MSIN0149 Corporate Finance
Paper 2020/21
Examination length: TWO (2) hours
There are FOUR (4) sections to the examination paper.
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You are advised to allocate your time between the sections and parts in proportion to the marks available.
Module Leader/Internal Examiner: and TURN OVER
MSIN0149 2018/19 LSA
SECTION 1: CAPITAL STRUCTURE AND EQUITY VALUATION (25 MARKS)
You are an entrepreneur with an investment opportunity. This is a project that lasts 1 year. The initial investment is £10,000. This investment generates the following final cash flows:
• If the economy is strong: £17,000
• If the economy is weak: £10,000
The probability that the economy is strong is 50%. The risk-free rate is 10%, and the risk premium associated with such cash flows is 10% (note: this is exclusively systematic risk). Financial markets are competitive.
1. If you finance this opportunity with your own money (as equity), what is the
expected rate of return? What is the NPV? (10 marks) • 35%
• NPV = 11250-10000=1250
2. Assumeyoufinancethisinvestmentwith60%debt,andtherestwithequity.What is the expected return on debt and equity, respectively? Is this capital structure preferable to full equity financing? Why? (8 marks)
• With 60% debt, the debt is safe. In that case, its expected return is the risk-free rate (10%).
• But the payoff to equity become riskier. As a result, the required return raises to 31.4%.
• There are no frictions, MM applies, the WACC is 20% as is the case above. In both cases, you (as the initial shareholder) capture the whole NPV.
3. What is the price, at the beginning of the year, of the Arrow security that promises to pay £1 when the economy is weak (and 0 if the economy is strong)? (6 marks)
• The price of this Arrow securities is ps=0.601 (and that of the other is pw=0.308).
• To find it, one just needs to solve a system of two equations. They are:
• (i) ps+pw=1/(1+rf); One of each security gives you 1 in a year for sure.
• (ii) 10,000pw+17,000ps=11,250; A simple replication argument (see lecture slides).
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4. Imaginethat,insteadofstandarddebt,youfinanceyourinvestmentwithafinancial innovation that you call “SoM coins”, and the rest with equity. Each coin can be re- exchanged at the end of the year for £5 if the economy is strong and £10 if the economy is weak. After that, they expire and are worth nothing. You issue 800 of these coins. What is the market price of a coin at the beginning of the year (i.e. at which price are you able to sell them)? How much equity do you need? (6 marks)
• Once we have the price of the arrow securities, it becomes easy to price any security.
• Indeed, each coin is a bundle of 5 Arrow securities that pay in the strong state and 10 that pay in the weak state. The price of a coin is therefore: 5ps + 10 pw = 7.548.
• The coins allow you to raise 800*7.548=6039.
• You therefore need to raise 3961 as equity.
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MSIN0149: Corporate Finance
MSIN0149 2018/19 LSA
SECTION 2: CAPITAL STRUCTURE PROBLEM WITHT FRICTIONS (25 MARKS)
Consider a firm in the following environment:
• There is only 1 period and there are two 2 states (H and L) equally probable.
• There is no tax, there are no bankruptcy costs, and risk is diversifiable.
• The current risk-free interest rate is equal to 0 (to simplify computations).
Initially, the firm has;
• 20 in cash;
• an existing project with cash flows (at the end of the period) equal to 120 (in state H) or 80 (in state L);
• debt with face value 90, which will mature at the end of the year, and will require a payment (interest included) of 95;
• equity with book value 20.
There is a risky investment opportunity: Investing 20, gives a payoff at date 2 of 30 (in
state H) or 15 (in state L). Consider 3 options:
1. Do nothing (that is, keep assets and liabilities as they initially are).
2. Use the cash to invest in the new project, and keep the rest as it is.
3. Use all the cash to pay a dividend, and keep the rest as it is.
Questions:
1. Compute the market values of debt and equity for the 3 options.
• Option 1: The debt is safe and r=0. Hence, D=95. Equity holders get 45 or 5 with equal probability. Hence, E=25.
• Option 2: The debt stays safe. D is still 95. Equity holders get 55 or 0 with equal probability. Hence E = 27.5. (The NPV of the new project is 2.5.)
• Option 3: The debt is risky. Debtholders get either 95 or 80. Hence, D=87.5. Equity holders get 20 to start with. Then, they receive either 25 or 0. Hence, after dividend, E=12.5.
2. Which option will the current shareholders prefer? Discuss.
MSIN0149 2018/19 LSA
• They will go for option 3. That is, they will prefer to pay themselves a dividend rather than go for the positive NPV project. This is a form of debt overhang.
