Problem Set 5 Solutions PDF

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Problem Set 5: Financial Economics Valuation of Stocks November 17, 2017 1. Mexican Motors stock sells for 200 pesos per share, and next year’s dividend is 8.5 pesos. Security analysts are forecasting earnings growth of 7.5% per year for the next five years. (a) Assume that earnings and dividends are expected to grow at 7.5% in perpetuity. What rate of return are investors expecting? D1 , then k must be 11.75%. If P 0 = k−g (b) Mexican Motors has generally earned about 12% on investments (ROI), and paid out 50% of earnings as dividends. Suppose it maintains the same ROI and payout ratio in the long-run future. i. What is the implication for g ? We have g = plowback × ROI = 6% ii. What is the implication for k ? Using the technique in (a) we have k = 10.25% 2. Compost Science Inc. (CSI) is in the business of converting Boston’s sewage sludge into fertilizer. The business in itself is not very profitable. However, to induce CSI to remain in business, the Metropolitan District Commission (MDC) has agreed to pay whatever amount is necessary to yield CSI a 10% book return on investments. At the end of the year CSI is expected to pay $4 in dividends. It has been reinvesting 40% of earnings and growing at 5% a year. (a) Suppose CSI continues on this growth trend. What is the expected long run rate of return from purchasing the stock at $100? D1 , k = 9%. Using P 0 = k−g (b) What part of the $100 price is attributable to the net present value of growth opportunities? The easiest way is to use the formula P 0 = Ek 1 + N P V of investments. You don’t have E1 but you can infer it from D1 using the plowback ratio. You should get E1 = $6.67. Thus, N P V of investments = P 0 − Ek1 = $25.93. 3. The Rusty Clipper Fishing Corporation is expected to pay a cash dividend of $5 per share this year. You estimate that the market capitalization rate for this stock should be 10% this year. If its current price is $25 per share, what can you infer about its expected growth rate of dividends? Using P 0 =

D1 , k−g

you should find that g = −10%. So it’s possible to have negative growth rates.

4. Tabled below are the relevant statistics for three competing firms. Capitalization rate k Return on new investment Retention rate Expected dividend D1

Winkin

Blinkin

Nod

15% 12% 40% $3.00

16% 14% 50% $1.00

18% 20% 60% $2.50

(a) Under the constant dividend growth model, what should be the current price per share for each company’s stock? The first two columns contain detials required for the problem. The other columns contain supplementary information that may be calculated from the given facts. 1

g Winkin Blinkin Nod

4.8% 7% 12%

P0 $3 = 15%−4.8% = $29.41 $1 = $11.11 = 16%−7% $2.5 = 18%−12% = $41.67

NPV of investments

E1

P/E ratio

-$3.92 -$1.39 $6.95

$5 $2 $6.25

5.88 5.56 6.67

(b) Which of these three firms could best be described as a growth firm? What is its growth rate? Only Nod can be described as a growth firm because its ROI is higher than its capitalization rate. This implies that its net present value of investment is positive. Note that the P/E ratio by itself is not a suffiicent indicator of whether a stock can be considered a growth stock, but it can be a good starting point, if the P/E ratio is higher than the average. In this example, the P/E ratios are not too different from each other. 5. Divido Corporation is an all-equity financed firm with a total market value of $100 million. The company holds $10 million in cash equivalents and has $90 million in other assets. There are 1,000,000 shares of Divido common stock outstanding, each with a market price of $100. What would be the impact on Divido’s stock price and on the wealth of its shareholders? Event (a) Of the payment of a cash dividend of $10 per share? (b) If the company repurchases 100,000 shares? (c) If the company paid out a 10% stock dividend? (d) If the company makes a 4 for 1 stock split?

Market value $90M $90M $100M $100M

Outstanding shares 1.0M 0.9M 1.1M 4.0M

Share price $90 $100 $90.90 $25

Under the Modigliani-Miller argument, there can be no effect of any of these transactions on the wealth of a shareholder as long as the financial environment is frictionless. This is because the shareholder can always undo/mimic the effect that he wants in such an environment.

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