% per year. Suppose that the accounting information for a standard plant with a three-year life built by Amalgamated Chemical (or one of its competitors) is as below (with all numbers in millions):

 Year

Zero

One

Two

Three

 Initial Investment -$100      
Revenues   $100 $100 $100
Operating Costs   -$50 -$50 -$50
Salvage Value       +$25
Depreciation   -$33.33 -$33.33 -$33.33
Pretax Income   $16.67 $16.67 $41.67
Tax at 40%   $6.67 $6.67 $16.67
Net After-Tax Income   $10 $10 $25
         
Cash Flow -$100 +$43.33 +$43.33 +$58.33
         

a. Calculate the net present value of investing in a plant.
b. Calculate the value of a one year old plant and of a two year old plant.
c. Suppose that technological breakthroughs create a new kind of plant--this new improved technology requires only half as large an initial investment (and half as large a salvage value), and produces the same output with only half the operating cost. This new technology is freely available to every firm producing in this competitive industry. What do you expect the annual revenues from operating a plant--either a new technology plant, or an old technology plant--to be after this technological breakthrough?
d. What is the net present value of investing in a new technology plant? In an old technology plant after the technological breakthrough?
e. Calculate the post-breakthrough value of a one year old old-technology plant and of a two year old old-technology plant.
f. Suppose that you could scrap a two year old plant and receive $25 million in salvage value (as opposed to waiting a year, producing in year three, and then scrapping the plant for $12.5 million in salvage value). Which is the best alternative?