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MSIN0149: Corporate Finance
MSIN0149 2018/19 LSA
SECTION 3: CAPITAL BUDGETING (20 MARKS)
Allied Investments (AI) is a diversified company with two operating divisions:
Division Cosmetics Mining
Percentage of Firm Value 40%
AI has no debt on its balance sheet. To estimate the cost of capital for each division, AI has identified one principal competitor for each of its two divisions. The competitors are pure-plays, i.e., they are not diversified and operate in only one industry each, and they maintain a constant Debt-Equity ratio at all times. Assume that the debt of the two competitors is riskless.
Competitor
Nova Cosmetics Blackshaft Mining
Estimated Equity Beta 0.9
Debt / Equity
1/9 0.10 1/4 0.20
Debt/(Debt+Equity)
Finally, assume these betas are accurate estimates and that the CAPM holds.
1. Estimate the asset beta (unlevered beta) for each of AI’s divisions (6 marks).
Under the assumptions made, the asset beta is the weighted average of the debt and equity betas: 𝜷𝑨𝒔𝒔𝒆𝒕𝒔 = 𝑬 𝜷𝑬𝒒𝒖𝒊𝒕𝒚 + 𝑫 𝜷𝑫𝒆𝒃𝒕. Since the debt of the
competitors is riskless, their debt betas are zero. So, 𝜷𝑵𝑪,𝑨𝒔𝒔𝒆𝒕𝒔 = 𝑬 𝜷𝑵𝑪,𝑬𝒒𝒖𝒊𝒕𝒚 =
2. Based on your estimates for the betas of AI’s operating divisions, what is your estimate of AI’s equity beta (5 marks)?
Since AI has no debt on its balance sheet, its equity beta equals its asset (or unlevered) beta. AI is a portfolio which consists of two divisions (or assets), and a portfolio beta is the weighted average of the betas of the component assets:
𝜷𝑨𝑰,𝑬𝒒𝒖𝒊𝒕𝒚 = 𝜷𝑨𝑰,𝑨𝒔𝒔𝒆𝒕𝒔 = 𝜷𝑷𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 = 𝒘𝑵𝑪𝜷𝑵𝑪 + 𝒘𝑩𝑴𝜷𝑩𝑴 = 𝟎. 𝟒 ⋅ 𝟎. 𝟖𝟏 + 𝟎. 𝟔 ⋅ 𝟏. 𝟏𝟐 = 𝟎. 𝟗𝟗𝟔.
3. Assume that the risk-free interest rate is 5% and that the expected return on the market portfolio is 12%. What is the cost of capital for each of AI’s divisions? What is the cost of capital for AI as a whole (5 marks)?
𝟎.𝟗⋅𝟎.𝟗=𝟎.𝟖𝟏, and𝜷𝑩𝑴,𝑨𝒔𝒔𝒆𝒕𝒔 = 𝑬 𝜷𝑩𝑴,𝑬𝒒𝒖𝒊𝒕𝒚 =𝟎.𝟖⋅𝟏.𝟒=𝟏.𝟏𝟐. 𝑫+𝑬
MSIN0149 2018/19 LSA CONTINUED
We have assumed that the CAPM holds. Hence the required rate of return on AI cosmetics is given by 𝑬[𝒓𝑨𝑰 𝑪𝒐𝒔𝒎𝒆𝒕𝒊𝒄𝒔] = 𝒓𝒇 + 𝜷𝑵𝑪,𝑨𝒔𝒔𝒆𝒕𝒔(𝑬[𝒓𝑴𝒌𝒕] − 𝒓𝒇) = 𝟓% + 𝟎. 𝟖𝟏(𝟏𝟐% − 𝟓%) = 𝟏𝟎. 𝟔𝟕%. The required return on AI mining is 𝑬[𝒓𝑨𝑰 𝑴𝒊𝒏𝒊𝒏𝒈] = 𝒓𝒇 + 𝜷𝑩𝑴,𝑨𝒔𝒔𝒆𝒕𝒔(𝑬[𝒓𝑴𝒌𝒕] − 𝒓𝒇) = 𝟓% + 𝟏. 𝟏𝟐(𝟏𝟐% − 𝟓%) = 𝟏𝟐. 𝟖𝟒%. Finally, the overall cost of capital for AI is 𝑬[𝒓𝑨𝑰] = 𝒓𝒇 + 𝜷𝑨𝑰,𝑨𝒔𝒔𝒆𝒕𝒔(𝑬[𝒓𝑴𝒌𝒕] − 𝒓𝒇) = 𝟓% + 𝟎. 𝟗𝟗𝟔(𝟏𝟐% − 𝟓%) = 𝟏𝟏. 𝟗𝟕%.
