Problems

1. Vernon Enterprises has current after-tax operating income of $ 100 million and a cost of capital of 10%. The firm earns a return on capital equal to its cost of capital.

a. If we assume that the firm is in stable growth, growing 5% a year forever, estimate the firm's reinvestment rate.

b. Given this reinvestment rate, estimate the value of the firm.

c. What is the value of the firm, if you assume a zero reinvestment rate and no growth?

2. Assume, in the previous example with Vernon Enterprises, that the firm will earn a return on capital of 15% in perpetuity.

a. If we assume that the firm is in stable growth, growing 5% a year forever, estimate the firm's reinvestment rate.

b. Given this reinvestment rate, estimate the value of the firm.

3. Cello Inc. is a manufacturer of pianos. It earned an after-tax return on capital of 10% last year and expects to maintain this next year. If the current years after-tax operating income is $ 100 million and the firm reinvests 50% of this income back, estimate the free cash flow to the firm next year.(After-tax Operating Income = EBIT (1-t)]

4. Cell Phone Inc. is a cellular firm that reported net income of $50 million in the most recent financial year. The firm had $ 1 billion in debt, on which it reported interest expenses of $ 100 million in the most recent financial year. The firm had depreciation of $ 100 million for the year, and capital expenditures were 200% of depreciation. The firm has a cost of capital of 11%. Assuming that there is no working capital requirement, and a constant growth rate of 4% in perpetuity, estimate the value of the firm.

5. Netsoft is a company that manufactures networking software. In the current year, the firm reported operating earnings before interest and taxes of $ 200 million (Operating earnings does not include interest income), and these earnings are expected to grow 4% a year in perpetuity. In addition, the firm has a cash balance of $ 250 million on which it earned interest income of $ 20 million. The unlevered beta for other networking software firm is 1.20, and these firms, have, on average, cash balances of 10% of firm value. If Netsoft has a debt ratio of 15%, a tax rate of 40%, a return on capital of 10% on operating assets, and a cost of debt of 10%, estimate the value of the firm. [The riskfree rate is 6% and you can assume a market risk premium of 5.5%.]

6. Gemco Jewellers earned $ 5 million in after-tax operating income in the most recent year. The firm also had capital expenditures of $ 4 million and depreciation of $ 2 million during the year, and the non-cash working capital at the end of the year was $ 10 million.

a. Assuming that the firm's operating income will grow 20% next year, and that all other items (capital expenditures, depreciation and non-cash working capital) will grow at the same rate, estimate the free cash flow to the firm next year.

b. If the firm can grow at 20% for the next 5 years, estimate the present value of the free cash flows to the firm over that period. You can assume a cost of capital of 12%.

c. After year 5, the firm's capital expenditures will decline to 125% of revenues, and the growth rate will drop to 5% (in both operating income and non-cash working capital). In addition, the cost of capital will decline to 10%. Estimate the terminal value of the firm at the end of year 5.

d. Estimate the total value of the operating assets of the firm.

7. Now assume that Gemco Jewellers has $ 10 million in cash and non-operating assets and that the firm has $ 15 million in outstanding debt.

a. Estimate the value of equity in the firm.

b. If the firm has 5 million shares outstanding, estimate the value of equity per share.

c. How would your answer to (b) change if you learn that the firm has 1 million options oustanding, with an exercise price of $ 5 and 5 years to maturity. (The estimated value per option is $ 7)

8. Union Pacific Railroad reported net income of $770 million in 1993, after interest expenses of $320 million. (The corporate tax rate was 36%). It reported depreciation of $960 million in that year, and capital spending was $1.2 billion. The firm also had $4 billion in debt outstanding on the books, rated AA (carrying a yield to maturity of 8%), trading at par (up from $3.8 billion at the end of 1992). The beta of the stock is 1.05, and there were 200 million shares outstanding (trading at $60 per share), with a book value of $ 5 billion. Union Pacific paid 40% of its earnings as dividends and working capital requirements are negligible. (The treasury bond rate is 7%.)

a. Estimate the free cash flow to the firm in 1993.

b. Estimate the value of the firm at the end of 1993.

