**ASSIGNMENT**

**Section A:Question 1**

i. Consider the following four risk-free government bonds: A, B, C, and D. All four bonds have a face value of £100 and pay annual coupons, but the coupon rates are different. Bond A has a coupon rate of 6%, B 7%, C 8%, and D 9%. Both A and B mature in two years while C and D mature in four years. Bonds A, B, C, and D are currently trading at £102.78, £104.65, £112.62, and £116.22, respectively.

a. Calculate the 1-year, 2-year, 3-year, and 4-year spot rate. What is the shape of the term structure? [10 marks]

b. Which theory of the term structure can explain the shape above? Explain the intuition. [5 marks]

ii. Suppose the price of espresso machines is risky, with a CAPM beta of 0.8. The monthly storage cost is $10, and the current spot price is $1,000. However, one can also rent out the machine to earn $5 per month. Storage costs and rent are paid at the end of each month. The expected rate of return on the market is 1.5% per month, with a risk-free rate of 0.5% per month. [Hint: for the purpose of this question, you may assume that there is no depreciation on the espresso machine.]

a. What is the required monthly return on an asset with the espresso machine’s beta? [2 marks]

b. Using your answer above, work out what price the espresso machine should sell for in 3 months (excluding storage costs). [3 marks]

c. Suppose that you need an espresso machine in 3 months. You believe that the price of the espresso machine in 3 months will be $1,050. Which of the following would be cheaper overall: buying the espresso machine today or buying it in 3 months? [5 marks]

**Question 2**

i. The following table lists prices of options on Apple’s stock.

a. Using the information above, derive the two missing prices. [5 marks]

b. How can you produce a bear call spread using the two calls above? What is the price of this bear call spread? [5 marks]

ii. Read the following statements. For each statement, first state whether it is true or false. Then explain your reasoning.

a. XYZ reported a profit of $270 million for 2020. At the same time, their share price dropped by 10% in the same year. The fact that the stock market reacted negatively to positive earnings suggests that it is not informationally efficient. [3 marks]

b. Your friend Jonny made a total return of 100% in 2020 by investing in GameStop, beating the market return by a big margin. In the same year, your friend Sammy made a total return of 5% by investing in government bonds, much lower than the market return in 2020. Given that Jonny outperformed Sammy substantially, Jonny must be a better investor. [3 marks]

c. Managers make superior returns on their purchases of their company’s stock.

This violates the strong form of market efficiency. [3 marks]

iii. Both Firm A and Firm B earn £20 per share every year. Firm A’s equity has a beta of 0.5 and Firm B’s equity has a beta of 1.5. The expected market return is 10% per year and the risk-free rate is 2% per year. Firm A pays out all its earnings to equityholders. Firm B retains half its earnings and pays out the other half to equityholders.

a. What are the required rates of return for A and B’s equity? [2 marks]

b. Suppose that the ROE is 15% for Firm B. The first dividend will be paid one year from today. Calculate the current share price for both Firm A and Firm B. Why are the two prices different? [4 marks]

**Section B:Question 3 (25 marks)**

CorVIR Inc. is a firm whose operations generate an expected EBIT (earnings before interest income, interest expenses and corporate taxes) of $80 per year in perpetuity. These are all the cash-flows that the firms’ operating assets are generating, and the company is currently all- equity financed. Given the risk of CorVIR’s operations, the market requires a return of 15%, i.e., the unlevered cost of capital is 15% for these cash-flows. In addition to its operating assets, CorVIR holds $150 of excess cash on its balance sheet, which is invested in Treasury-bills generating a risk-free return of 4% every year before corporate taxes. The corporate tax rate is 40%. CorVIR is listed on a stock exchange and has 1,000 shares outstanding.

i. Assume the market believes that CorVIR will keep the $150 of cash on its balance sheet forever and never take on any debt. What is the market value of CorVIR’s equity and the price of CorVIR’s stock? (Hint: Excess cash invested in treasury is similar to carrying negative debt and therefore features tax disadvantage that is opposite to the usual interest tax shield) (6 marks)

Now assume that CorVIR announces that the firm will undertake a leveraged recapitalisation.

