Coursera Wharton Foundation Series

Introduction to Corporate Finance – Professor Franklin Allen

Final Exam

1. Please use the information below to answer questions 1 through 4. There are two periods of

time, t0 and t1. Michael has a wealth of $100 million. Michael has three potential investment

opportunities. The first investment opportunity is building a shopping center; the cost is $60

million at t0 and pays off $72 million at t1. The second investment opportunity is building a

parking garage, which would cost $40 million at t0 and pays off $55 million at t1. The third

project is building a club for $5 million at t0 which pays off $15 million at t1. The local bank lets

Michael lend and borrow at the same rate, which is 15% per period. Michael does not value

future consumption, and instead only cares about consumption today at t0. He does not value

consumption at t1 at all. Please give your answers in $ millions, to two decimal places. For

example, if the answer is $53.247 million, please input 53.25.

What is the NPV of the project which has the highest NPV?

2. What is the most that Michael can consume at t0?

3. Suppose the three projects were mutually exclusive. What is the most Michael can consume at

t0?

4. The bank has now decided to charge Michael 20% when he wants to borrow, but he can only

lend to the bank at 10%. What is the most that Michael can consume at t0, given this new

condition? Do not assume for Question 4 that the projects are mutually exclusive.

5. Please use the information below to answer questions 5 through 8. Rahul is considering three

projects which have the following cash flows.

C0 C1 C2 C3

A -5000 2500 1500 2100

B -700 450 300 400

C -400 100 150 200

What is the IRR of project A?

6. What is the IRR of project B?

7. If the discount rate is 6%, would Rahul choose to do project C?

8. Suppose all three projects are mutually exclusive. What is the highest opportunity cost of

capital for which Rahul would choose project A?

9. Please use the information below to answer questions 9 through 16. Michelle is a manager at

the Industrial Production Company. She is evaluating a project to build a factory that makes

refrigerators. Today is date 0. The cost of the plant today is $12 million. Five years ago, the

firm spent $3 million (in real terms) on a feasibility study. She expects the plant to produce

furniture for the next 6 years, at which time she expects the salvage value of the factory to be

$3 million (nominal). Every year the factory operates, analysts predict that they will be able to

produce and sell 2,000 refrigerators. The price of the refrigerators is $4,000 each at date 0, and

this price is expected to remain constant in real terms throughout the lifetime of the factory.

The materials needed to build each refrigerator costs $1,200 in real terms and remains constant

over the life of the project. The total annual labor cost is currently (as of date 0) expected to be

$1,000,000 per year, and due to rising wage pressure, the labor cost is expected to grow at 2%

per year in real terms throughout the lifetime of the factory. The land that the factory will be

built on belongs to the company, and they could instead rent it out for $400,000 per year in real

terms. Michelle estimates that for this type of project, the firm’s cost of capital is 10% per year

in nominal terms. Economists forecast the inflation to be 3% per year over the next ten years.

The firm faces a 35% corporate tax rate. For tax purposes, depreciation is nominal and the firm

uses straight-line depreciation. Michelle recognizes that the firm has profitable ongoing

operations to offset losses for tax purposes. All cash flows occur at the end of the year, unless

otherwise noted.

What is the market price of a refrigerator in the 6th year in nominal terms?

10. What is the total amount of labor cost in the 6th year in nominal terms? Please give answer in

$ thousands.

11. What is the amount of the depreciation tax shield per year? Recall that the tax code is written

in nominal terms. Please give answer in $ thousands.

12. What is the total sales revenue (sales price X quantity sold – materials costs X quantity sold –

labor costs) in the 6th year in nominal terms? Please give answer in $ thousands.

13. What is the total cash flow in the 6th year in nominal terms? Please give answer in $ thousands.

14. What is the 6 year nominal discount factor?

15. What is the NPV of the project? Please give answer in $ thousands.

16. What is the IRR of the project?

17. Please use the information below to answer questions 17 through 19. Jonathan is allocating his

portfolio between two risky stocks, A and B. Stock A has an expected return of 15% with a

standard deviation of 30%. The expected return and standard deviation for Stock B are 10% and

12%, respectively. The two stocks are positively correlated, with a correlation coefficient of +0.4.

Jonathan’s wealth advisor suggests allocating 30% of his wealth in A and 70% of his wealth in B.

What is the expected return of Jonathan’s portfolio, if he listens to his wealth advisor?

18. What is the standard deviation of Jonathan’s portfolio, if he listens to his wealth advisor?

19. What is the standard deviation of Jonathan’s portfolio, if he instead invests 50% of his wealth in

Stock A, and puts the rest in a risk-free asset which has a return of 3%?

20. Mary lives in a country whose financial markets satisfy the assumptions of the Capital Asset

Pricing Model (CAPM). In this economy, there are two risky assets, Spruce Company and Walnut

Corporation, along with a risk-free asset. Mary has invested 30% of her portfolio in the risk-free

asset, 40% in Spruce, and the remaining 30% in Walnut. In the entire economy, the total

valuation of the Spruce Company is $4 million dollars.

What is the total valuation of the Walnut Corporation, in millions of dollars?

21. Please use the information below to answer questions 21 and 22. Let’s assume that the CAPM

assumptions are all satisfied. Research analysts at your securities firm have identified four well-

diversified investment funds that have no unique risk. The characteristics of the funds are as

follows:

Fund Name Expected Return Beta

Alpha 34% 1.2

Beta 40% 1.5

Gamma 48% 1.7

Delta 58% 2.4

Three of the funds are correctly priced, and one of the funds is mispriced. Please identify the

investment fund that is being mispriced by the market.

22. Is the expected return of the mispriced fund too high, too low, or exactly right, given its beta?