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FN2191

PRINCIPLES OF CORPORATE FINANCE

2022

Question 1

Virgin Atlantic is considering initiating a perpetual service between London and Rio. To enter this market, Virgin must purchase one or more new aircraft. In particular, Virgin is contemplating buying either Boeing 787s which can carry 300 passengers or Airbus A380s which can carry 600 passengers. The prices and operating costs of the two aircraft are shown below.

Boeing 787		Airbus A 380
Purchase price (£ million )	150	3 00
Annual operating cost (£ million )	1 2	1 5
Passenger capacity	3 00	600

The primary source of uncertainty facing Virgin is the level of demand. First year demand is known with certainty: 300 round-trip passengers per day. However, demand in subsequent years is uncertain. With 50% probability, next year's demand will increase to 600 round-trip passengers per day and will remain at 600 in all subsequent years. With 50% probability, demand will stay at 300 round-trip passengers per day forever. Revenue will be £0.1 million annually per daily round-trip (or £30 million annually per 300 daily round trips). For simplicity, assume that the aircraft last forever with no depreciation and have a resale value of zero. Also assume that first year cash flows are received immediately (concurrent with the purchase price), next year's cash flows are received one year from now, and so on. Further assume that the appropriate discount rate is 10%.When answering this question, state any additional assumptions you may need to make. Show your calculations.

(a) What is expected demand next year?

(3 marks)

(b) Calculate the NPV of purchasing one A380. Remember, the first year's revenues and costs occur immediately.

(6 marks)

(c) If the 787 is purchased this year, an additional 787 aircraft will have to be purchased next year to service the route fully in the case that demand increases. Suppose that Virgin's decision to take delivery of the second 787 must be made today, but they pay for the aircraft next year (when it's delivered). Assuming that Virgin commits to taking delivery of the second 787 next year, what is the NPV associated with using 787s to serve the London to Rio route?

(7 marks)

(d) Suppose that Boeing offers to waive the requirement that Virgin commit to the purchase of the second 787 immediately. What is the maximum amount Virgin should pay for this waiver?

(9 marks)

Question 2

Mr Ron Sau, a young entrepreneur, starts a new venture which promises to revolutionize the ring-forging business. His project, a new type of ring which will ensure him dominance of the market, costs 10 today (year 0) and delivers a FCF of 0 in the first year and 80 in the second year if successful. In year 1 Mr Sau Ron will know if the project will be successful, if not he will terminate the venture with a cash-flow of 0. From today’s perspective, the project has a 25% percent probability of being successful. The risk of such a project is perfectly diversifiable; the risk-free rate is 10% per year; and corporate taxes are at 0%.

a) Draw the timeline of Ron Sau project, be sure to include relevant cash-flows. Calculate the project’s NPV and expected return

(3 marks)

Ron seeks the advice from Mr Alf “ Alfie” Gand, an old angel investor who calls himself the Wizard of Financing. Mr Gand Alf tells Ron that he should issue a lot of debt and avoid equity financing at all costs, due to information asymmetry, and savings on tax liabilities, which Mr Gand refers to as the “ Interest Tax shield” .

b) Comment on Alf’s strategy. Which benefit(s) of debt does he want Mr Sau (Ron) to take advantage of? Does the benefit (do these benefits) apply to Mr Sau’s company?

(4 marks)

Ron accepted to issue a zero-coupon bond to Alf with 60 face value and two years maturity in exchange of the 10 needed for initial invest (Mr Gand (Alf) is not very good at math given his age…).

c) Calculate the fair values of debt (Alf holds) and equity (Ron holds) today. Compare the equity value with the NPV in a) and comment why they are the same or different.

(5 marks)

Now, suppose Mr Sau (Ron) suddenly realizes that if the company invests 2 more today, the forging technology can be patented. This patent can be sold for 10 in year 2, if and only if the project fails. In order to get the additional 2, Ron approaches the Great Investments Management Limited (GIMLI for short) to issue fresh equity.

d) Calculate the NPV of the additional project. Will Mr Sau Ron be able to sell equity to GIMLI? If so, how much fraction of the company? If not, why? Is Mr Sau better off with the new investment? Show your work.

Q 2 d ( i ): 160 words (8 marks)

e) Comment on the costs of debt financing using examples from this question.

(5 marks)

Question 3

Devil Apps, Inc. (DA) is a publicly-traded company with 25 million shares outstanding that is in the business of selling discounted mobile phone software applications. In addition to this business asset, DA also has cash equal to 200 million pounds. The market does not yet know which state DA is in, but the market does know the value of DA's two assets in each of the three possible states, tabulated below in millions of pounds:

State 1		State 2	State 3
Devil Apps Business Asset	8 70	8 60	600
C ash	2 00	2 00	2 00

The market also knows that state 1 is twice as likely as each of the other two possibilities and that DA has an equity beta of 0.8. Throughout the problem, assume that managers act in the best interest of existing shareholders.

Assume for parts (a) and (b) that DA is an all-equity firm with no additional positive NPV project. When answering this question, state any additional assumptions you may need to make. Show your calculations.

(a) What is the stock price of DA before the market learns the true state of the world? (5 marks)

(b) The CEO of DA has decided to announce tomorrow that they will pay £42.8 in dividends per share. How would you expect DA's stock price to react to the announcement? Why? Explain completely.

