You have been hired to advise an investment management firm. The firm currently has assets held as cash worth £100 million and liabilities that consist of payments of £15 million in 2 years, £20 million in 3 years, £30 million in 4 years, and £50 million in 5 years. The term structure is flat at 4% per year.
What is the present value of the liabilities? [2 marks]
What is the Macaulay duration of the liabilities? [3 marks]
In terms of risk management, explain what your concern is for the investment man- agement firm from holding all their assets in cash. [2 marks]
The following portfolios all have a present value of £100 million. Which one of the portfolios do you recommend the investment management firm invest its cash in to manage interest rate risk? Explain. [2 marks]
Portfolio A Portfolio B Portfolio C Portfolio D Portfolio E Modified Duration 4.7 3.5 4.2 3.8 2.4
Explain why the strategy you recommend in part (iv) is not a perfect hedge.
[2 marks]
You are a bond trader in the City of London and observe the following information on U.K. default-free government bonds, where all bonds pay annual coupons and have a par value of £100:
Price Maturity Coupon Rate
Bond A £89.760 2 years 4%
Bond B £93.318 2 years 6%
Bond C 2 years 12%
Using Bond A and Bond B, what is the current term structure of interest rates?
[4 marks]
Explain the current term structure of interest rates from part (i) using term structure theories. [6 marks]
How many units of Bond A and Bond B do you need to buy/short to replicate the cash flows of Bond C? What is the price of this replicating portfolio? If Bond C is currently trading in the market for £103, is there an arbitrage opportunity? If so, clearly detail the arbitrage strategy and show all resultant cash flows. [4 marks]
Question 2
When answering the question, state any additional assumptions you may need to make. Show all working/calculations.
The financial director of a new start up company has decided to reinvest all earnings back into the firm for the first 5 years. The first dividend is forecast to be £1 in 6 year’s time, grow at 5% for the next 2 years, and then grow at 2% per year indefinitely. Given that the appropriate annual discount rate is 4% what is the value of the share price today? [4 marks]
Using European options only, how can you replicate the payoff of a long forward contract on one unit of IBM stock with 2 months to maturity with a forward price of £120, assuming IBM pays no dividends over the next 2 months? [2 marks]
Prove it is never optimal to exercise early an American call option on a non-dividend paying stock. [4 marks]
BT has a current stock price of £120 which will either go up or go down by 20% in each year for the next two years. BT will not pay any dividends over the next 2 years and the annual risk-free rate is 2%. Use the risk-neutral method to calculate the no-arbitrage price of an American put option on BT with 2 years to maturity that has an exercise price of £120.
[5 marks]
Given that the CAPM holds, what is the lowest possible standard deviation for an investor who requires an expected return of 7%? [5 marks]
Asset Expected Return Standard Deviation
Stock A 0.07 0.15
Market 0.1 0.1
Risk-free 0.05 0
Given the following information, derive an expression for the minimum-variance portfolio of Stock A and B. What are the weights of A and B in this portfolio?
Stock Expected Return Standard Deviation
A 0.03 0.4
B 0.04 0.5
The Corr(RA, RB) is 0.4. [5 marks]
Section B: Answer two questions from this section and another two from Section A
Question 3
Assume a Modigliani-Miller (MM) world. AntiVaxer, PaleoBro, and Boop are three similar com- panies in the wellness industry with the following capital structures and cash flows:
AntiVaxer PaleoBro Boop
Shares outstanding (millions) 10 6 20
Share price $30 $35 $10.50
Market value of perpetual debt ($million) – 105 390
Expected earnings before interest ($million) 45 45 90
Interest expense ($million) – 5.25 19.5
Dividends ($million) 45 39.75 70.5
All three firms share identical business and operating risk characteristics, producing perfectly correlated earnings. Expected earnings will remain constant in perpetuity. All earnings are paid out as interest or dividends every year; these payouts are also expected to remain constant.
When answering the question, state any additional assumptions you may need to make. Show all working/calculations.
Calculate the market-implied weighted average cost of capital (WACC) for AntiVaxer and PaleoBro. Explain why your results indicate the presence of an arbitrage opportunity.
[4 marks]
You work for Paltrow Capital, a fund manager that currently holds 8% of the debt issued by PaleoBro. Show that by taking positions in the equity of AntiVaxer and PaleoBro, your employer can profitably exchange its current holdings for an alternative investment with identical future cash flow characteristics. Make sure to fully demonstrate the arbitrage.
