Introduction to Finance - Busfin 1030 - Problem Set 3

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- VAR(RP) = 0.52 × 0.0188562 + 0.52 × 0.197992 + 2 × 0.5 × 0.5 × –0.0037333 =

–0.008022

SD(RP) = 8.957%

- E(RP|Boom) = 0.5 × 0.10 + 0.5 × -0.02 = 0.04 (4%)

E(RP|Recession) = 0.5 × 0.06 + 0.5 × 0.40 = 0.23 (23%)

Hence, E(RP) = 2/3 × 0.04 + 1/3 × 0.23 = 0.10335 (10.335%)

And, SD(RP) = [2/3 × (0.04-0.10335)2 + 1/3 × (0.23-0.10335)2]0.5 = 0.08957 (8.957%)

Problem 3:

You are thinking about a portfolio where you put half your money in stock A (see problem 2) and half your money in the risk free asset (like a Treasury bill). The risk free asset has a return of 5%.

- What is the variance and standard deviation of the risk free asset?

- What is the covariance between stock A and the risk free asset?

- What is the expected return on your portfolio?

- What is the variance on your portfolio?

- What is the standard deviation on your portfolio?

ANSWER

- By definition they are both zero (0).

- Again, by definition the answer is zero (0)

- Portfolio weights: WA=0.5 and WF=0.5:

E(RP) = 0.5 × 0.0867 + 0.5 × 0.05 = 0.06835 (6.835%)

- VAR(RP) = 0.52 × 0.0188562 = 0.0000889

- SD(RP) = 0.00008890.5 = 0.009428 (0.9428%)

Problem 4:

Frozen Fruitcakes International Inc. is considering the following project. They want to introduce a new line of pastries and desserts. The sales for this division are expected to be $500,000 per year for each of the next 3 years. For this expansion you are able to use some of your existing machines that are currently not being used. Four years ago you paid $250,000 for these machines and the current market value of the machines is $110,000. You have been using a 5-year straight-line full depreciation on these machines. There is no need to buy any additional equipment. Variable costs for the division are projected at 65% of sales. Fixed costs are 100,000 per year. Total net working capital requirements are $75,000 at the start, $100,000 in year 1, and $50,000 in year 2. Net working capital will be recovered at the end of three years. The tax rate is 34%.

- What is the cash flow from assets for this project in each year?

- What is the NPV of this project if the discount rate is 10%?

- If Frozen Fruitcakes International Inc. is expected to pay a dividend of $1.45 next time, and the dividends are expected to grow at 4.5% forever, what is the cost of equity (or required rate of return on equity) for Frozen Fruitcakes International Inc. if the current stock price is $29. (Hint: you do not need any information from part a. or the previous page for answering this question).

- If Frozen Fruitcakes International Inc. has 10% debt in its capital structure, with a YTM of 6%, what is the weighed cost of capital, RWACC, for Frozen Fruitcakes International Inc.?

- What is the NPV of the new project if it has the same risk as Frozen Fruitcakes International Inc. as a whole? (Use the information in c. and d.)

- Assuming the dividend-growth model you used in part c. is correct, and the return on the market portfolio is 13% and the risk-free rate of return is 2%, what must be the beta of this project? (Hint: use the CAPM or SML)

ANSWER

- Cash Flow = Operating Cash Flow - Net Capital Spending - Additions to Net Working Capital

Operating Cash Flows for each year are EBIT+ Depreciation - Tax. Given that the firm does not purchase any new equipment, there are no incremental depreciation expenses from operating activities:

EBIT = $500,000 - 325,000 - 100,000 = $75,000

Tax = 0.34 × 80,000 = $25,500

Operating Cash Flow = $75,000 - 25,500 = $49,500 per year.

Opportunity Cost (in place of Net Capital Spending) = $110,000 - tax

Tax = 0.34 × Profit, where Profit = Market Value - Book Value.

Book Value = $250,000 - 4 × 50,000 (Depreciation per year) = $50,000

Profit = $110,000 - 50,000 = $60,000 and Tax = 0.34 × $60,000 = $20,400

Opportunity Cost = $110,000 - 20,400 = $89,600

Cash Flows:

Year

OCF

NCS*)

Additions NWC

Cash Flow

0

-

-89,600

-75,000

-164,600

1

49,500

-

-25,000

24,500

2

49,500

-

+50,000

99,500

3

49,500

-

+50,000**)

99,500

*) Opportunity Cost

**) Recovery of NWC

- NPV = -164,600 + 24,500 / (1.1) + 99,500 / (1.1)2 + 99,500 / (1.1)3 = $14,659.96

- P0 = D1 / (RE - g), hence we have RE = D1/P0

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