c. Estimate the value of equity at the end of 1993, and the value per share

9. Lockheed Corporation, one of the largest defense contractors in the US, reported EBITDA of $1290 million in 1993, prior to interest expenses of $215 million and depreciation charges of $400 million. Capital Expenditures in 1993 amounted to $450 million, and working capital was 7% of revenues (which were $13,500 million). The firm had debt outstanding of $3.068 billion (in book value terms), trading at a market value of $3.2 billion, and yielding a pre-tax interest rate of 8%. There were 62 million shares outstanding, trading at $64 per share, and the most recent beta is 1.10. The tax rate for the firm is 40%. (The treasury bond rate is 7%)

The firm expects revenues, earnings, capital expenditures and depreciation to grow at 9.5% a year from 1994 to 1998, after which the growth rate is expected to drop to 4%. (Capital spending will offset depreciation in the steady state period.) The company also plans to lower its debt/equity ratio to 50% for the steady state (which will result in the pre-tax interest rate dropping to 7.5%).

a. Estimate the value of the firm.

b. Estimate the value of the equity in the firm, and the value per share.

10. In the face of disappointing earnings results and increasingly assertive institutional stockholders, Eastman Kodak was considering the sale of its health division, which earned $560 million in earnings before interest and taxes in 1993, on revenues of $5.285 billion. The expected growth in earnings was expected to moderate to 6% between 1994 and 1998, and to 4% after that. Capital expenditures in the health division amounted to $420 million in 1993, while depreciation was $350 million. Both are expected to grow 4% a year in the long term. Working capital requirements are negligible.

The average beta of firms competing with Eastman Kodak's health division is 1.15. While Eastman Kodak has a debt ratio (D/(D+E)) of 50%, the health division can sustain a debt ratio (D/(D+E)) of only 20%, which is similar to the average debt ratio of firms competing in the health sector. At this level of debt, the health division can expect to pay 7.5% on its debt, before taxes. (The tax rate is 40%, and the treasury bond rate is 7%.)

a. Estimate the cost of capital for the division.

b. Estimate the value of the division.

11. You have been asked to value Alcoa and have come up with the following inputs.

• The stock has a beta of 0.90, estimated over the last 5 years. During this period, the firm had an average debt/equity ratio of 20% and an average cash balance of 15%.

• The firm's current market value of equity is 1.6 billion and its current market value of debt is $800 million. The current cash balance is $ 500 million.

• The firm earned earnings before interest and taxes of $ 450 million, which includes the interest income on the current cash balance of $ 50 million. The firm's tax rate is 40%.

• The firm is in stable growth, and its earnings from operations are expected to grow 5% a year. The net capital expenditures next year are expected to be $ 90 million.

Estimate the value of the non-cash assets of the firm, its total value, and the value of its equity.

12. You are analyzing a valuation done on a stable firm by a well-known analyst. Based upon the expected free cash flow to firm, next year, of $30 million, and an expected growth rate of 5%, the analyst has estimated a value of $750 million. However, he has made the mistake of using the book values of debt and equity in his calculation. While you do not know the book value weights he used, you know that the firm has a cost of equity of 12%, and an after-tax cost of debt of 6%. You also know that the market value of equity is three times the book value of equity, while the market value of debt is equal to the book value of debt. Estimate the correct value for the firm.

13. You have been asked to value Office Help Inc., a private firm providing office support services in the New York area.

• The firm reported pre-tax operating income of $ 10 million in its most recent financial year on revenues of $ 100 million. In the most recent financial year, you note that the owners of the business did not pay themselves a salary. You believe that a fair salary for their services would be $ 1.5 million a year.

• The cost of capital for comparable firms that are publicly traded is 9%. (You can assume that this firm will have similar leverage and cost of capital).

• The firm is in stable growth and expects to grow 5% a year in perpetuity. The tax rate is 40%.

While the average illiquidity discount applied to private firms is 30%, you have run a regression and arrived at the following estimate for the discount:

Illiquidity Discount = 0.30 - 0.04 (ln (Revenues in millions)) Estimate the value of Office Help for sale in a private transaction (to an individual).

14. National City Corporation, a bank holding company, reported earnings per share of $2.40 in 1993, and paid dividends per share of $1.06. The earnings had grown 7.5% a year over the prior five years, and were expected to grow 6% a year in the long term (starting in 1994). The stock had a beta of 1.05 and traded for ten times earnings. The treasury bond rate was 7%.

a. Estimate the P/E Ratio for National City Corporation.

b. What long term growth rate is implied in the firm's current PE ratio?

15. The following were the P/E ratios of firms in the aerospace/defense industry at the end of December, 1998, with additional data on expected growth and risk:

Company

P/E Ratio

Expected Growth

Beta

Payout

Boeing

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