Midterm 2Spring 2022Solutions

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School
Wilfrid Laurier University **We aren't endorsed by this school
Course
BUSINESS SALES
Subject
Finance
Date
Oct 28, 2023
Pages
14
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1 Question 1: (10.5 marks) HappyOil Inc. is all-equity financed and will be liquidated after 2 years. It has 1 million shares outstanding, with an equity cost of capital of 20%. Its free cash flows will be $10 million at the end of year 1 and $20 million at the end of year 2. Currently the firm's policy is to pay out all its free cash flows as dividends each year. Assume that the firm operates in a world with perfect capital markets. a. ( 2 marks ) What is the value of HappyOil today? What is its current share price? b. ( 3 marks ) Suppose that Alan owns 1,000 shares of HappyOil Inc. and he desires an income of $15,000 from the firm at the end of year 1. Show how Alan can achieve this wit hout changing the firm's dividend policy. (Assume Alan will buy or sell stocks only at the end of year 1 on the ex-dividend date, i.e., after the dividend is paid). What will his income be at the end of year 2? c. ( 5.5 marks ) Suppose that the firm is considering a change in its dividend policy. The firm plans to repurchase shares (instead of paying a dividend) using all the $10 million free cash flows generated at the end of year 1, and pay a dividend at the end of year 2. (c1). ( 1.5 marks ) If an investor sells some shares to the firm at the end of year 1, how much is he willing to sell a share for? (Hint: get the share price at the end of year 1 immediately before the share repurchase) (c2). ( 2 marks ) If an investor does not sell shares to the firm at the end of year 1, what will be his dividend per share at the end of year 2? (Hint: calculate the number of shares repurchased by the firm at the end of year 1) (c3). ( 1 mark ) Would an investor rather sell some shares to the firm at the end of year 1, or keep all his shares till the end of year 2? (Hint: compare the value per share between the two options). (c4) ( 1 mark ) Would an investor prefer that the firm changes to this new dividend policy (repurchase at the end of year 1 and pay dividend at the end of year 2) or keep the old dividend policy (pay out all cash as dividends each year)? You do not need to show any calculations, just give the intuition. (Hint: perfect capital markets). Solution: This is similar to class slides and problem set 4 (additional 2 and 3) and practice exam. (a) The value of the firm is: 𝑉 0 = $10,000,000 1.20 + $20,000,000 1.20 2 = $22,222,222 The share price is then: 𝑃 0 = $22,222,222 1,000,000 = $22.22
2 (c) (c1) (1.5 marks) Firm value at the end of year 1 (immediately before share repurchase): 𝑉 1 = 10,000,000 + $20,000,000 1.20 = $26,666,667 Share price at the end of year 1 (immediately before share repurchase): 𝑃 1 = $26,666,667 1,000,000 = $26.67 So the investor will be willing to sell the share to the firm at $26.67 per share. (c2) (2 marks) number of shares repurchased = $10,000,000 $26.67 = 375,000 Alternatively, get the dividend per share first: Div1 = $10m/1m = $10 Div2 = $20m/1m = $20 So 𝑃 0 = $10 1.20 + $20 1.20 2 = $22.22 (b) Without changing the firm's dividend policy, since Alan owns 1,000 shares, at the end of year 1 he receives ($10,000,000 / 1 million shares) = $10,000. (Alternatively, Div1*1,000 = $10,000) To change this amount to the desired CF of $15,000, Alan should sell $15,000-$10,000 = $5,000 worth of shares at the end of year 1 at the ex-dividend date (after he got his dividend). The firm value then is: 𝑉 1 = $20,000,000 1.20 = $16,667,667 This implies a share price of: 𝑃 1 = $16,667,667 1,000,000 = $16.67 (or P1 is present value of dividend at year t=2, or $20/1.2 = $16.67) This means that Alan should sell $5,000/$16.67 = 300 shares on the ex-dividend date. He would then receive (1000 - 300 ) * $20 = $14,000 at the end of year 2.
3 Dividend per share at year 2 = $20,000,000 (1,000,000−375,000) = $32 (c3) (1 mark) Compare the present value of a stock at the end of year 1: Sell share: P1 = 26.67$ Keep share: P1 = 32 / 1.2 = 26.67$ ➔ Indifferent between selling or keeping the share. Alternatively, compare the present value of a stock at the beginning of year 1: Sell share: P1 = 26.67 / 1.2 = 22.22$ Keep share: P1 = 32 / 1.2^2 = 22.22$ ➔ Indifferent between selling or keeping the share. It's OK if students calculate the future value at the end of year 2 and argue they are the same. (c4) (1 mark) In perfect capital markets, investors should be indifferent between different payout policies.
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