Stockholm School of Economics in Riga Financial Economics, Spring 2010 Tālis Putniņš

Problem Set IX: Valuing common stocks, and payout policy Exercise 1: Valuing common stocks Computer stocks currently trade at a required return on equity of 16%. Krāslavas Kompji, a large computer company will pay a year-end dividend of $2 per share. a) If the stock is selling at $50 per share, what must be the market’s expectation of the growth rate of dividends? b) If dividend growth forecasts for Krāslavas Kompji are revised downward to 5% per year, what will happen to the price of Krāslavas Kompji stock? What (qualitatively) will happen to the company’s P/E ratio?

Exercise 2: Valuing common stocks You believe that next year Brāļu Corp. will have earnings per share equal to 6 on its common stock. Thereafter you expect earnings to grow at a rate of 8% p.a. in perpetuity. The payout ratio is 1/3. You require a return of 12% on your investment. a) How much should you be prepared to pay for the stock? b) Compute the return on equity (ROE) and present value of growth opportunities (PVGO). c) Assume that ROE has changed to 10%. How much should you be prepared to pay for the stock? Compute PVGO. d) Assume that ROE has changed to 15%. How much should you be prepared to pay for the stock? Compute PVGO.

Exercise 3: Valuing common stocks Čiptek is an established computer chip manufacturer with profitable existing projects and new products in development. The company earned $1 per share last year and just paid a $0.50 dividend. The required return on equity in the computer chip

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manufacturing industry is 15%. Investors believe the company will maintain the payout ratio of 50% and that the ROE of 20% will persist. a) What is the market price of Čiptek stock? b) Suppose you discover that Čiptek’s competitor has developed a new chip that will eliminate Čiptek’s technological advantage. The new product will reduce Čiptek’s ROE in 2 year’s time to 15% and at this time Čiptek will have to reduce its plowback ratio to 40% due to falling demand. What is your estimate of Čiptek’s intrinsic value per share? c) No one in the market will become aware of the change to Čiptek’s competitive status until the end of year 2. What will be rate of return on Čiptek stock in each of the 3 years from now (years 1, 2, and 3)?

Exercise 4: Valuing common stocks Bauskas Corp.’s cash flows from operations before interest and taxes were $2m in the year just ended and management expects that they will grow by 5% per year forever. To make this happen the firm will have to invest 20% of pretax cash flow each year. The tax rate is 35%. Depreciation was $200,000 in the year just ended and is expected to grow at the same rate as operating cash flows. The company’s weighted average cost of capital is 12%, the firm currently has $2m worth of debt outstanding and 1m shares on issue. Use the free cash flow approach to find the intrinsic value of a share.

Exercise 5: Valuing common stocks Lodiņu Corp. currently reinvests all earnings (pays no dividends) and is expected to continue doing so for the next 5 years. Its latest EPS was $10. The firm’s ROE for the next 5 years is 20% per year. In the 6th year from now ROE on new investments is expected to fall to 15% and the company is expected to start paying out 40% of earnings as dividends. The required return on equity is 15%. a) What is Lodiņu Corp.’s intrinsic value per share? b) Assuming the current market price equals intrinsic value what will happen to its stock price over the next year? Next two years? Between years 6 and 7? c) What is the dividend yield expected to be in the 10th year? d) Suppose Lodiņu Corp. only pays out 20% of earnings starting year 6. What effect will this have on your estimate of intrinsic value?

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Exercise 6: Valuing common stocks The market consensus is that Līvu Corp. has ROE = 9%, a beta of 1.25 and plans to indefinitely maintain its plowback ratio of 2/3. This year’s earnings were $3 per share and the annual dividend was just paid. The consensus estimate of the coming year’s market return is 14% and T-bills currently offer a yield of 6%. a) Find the price at which a share in Līvu Corp. should sell. b) Calculate the forward P/E ratio. c) Calculate the present value of growth opportunities. d) Suppose your research convinces you that Līvu Corp. will shortly announce that it will immediately reduce its plowback ratio to 1/3. Find the intrinsic value of the stock. Why is the intrinsic value different from the current market price?

Exercise 7: Valuing common stocks A stock has just paid a dividend of $0.50 per share. The dividend is expected to grow at a rate of 6% p.a. for the next 20 years, after which it will level off. If the discount rate of shares of similar risk is 9% p.a., what is the value of the shares?