4. Would your estimate of the divisional costs of capital increase, decrease, or stay the same if you learned that the debt of the two competitors had a beta of 0.5 rather than 0.0? Note: There is no need to do any calculations for this part (4 marks).
A higher debt beta for the comparables implies a higher estimate for the comparables’ asset betas. This in turn leads to a higher estimate for the asset betas of AI’s divisions, and hence to higher estimates for the costs of capital.
7 TURN OVER
MSIN0149: Corporate Finance
MSIN0149 2018/19 LSA
SECTION 4: RISK MANAGEMENT (30 MARKS)
Make America Sell Again (MASA) is a British importer of U.S. computer hardware exclusives. Its business is to collect pre-orders in GBP in advance (paid upon delivery), pay for exclusive products in USD (upon release), then immediately ship these products to its U.K. customers. Next year, MASA expects to be able to purchase 10,000 units of computer hardware at the average cost per unit of USD 1,000. Pre- orders are non-refundable, unless MASA is unable to deliver the product, and are placed by its U.K. customers today for the entire expected supply. The average pre- order price is set at GBP 1,200. Ignore net working capital, net capex, taxes, and all market imperfections, and assume that the firm is all-equity financed.
1. Draw the payoff diagram of MASA’s free cash flow as a function of the GBP/USD exchange rate 𝐸 (5 marks).
0… 0.7… FCF = 10K ⋅ (1,2K – 𝑬 ⋅ 1K) = GBP 12 mln – 𝑬 ⋅ USD 10 mln.
2. How can MASA completely eliminate its exposure to exchange rate risk using forward contracts and secure a constant hedged free cash flow at the level of MASA’s free cash flow when 𝐸 = 0.7? Assume that the forward price is 𝐹 = 0.7 (6 marks).
Buy a forward contract which requires that MASA purchase USD 10 million next year for GBP 7 million, for a payoff of 𝑬 ⋅ USD 10 mln – GBP 7 mln. The combined payoff (of the free cash flow and the forward contract) is GBP 5 million.
3. Additional market research shows that in fact, the number of units MASA can purchase depends on the state of the U.S. economy. 10,000 units are only guaranteed if the U.S. economy is not in a decline, i.e., 𝐸 is above 0.7. If the U.S. economy is in a
MSIN0149 2018/19 LSA CONTINUED
recession, i.e., 𝐸 is between 0.6 and 0.7, MASA can purchase 10,000 ⋅ 1 units 2.4−2𝐸
(note that at 𝐸 = 0.7, this is still 10,000 units). If the U.S. economy is in a depression, i.e., 𝐸 is below 0.6, MASA can only purchase max (0, 10,000 ⋅ 5𝐸−2 ) units.
Draw the new payoff diagram of MASA’s free cash flow as a function of 𝐸 (7 marks).
MSIN0149: Corporate Finance
4. MASA still wants to completely eliminate its exposure to exchange rate risk. It is therefore thinking of using put and call options as a hedge. Current prices of European puts and calls (in GBP per USD 1 of the underlying) with different exercise prices are:
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MSIN0149 2018/19 LSA
What options must MASA use to completely eliminate its exposure to exchange rate risk? List all combinations of option type (put or call) and exercise price that should be in the hedging portfolio. For this question, ignore quantities of options (4 marks).
You will need C(0), P(0.6), C(0.4), C(0.6), and C(0.7).
Alternatively, you will need C(0), P(0.4), C(0.4), C(0.6), and C(0.7) – there are several ways to create the same hedging portfolio.
Alternatively, you only need P(0.4), P(0.6), and C(0.7).
5. What is the exact hedging portfolio that (ignoring the hedging portfolio premium) delivers the constant hedged free cash flow at the level of MASA’s free cash flow when 𝐸 = 0.7? What is the all-in hedged free cash flow in this case (8 marks)?
Below, you can find three solutions that give exactly the same hedging portfolio. The second one is the one Karen presented in Week 10. The solutions do not have to be this long: extra detail is provided for clarity.
Solution 1.
Start from the y-axis and move to the right.
