Examiners' commentaries 2011

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92 Corporate finance 10 Approaching the question Part A Suppose Green Papaya’s dividend grows at 5% p.a. in the foreseeable future before the takeover. Share price, S = $0.8(1.05)/0.1 – 0.05 = $16.80 Value, V = $16.80 2,000,000 = $33,600,000 Part B New share price after the merger, S = 0.8 1.05 /(0.08 – 0.1) = $28.00 New value after the merger, V = $28 2,000,000 = $56,000,000 Part C Equity issue, raising cash Cost of acquisition = $8 5m = $40,000,000 Net cost = 40,000,000 – 33,600,000 = $6,400,000 Gain = $56,000,000 – $33,600,000 = $22,400,000 Net gain = $22,400,000 – $6,400,000 = $16,000,000 Share exchange Value of the combined company = $1,000,000,000 + $56,000,000 = $1,056,000,000 New share price = $1,056m/104m = $10.15 Cost of acquisition = $10.15 4m = $40,615,385 Net cost = $40,615,385 – $33,600,000 = $7,015,385 Gain =$56,000,000 – $33,600,000 = $22,400,000 (same as in the cash offer) Net gain = $22,400,000 – $7,015,385 = $15,384,615 The advantages and disadvantages of cash and share exchange in M&A can be summarised as follows: Cash Acquired Acquiring Advantages Shareholders will receive a Acquiring firm’s shareholders certain cash flow when they sell will have full control over the their shares to the acquiring combined operation. firm. It implies that they will obtain a certain return on their investment. Disadvantages The receipt of cash is deemed to a disposal of shares which will attract capital gains tax and shareholders will lose ownership. Share exchange Advantages The acquired firm’s shareholders will maintain some form of ownership in the combined operation. Disadvantages The return on investment from the combined operation might be uncertain. There is a liquidity implication. Acquiring firm needs to raise sufficient cash flows for the acquisition. There is no cash outflow in this type of acquisition. Acquired firm’s shareholders need to share ownership with the shareholders from the acquiring firm.
Question 8 a. Orchard plc’s share price, S, can either go up to S or down to S in the next H L period. Derive the price of a put option written on S in terms of a position in the stock and a risk free asset. (7 marks) b. Orchard plc’s shares are currently traded at $20 each. Its share price will go up to $22 or down to $17 in three months’ time. The effective interest rate for the next three months is 3%. What is the price of a put option on Orchard’s share with an exercise price of $20.5? (5 marks) c. Explain clearly why the price of a put option does not depend on the investor’s risk preference and the probabilities of the future states of the economy. Determine the risk neutral probabilities of the two states of the economy in (b). (13 marks) Reading for the question Subject guide, pp.60–63. Approaching the question a. Derive the option price Form a portfolio with a% in S and b in risk-free asset. This portfolio mimicks the payoff of a put option: P = aP + b(1 + r ) H H f P = aP + b(1 + r ) L L f Solving the two equations we have: a = P – P / S – S H L H L b = S P – S P / (1 + r )(S – S ) L H H L f L H The value of a put, P = aS + b b. Given the information in the question, we can determine that: P = 0 H P = 3.5 L S = 22 H S = 17 L Substituting into the two equations in (a) we have: a = (0 – 3.5)/(22 – 17) = –3.5/5 = –0.7 b = (17 0 – 22 3.5) / (1.03 –5) = 14.951 The value of the put, P = –0.6 20 + 14.951 = 0.9515 c. If S = uS (u percentage of S) and S = dS (d percentage of S), then H L a = (P – P )/(u – d)S H L b = (uP – dP )/(u – d)R L H and P = aS + b = (P – P )/(u – d)+ (uP – dP )/(u – d)R H L L H = [qP + (1 – q)P ]/R where q=(R – d)/(u – d), the risk neutral probability H L Using the information in (b), R = 1.03; d = 0.85; u = 1.1 q = 1.03 – 0.85 / 1.1 – 0.85 = 0.72 Information about the probability and risk are already priced in the underlying asset. Therefore the option prices which derived their values from the underlying asset will reflect these two pieces of information. Examiners’ <strong>commentaries</strong> <strong>2011</strong> 11
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Examiners' commentaries 2011

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