Answer the following questions. Show all your work clearly.

1. Calculate the price of following stocks.

(a) [7 points] A stock that just paid its $2 annual dividend. The expected growth rate in dividends is 4%

per year and this trend is expected to continue forever. The appropriate discount rate for this stock is

known to be 10%.

(b) [8 points] A stock that just paid its $2 dividend. The dividend is projected to grow at 15% for two

years (i.e., growth at 15% in years 1 and 2), at 10% for the following one year (i.e., growth at 10% in year 3), and then at 5% for all subsequent years. The appropriate discount rate for this stock is 8%.

2. MC Petroleum, Inc., is trying to evaluate the following two mutually exclusive projects. Whichever project the firm chooses, it requires a 13% return on its investment.

(a) [5 points] If you rely on the payback period method, which investment will you choose? Support your answer with relevant calculations.

(b) [5 points] If you use the NPV rule, which investment will you choose? Support your answer with relevant calculations.

(c) [5 points] Calculate IRRs of Projects A and B. Explain what specific problems the firm would have if the firm uses the IRR rule to choose between these two mutually exclusive investments.

(d) [5 points] Over what range of discount rates would Project A have higher NPV than Project B? Explain your answers.

3. ABC Company is considering a new line of business. The basic information on the project is as follows.

- Unit price of products starts at $100 and will drop to $90 after 2 years because of expected competition.

- Projected unit sales are 6,000 for the first 2 years and 5,000 for the next 2 years (4-year project)

- The project requires $30,000 as net working capital in the beginning (year 0) and subsequently 10% of sales

from year 1 to year 3. The working capital will be fully recovered at the end of year 4.

- Variable costs: $50 per unit.

- Fixed costs: $40,000 per year.

- Initial costs: $400,000 to buy the equipment necessary and no salvage value expected after the project. - Depreciation: straight-line depreciation to zero by the end of the project.

- Consulting fees of $50,000 already paid last year.

- Tax rate: 20%

- Required return for the firm's existing lines of business: 11%

- Required return for this new line of business: 13%

(a) [8 points] Provide the pro forma income statement of this project and calculate projected operating cash flows each year for 4 years.

(b) [8 points] Estimate project cash flows (i.e., CFFA) each year.

(c) [4 points] Compute the net present value of this project. Should the firm accept this project?

Year

Cash Flow (A)

Cash Flow (B)

0

-500,000

-50,000

1

80,000

4,000

2

100,000

30,000

3

250,000

20,000

4

380,000

30,000

4. [15 points] You are given the choice between two copy machines, both of which will produce similar quality copies. Machine A is cheaper to purchase, but it is more expensive to operate and will last only for 4 years, while machine B will last for 6 years. The relevant data is reported below and the discount rate is 8%. You are planning on having a copy machine forever, so you intend to replace machines as they wear out for the foreseeable future. What machine should you choose?

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6

Machine A

Initial cost = 40,000

Operating cost = 8,000 Operating cost = 8,000 Operating cost = 8,000 Operating cost = 8,000 + replace

Machine B

Initial cost =60,000

Operating cost = 5,000 Operating cost = 5,000 Operating cost = 5,000 Operating cost = 5,000 Operating cost = 5,000 Operating cost = 5,000 + replace

5. Consider a project with the following data: Initial investment to purchase the equipment for the project = $400,000, selling price per unit = $10,000, variable costs per unit = 6,000 units, fixed costs per year = $140,000, life = 5 years, required return = 12%. The equipment will be depreciated to zero using the straight-line approach. Assume that there is no net working capital change during the life of the project and no salvage value after the project is completed. There are no taxes.

(a) [5 points] Find the accounting break-even quantity. (b) [5 points] Find the cash break-even quantity.

(c) [5 points] Find the financial break-even quantity.

6. Use the following information to answer the questions below. We also know that the market risk premium is 10% and the risk free rate is 3%.

(a) [5 points] Which stock is riskier in terms of total risk of returns? Support your answer by relevant calculations.

(b) [5 points] Which stock is riskier in terms of systematic risk of returns? Support your answer by relevant calculations. Assume that both stocks are on the security market line.

(c) [5 points] If you already have a fully-diversified portfolio, according to the systematic risk principle,

which stock would be a better addition for you to decrease total risk in your portfolio? Explain your answer.

State of economy

Probability of state

Stock A return

Stock B return

Boom

30%

24%

20%

Normal

40%

12%

18%

Recession

30%

4%

-10%