In this transaction, CorVIR will take on $250 of new permanent fixed debt and use the proceeds from the debt issue, together with the $150 of cash it already holds, to pay a special dividend to shareholders of $400 (40 cents per share). Assume that the risk of the tax shield of the debt is the same as the risk of the debt. The interest rate on the debt will be 6%.

ii. What will happen to the price of CorVIR’s stock when this recapitalisation plan is announced? (6 marks)

iii. Assume now that CorVIR goes ahead with this recapitalisation, i.e., raises $250 of debt and pays a dividend of $400. What will be the market values of CorVIR’s equity and debt after this transaction has been completed? What will be the stock price? What is the change in total shareholder value from this transaction (vis-à-vis the case before the transaction was announced)? (7 marks)

iv. Assume now that CorVIR, instead of paying a dividend, uses the $400 (the excess cash plus the proceeds from the debt issue) to repurchase its own shares. How many shares will CorVIR be able to acquire? What will be the stock price of CorVIR after the share buyback? What is the change in shareholder value from this transaction (vis-à-vis the case before the transaction was announced)? (6 marks)

**Question 4 (25 marks)**

Los Pollos Inc.’s shares trade at $30, and the company has 100 million shares outstanding. Hermanos Ltd.’s shares trade at $20, and the firm has 30 million shares outstanding. The two companies are fully equity financed. The free cash-flows for Los Pollos Inc. are expected to be $300 million next year, while Hermanos Ltd. predicts its free cash-flows to be $72 million next year. Both companies think that the level of cash-flows will stay constant thereafter (forever).

Los Pollos Inc. plans to acquire Hermanos Ltd. Assume that there are no other informational effects other than the ones described in the text. The market risk premium is 7% and the risk- free rate is 3% in this economy.

i. Compute the unlevered (asset) Beta and the unlevered cost of capital of the combined firm assuming no synergies are created in the deal. (3 marks)

The manager of Los Pollos Inc. is convinced that the acquisition will generate economies of scope. These savings amount to an additional free cash-flow of $30 million starting next year, which will subsequently occur annually and remain constant.

ii. Compute the present value of the synergies and the value of the combined firm. Use the unlevered cost of capital calculated in (i) as the discount rate for the synergies. (3 marks)

iii. What is the maximum percentage premium that Los Pollos Inc. could pay in a cash transaction without losing money on the acquisition? If, instead, the acquisition took place via a stock-swap transaction, what is the highest exchange ratio Los Pollos could offer? (4 marks)

You are a senior analyst at a hedge fund specialising in merger arbitrage. A version of the investment strategy trades target shares after a merger announcement and closes the position once the outcome of a merger is certain. Let’s implement this strategy. Assume that you can both take long and short positions in stocks.

iv. Suppose that Los Pollos and Hermanos agree to a cash offer at $27 per share. Following the announcement, Hermanos’ share price jumps to $26.3. What is the market-implied probability of the merger failing (e.g., the regulator may not approve the deal)? (3 marks)

v. Your team of SSE interns independently estimated the probability of the merger failing.

You trust your interns to know better than the market. For which range of possible SSE- intern-estimated failure probabilities would you buy Hermanos’ shares after observing the share price jump to $26.3 after the announcement? What would be the maximum profit per share traded? For which range of possible SSE-intern-estimated failure probabilities would you (short) sell Hermanos’ shares after observing the share price jump to $26.3 after the announcement? What would be the maximum profit per share traded? (6 marks)

vi. Suppose instead that Los Pollos Inc. and Hermanos Ltd. agree to a stock-swap merger with an exchange ratio of 0.9. Right after the announcement of the stock-swap merger at these terms, the Hermanos Ltd. share price jumps to $26.5. What is the implied probability of the merger not going through? (6 marks)