Exercise 8: Payout policy Užavas Corp. has 1 million shares outstanding with a total market value of $20 million. The firm is expected to pay $1 million of dividends next year, and thereafter the amount paid is expected to grow by 5% per year in perpetuity. Thus the expected dividend is $1.05 in year 2, $1.105 in year 3 and so on. The company has heard that that the value of a share depends on the flow of dividends, and therefore it announces that next year’s dividend will be increased to $2 million and that the extra cash will be raised by an issue of shares immediately after the stock goes ex-dividend (i.e., the new shares are not entitled to the $2 dividend). After that the total amount paid out each year will be as previously forecast, i.e., $1.05 in year 2, $1.105 in year 3 and so on. a) At what price will the new shares be issued in year 1? b) How many shares will the firm need to issue? c) What will be the expected dividend payments on these new shares, and what, therefore, will be paid out to the old shareholders after year 1? d) Show that the present value of the cash flows to the current shareholders remains $20 million. e) Now assume the new shares are issued in year 1 at $10 a share. Who gains and who loses? Is dividend policy still irrelevant? Why or why not?

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Exercise 9: Payout policy Adherent of the “dividends-are-good” school sometimes point to the fact that stocks with high dividend yields tend to have above-average P/E multiples. Is this evidence convincing? Discuss.

Exercise 10: Payout policy Suppose there are just three types of investors with the following tax rates:

Dividends Capital Gains

Individuals 50% 15%

Corporations 5% 35%

Institutions 0% 0%

Individuals invest a total of $80 billion in stock and corporations invest $10 billion. The remaining stock is held by institutions. All three groups simply seek to maximize their after-tax income. These investors can choose from three types of stock offering the following pretax payouts:

Dividends Capital Gains

Low payout $5 $15

Medium payout $5 $5

High payout $30 $0

These payouts are expected to exist in perpetuity. The low-payout stocks have a total market value of $100 billion; the medium-payout stocks have a value of $50 billion; and the high-payout stocks have a value of $120 billion. a) Who are the marginal investors that determine the prices of the stocks? b) Suppose that this marginal group of investors requires a 12% after-tax return. What are the prices of the low-, medium-, and high-payout stocks? c) Calculate the after-tax returns of the three types of stock for each investor group. d) What are the dollar amounts of the three types of stock held by each investor group?

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Exercise 11: Payout policy Your company has been under pressure from some investors to increase dividends. The following table provides historic information about your company’s dividend policy. Year 2009 2008 2007 2006 2005 2004

EPS $2.05 $1.55 $1.70 $0.90 $0.85 $1.02

Dividends per share $0.30 $0.30 $0.25 $0.25 $0.25 $0.25

Price $20.30 $12.30 $14.20 $9.80 $8.50 $10.20

The average payout ratio in the industry is about 25%. You also notice that on the exdividend date the company’s stock price tends to drop in the range of 60% to 80% of the amount of the dividend. a) Calculate the average dividend payout ratio and dividend yield for the company for the last few years. Does the firm’s dividend policy deviate from the industry average significantly? b) If the tax on capital gains is 15%, what is the range of the marginal investor’s tax rate on dividends? c) How would a pension fund that pays no tax on capital gains and no tax on dividends make profits on the ex-dividend day? Are there any risks involved in your suggested strategy?

Exercise 12: Payout policy A corporation operates two identical projects, each yielding annual cash flows of $50 million. The corporation has 1000 million shares on issue and currently pays all its cash flows out as dividends. If the corporation decides to increase its dividend by 50 cents per share, and the cost of issuing new shares is 0.5%, calculate the impact on shareholder wealth of the corporation’s strategy. Assume a discount rate of 10%.

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Exercise 13: Payout policy Piebalgas Corp. must decide how much to pay out as dividends to its shareholders. It expects to have a net income of $1,000 (after depreciation of $500), and has the following investment opportunities: Project A B C

Initial investment $500 $600 $500

Beta 2.0 1.5 1.0

IRR 22% 20% 12%

The current T-bond rate is 9% and the expected premium on the stock market index is 6%. The firm has revenues of $5,000, which it expects to grow at 8%. Working capital will be maintained at 25% of revenues. How much should the firm return to shareholders as a dividend?

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