(7 marks)

(c) Now, instead assume DA had issued debt as well as equity. Last year it issued a one-year bond at par with a total face value of 800 million pounds. In addition to returning the 800 million pounds of principal, the bond also pays a single coupon at maturity. The beta of DA's debt is 0.5, the market risk premium is 6% and the risk- free interest rate is 2%. Also assume that the costs of financial distress in case the firm has to liquidate are equal to 50 million. What was the coupon rate on DA's debt when it was issued? Explain fully.

Q 3 c : 100 words

(8 marks)

(d) When the debt was issued, Mr. Gold, DA's CFO, was considering hedging the risk in DA's cash flows. However, his accountant recommended against it. The accountant claimed that since the firm was taking on a lot of debt, the creditors were bearing all the risk. As a consequence, it would not be in the best interest of shareholders to pay hedging costs to protect the creditors. Do you agree or disagree with the accountant's analysis? Explain completely.

Q 3 d : 130 words

(5 marks)

Question 4

Every point in time mentioned in this problem is at the beginning of each year. It is now 2016. Gravitational Waves (GW) Company is a start-up, founded in 2015 with a potentially profitable idea. GW has already spent its £7M endowment over the past year on developing this idea and now the company has a reasonable outlook for it. The idea still requires £10M and one more year to refine before one can definitively see its potential. Unfortunately, GW has run out of money and therefore approaches a VC and asks for a £10M equity contribution.

In 2017, GW's idea will be either a complete failure with 0 value or a great success generating annual earnings of £20M forever starting from 2018. The probability of success is 0. 1, and the appropriate discount rate is 20%. Earnings will be paid out as dividends.

(a) What's the fair valuation of the company at 2017 after the idea proves to be successful?

(2 marks)

Now assume that GW goes public in 2017 if the idea turns out to be successful and raises an additional £100M. Post-IPO the company has 10M shares. Assume that the VC cashes out immediately after IPO.

(b) What is the share price after IPO at 2017? How many shares are sold to the public?

(4 marks)

(c) Will the VC contribute the £10M capital in 2016? If so, what is the VC's percentage ownership of the company after the contribution in 2016?

Q 4 c : 120 words

(4 marks)

Unfortunately markets rarely give a fair valuation. This mis-valuation gives GW the option to choose the ideal timing to go public (so-called ‘ market timing’). Suppose GW can choose to conduct the IPO in 2017, 2018 or 2019 at prices of £22, £32, and £34 per share respectively. Continue assuming that GW raises an additional £100M at IPO and post-IPO the company has 10M shares.

(d) When should GW go public in order to maximize its pre-IPO expected valuation in 2017?

Q 4 d : 180 words

(6 marks)

(e) Given the possibility to ‘ time the market’, redo question (c).

(5 marks)

(f) Compare what you find in (c) and (e). Is IPO market timing good or bad for

efficient project selection?

(4 marks)

Question 5

(a) Briefly explain the risk-shifting problem.

(2 marks)

Consider a risk neutral entrepreneur who has two investment opportunities. Both require an investment of £100 upfront with the following payoffs in the next year:

A pays: £200 with probability 0.4 and £0 with probability 0.6.

B pays: £120 for sure.

The risk free rate is normalized to 0 for your computational convenience.

(b) If the entrepreneur has £100 in cash to fund the investment, which project will he choose? Show your calculations.

(2 marks)

(c) Now, suppose the entrepreneur has no cash and must issue straight debt with one year maturity to raise the required investment of £100. If the entrepreneur can commit to take project B, what is the required face value of debt such that the market value of debt is £100? After the debt is in place, which project will the entrepreneur choose? Show your calculations.

(4 marks)

(d) If you were a sophisticated bank, expecting the entrepreneur’s choice of investment after taking the loan, would you make the loan at any face value? If not, why? If so, at what face value can you break even?

Q 5 d : 150 words

(2 marks)

Now consider an alternative world in which the entrepreneur issues convertible debt (one year maturity). Suppose the company has 10 shares outstanding at the time of debt issuance. The convertible debt has a face value of £100. It can be converted into 40 shares at maturity if the debt investor wishes.

(e) Should the investor convert if project A is taken and £200 is realized? Should the investor convert if B is taken and £120 is realized?

(5 marks)

(f) Given the conversion decision in €, what is the entrepreneur’s expected pay-off

with project A? How about the pay-off with project B? Which project will the entrepreneur choose under convertible debt financing?

(5 marks)

(g) Compare your findings in (c) and (d) with (e) and (f). What can you say about straight debt financing and convertible debt financing under conflict of interest between debt and equity?

(5 marks)

Question 6

Your company has earnings per share of £4. It has 1 million shares outstanding, each of which has a price of £40. You are thinking of buying DeltaCo, which has earnings per share of £2, 1 million shares outstanding, and a price per share £25. You will pay for DeltaCo by issuing new shares. The synergy as a result of this acquisition will increase your original company's EPS and share price both by 25%.

(a) If you pay no premium to buy DeltaCo, what will your earnings per share be after the acquisition?

(4 marks)

Starting from this point, suppose you pay a 20% premium to buy DeltaCo.

(b) What will your earnings per share be after the acquisition?

(6 marks)

(c) Are you better off with this acquisition? What is the maximum percentage premium you are willing to pay before DeltaCo becomes too expensive to acquire?

(7 marks)

(d) Instead of using pure equity to pay for the deal, now assume you pay the deal with 50% cash coming from your old company and 50% newly issued shares. What is the number of shares issued?

(8 marks)