Any payoff that does not start from the origin involves put options (since they are the only ones that pay positive when the exchange rate is zero). And anything with a slope of 0 at the origin can be created either by (a) buying a put and call with the strike of zero, which is just the currency, or (b) buying a put with a high strike and and selling a put with a low strike. Let’s try (a). The flat part of the payoff from E=0 to 0.4 can be replicated by a put with the strike of 0.4 in the amount of 5/0.4 (which will pay 5/0.4*4 = 5 exactly when E=0) and a call with the strike of 0 (which is just the currency) in the same amount.
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Hedging portfolio
Hedged FCF
After this first step, our hedging strategy is shown with the green line:
On the second step, we need to change the slope of the hedging payoff of 5/0.4 (when E is above 0.4) to -5/0.2 (the slope of the goal hedging payoff between 0.4 and 0.6). To do so, we sell call options with the strike of 0.4 in the amount of (5/0.4+5/0.2) = 3*5/0.4. After the second step, our hedging strategy is shown with the green line:
On the third step, we need to change the slope of the hedging payoff of -5/0.2 (when E is above 0.6) to 0 (the slope of the goal hedging payoff between 0.6 and 0.7). To do so, we buy call options with the strike of 0.6 in the amount of 5/0.2. After the third step, our hedging strategy is shown with the green line:
MSIN0149: Corporate Finance
Hedged FCF
Hedging portfolio
Hedged FCF
MSIN0149 2018/19 LSA
11 TURN OVER
Hedging portfolio
The final step is to buy call options with the strike of 0.7 in the amount of
5/0.5 (to match the slope of the goal hedging portfolio after 0.7).
The hedging portfolio = 5/0.4 ⋅ C(0) + 5/0.4 ⋅ P(0.4) – 3*5/0.4 ⋅ C(0.4) + 5/0.2 ⋅ C(0.6) + 5/0.5 ⋅ C(0.7). The price of the hedging portfolio is 5/0.4 ⋅ 0.75 + 5/0.4 ⋅ 0.00002 – 3*5/0.4 ⋅ 0.35989 + 5/0.2 ⋅ 0.17162 + 5/0.5 ⋅ 0.09687 = GBP 1.139 million. So, the all-in hedged free cash flow is 5-1.139 = GBP 3.861 million.
Solution 2.
MSIN0149 2018/19 LSA CONTINUED
Hedging portfolio
Hedged FCF
Hedging portfolio
Hedged FCF
An alternative approach is to notice that the goal hedging portfolio is a strangle with an extra flat part for low E. So, as with the strangle, we can start with P(0.6) and C(0.7). The flat part of the payoff from E=0 to 0.4 can be replicated by a put with the strike of 0.6 in the amount of 5/0.6 (which will pay 5/0.6*6 = 5 exactly when E=0) and a call with the strike of 0 (which is just the currency) in the same amount.
This first step will give you a flat payoff all the way until E = 0.6, and a positive slope of 5/0.6 when E is above 0.6. But we need the slope of the payoff to decrease to -5/(0.6-0.4) = -5/0.2 when E is between 0.4 and 0.6. This can be achieved on the second step by selling 5/0.2 of the call with the strike of 0.4.
After the second step, our hedging strategy will have the slope of -5/0.3 when E is above 0.6 (5/0.6 from C(0), -5/0.2 from C(0.4), and 0 from the put that is not exercised). But we need the slops ot tha payoff to be 0 when E is between 0.6 and 0.7. So, on the third step we need to buy 5/0.3 of the call with the strike of 0.6. Finally, on the last step, as before, we need to buy 5/0.5 of the call with the strike of 0.7.
The second hedging portfolio = 5/0.6 ⋅ C(0) + 5/0.6 ⋅ P(0.6) – 5/0.2 ⋅ C(0.4) + 5/0.3 ⋅ C(0.6) + 5/0.5 ⋅ C(0.7). The price of the hedging portfolio is 5/0.6 ⋅ 0.75 + 5/0.6 ⋅ 0.00681 – 5/0.2 ⋅ 0.35989 + 5/0.3 ⋅ 0.17162 + 5/0.5 ⋅ 0.09687 = GBP 1.139 million. So, the all-in hedged free cash flow is 5-1.6 = GBP 3.861 million. It is exactly the same as the first hedging portfolio (which is not surprising, otherwise there is arbitrage!).
Solution 3.
The third hedging portfolio is simple: 15/0.6 ⋅ P(0.6) – 10/0.4 ⋅ P(0.4) + 5/0.5 ⋅ C(0.7). Please try to prove this yourself. The all-in hedged free cash flow is still GBP 3.861 million.
END OF PAPER
13 TURN OVER
MSIN0149: Corporate Finance
MSIN0149 2018/19 LSA
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