[5 marks]
Your friend owns 500,000 Boop shares. How would you replicate the future cash flows of your friend’s investment using a leveraged equity holding in PaleoBro? Assume you can borrow and lend at 5%. [6 marks]
Now assume companies must pay corporation tax at a rate of 30%. Interest is tax-deductible, there are no personal taxes, and markets are semi-strong form efficient. All other MM assump- tions still hold.
Re-compute the fair share price for each company. Remember, the cash flows in the table above are in an MM world (i.e. no taxes). Assume AntiVaxer shares and all debt securities are priced at fair value in the MM world. [3 marks]
Suppose AntiVaxer announces plans to restructure by raising sufficient perpetual debt at an interest rate of 5% to repurchase 2 million shares. How much debt will be raised and at what price will shares be repurchased? How will its price-earnings ratio (P0/EPS1) change as a result of the restructure? Without doing any additional calculations, explain why this change would be bigger/smaller in an MM world. [7 marks]
Question 4
Assume a Modigliani-Miller (MM) world. Nymeria Ltd. is an all-equity firm with 10 million shares outstanding. Its only asset is $100 million cash invested in the risk-free asset, which pays 10% per year. Nymeria can invest $50 million of its cash today into one of two mutually exclusive projects, A or B. Project A is expected to generate a perpetual stream of free cash flows, start- ing with $13.5 million in exactly one year, thereafter growing at an expected rate of 3% per year. Project B, also perpetual, is expected to produce free cash flow of $10 million in exactly one year’s time, growing at an expected rate of 5% per year thereafter. The risk of both projects is diversifiable.
When answering the question, state any additional assumptions you may need to make. Show all working/calculations.
Calculate the NPV and IRR of each project. If the NPV and IRR rankings disagree, explain the source of the conflict. Which project should Nymeria choose? Why? [5 marks]
Assume Nymeria invests in project B. What is the firm’s new share price after investment?
[2 marks]
After taking project B, Nymeria considers acquiring Frey Corp., an all-equity firm with 20 million shares outstanding, currently trading at $2 per share. The difficulties of integrating disparate organisations means the synergies from the acquisition are uncertain. With probability 60%, in- tegration will be successful, in which case the value of Frey’s assets will improve by 30% under the new management. However, if the merger is implemented poorly (probability 40%), the ac- quisition will destroy 20% of Frey’s asset value.
Remember that information in an MM world is symmetric – insiders at both firms and the market are equally informed about the synergy outcome, which will only be revealed after the acquisi- tion is completed. Assume managers always act in the interest of existing shareholders and that all participants are risk-neutral. Also assume that in any takeover, 100% of target shares are acquired by the bidder.
Assume Nymeria does not have to pay a premium to acquire Frey. Advise Nymeria on the merits of the acquisition. If it financed the takeover using shares in the combined entity, how many shares will Nymeria need to offer for each Frey share? Would Nymeria’s share- holders be better off (in expectation) if the acquisition was financed using cash from the company accounts instead? Explain. [5 marks]
For each payment method (i.e. shares vs cash), determine the post-acquisition wealth of Nymeria and Frey shareholders in the good and bad synergy states. What do your calcula- tions say about how the method of payment affects how the risks from an acquisition are shared between bidder and target shareholders? [4 marks]
Nymeria’s CEO, Edmure “Ed” Proudman, has never lacked self-belief. This unshakeable faith in his own ability leads Ed to hold two incorrect beliefs. First, that the market’s estimate of Project B’s growth rate (5%) is too low; Ed feels that a growth rate of 6.5% is a more accurate reflection of his managerial and entrepreneurial genius. Second, Ed is convinced that under his steward- ship, the probability of a successful merger integration is 80%.
For part (e), assume that instead of $2, the stand-alone share price of Frey Corp is $7.50 per share. Also assume that Frey’s shareholders require a 5% acquisition premium on a market- value basis.
Suppose any acquisition of Frey will be financed using a combination of cash and shares. Specifically, Nymeria will use all of its cash, with the remainder being paid via shares in the combined firm. If Nymeria’s CEO acts according to his beliefs, determine if he will decide to pursue the acquisition. (Hint: the market, which is efficient, does not reflect the CEO’s in- correct beliefs. Frey’s shareholders care about the market value of any shares they receive.)
[5 marks]
How does what you find in (e) demonstrate a cost of CEO overconfidence, and what does it suggest about the preferences of overconfident bidder CEOs regarding cash vs. share deals? Explain. [4 marks]
