Suppose that the interest rate is 2.5%. What is the one year discount factor if the interest rate is annually compounded?

Discount factor with annual compounding:

Answer: DF = 1 / (1 + .025) * 1 = 0:97561

Formula: Discount factors. If the interest rate is r% per year, the t year discount factor is:

DF = 1 / (1 + r)^{t}

Shark Attack plc has just launched a takeover bid for Soft Target plc. Shark Attack believes that it has identified £20,000,000 of annual efficiency savings at Soft Target. Shark Attack’s investors demand a return of 8% for the risk associated with an investment in Soft Target, and the corporate tax rate is 40%. What is the maximum premium that Shark Attack is prepared to pay over Soft Target’s pre-bid value?

Shark Attack expects to make a pre-tax income £20,000,000 in perpetuity from its investment in Soft Target. This corresponds to an after-tax figure of £20,000,000(1 - 0.4) = £12,000,000. It can be valued using the standard formula for a perpetuity: Takeover premium = £12,000,000 / 0.08 = £150,000,000

Perpetuity Formula:

The value of a payment of C, received every

year for ever starting in one year, is:

PV = C / r

where r is the discount rate. If the perpetuity grows at a

rate g per year, then

PV = C / r-g

In a bookbuilt IPO:

(a) The bookrunner sells to different investors at the same price

(b) The issuer and bookrunner do not have discretion about which investors to allot

(c) The price is always set at the highest possible clearing price

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(a) The bookrunner sells to different investors at the same price

You own a gold mine, and have no other exposure to gold. You have no other financial positions.

(a) Buying a call option on a gold index is a bet.

(b) Buying a put option on a gold index is a bet.

(c) Buying gold is a hedge.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(a) Buying a call option on a gold index is a bet.

The Credit Rating industry:

(a) Operates an investor-pays business model

(b) Are unregulated in the U.S. and Europe

(c) Is very competitive and has no barriers to entry

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b) and (c)

(h) None of the above

(h) None of the above

Alpha:

(a) Measures the sensitivity of a stock to market risk

(b) Is the difference between a stock’s expected return and the expected return of the stock as predicted by the CAPM

(c) When alpha is nonzero, this is evidence that not all stocks lie on the security market line

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) When alpha is nonzero, this is evidence that not all stocks lie on the security market line.

Company ABC has a total market capitalization of £1 billion, it is entirely equity financed, and its equity has a beta of 1.1. The risk-free rate is 2% and the market risk premium is 5.5%.

(a) ABC plans to issue a £300 million bond issue, which it will use to fund a one-off £300 million dividend to shareholders. The bond will have a yield to maturity of 5%, and it will have a maturity of 10 years. ABC anticipates that it will refinance (i.e. replace) the bond when it matures, so that it will always have £300 million of debt outstanding. The corporate tax rate is 35%. What will the effect of the bond issue be upon the value of ABC before the one-off dividend? [3 marks]

(b) What will ABC’s cost of equity be after the one-off dividend of part (a) above?

[7 marks]

(a) The value of the tax rebate is D× τ = 300m × 35% = 105m. So the value of the firm will increase by £105m.

Forumla: Present value of tax shield on perpetual debt. This is given by 𝐷 ∗ 𝜏, where D is the amount of perpetual debt and τ is the corporate tax rate.

(b) Asset beta is 1.1 so 𝑟𝐴 = 2% + 1.1 × 5.5% = 8.05%

After the dividend, equity value = 1*bn* − 300𝑚𝑚 + 105𝑚𝑚 = 805𝑚𝑚

𝑟𝐸 = 𝑟𝐴 + (𝐷 / E) (𝑟𝐴 − 𝑟𝐷)

𝑟𝐸 = 8.05% + (300/805) (8.05% − 5%) = 9.187%

Formula: Weighted Average Cost of Capital (WACC)

The equation in the answer is just rewriting the WACC.

WACC is 𝑟𝐴 = (𝐷/V)𝑟𝐷 + (𝐸/𝑉)𝑟𝐸 . You know rA, D, E, rD, and V(which is D+E). Plug those values into the WACC and solve for rE.

And you have the WACC in the formula sheet.

A firm’s WACC is calculated as follows:

𝑟𝐴 = (𝐷/V)𝑟𝐷 + (𝐸/𝑉)𝑟𝐸

where rD and rE are the firm’s costs of debt and equity

capital, respectively, V is the value of the firm, and D and E are the respective values of the firm’s outstanding debt and equity.

Suppose the expected one-year return of the market is 8%, the standard deviation of market returns is 10%, and the risk-free one-year return is 2%.

(a) Project X has an expected one year return of 11% and a standard deviation of 25%.What is the correlation between the returns of project X and the market

returns?

(b) If project Y makes a guaranteed payment of 100 in one year, what is project Y worth today?

(c) If project Z has the same risk characteristics as project X and has an expected payoff of 100 in one year, what is project Z worth today?

(a) First calculate the beta of project X: (0.11−0.02) /

(0. 08−0.02) = 1.5

Rearrange the equation to:

𝛽𝑖,𝑃 = 𝜎𝑖 /𝜎𝑃 𝜌𝑖,𝑃 to give 𝜌𝑖𝑃 = 𝜎𝑃 / 𝜎𝑖 𝛽𝑖,𝑃 = 0.1 / 0.25 × 1.5 = 0.6

(b) 100/1.02 = 98.039

(c) 100/1.11 = 90.09

Formula: Beta. The beta of stock i with respect to portfolio P is

𝛽𝑖,𝑃 = 𝜎𝑖,𝑃/𝜎^{2}𝑃 = 𝜎𝑖/𝜎𝑃 = 𝜌𝑖,𝑃

where 𝜎𝑖,𝑃 is the covariance of the stock’s returns with

those of the portfolio, σi and σP are the standard deviation of returns for the stock and the portfolio, respectively, and 𝜌𝑖,𝑃 is the correlation coefficient between the returns of the stock and those of the portfolio.

The following table shows the expected return (μ) and the standard deviation of returns (σ ) for two stocks. The correlation of returns between stock A and stock B is 0.6.

__________________________________________

Stock Expected Return Standard Deviation of Ret

(μ) (σ)

__________________________________________

A 12% 18%

B 20% 28%

__________________________________________

Compute the expected return and the standard deviation of returns for a portfolio whose value is comprised 30% of stock A, and 70% of stock B.

Expected return is:

0.176=0.3*0.12+0.7*0.2

We can sum:

(0.3)^2*(0.18)^2 + (0.7)^2*(0.28)^2 + 2*(0.3)*(0.7)*(0.18)*(0.28)*(0.6)

The sum is the variance of returns, 0.0540328. The standard deviation of returns is 23.24%.

Formulas:

Expected return of a portfolio. The return of a portfolio

comprising stocks 1, 2, 3,…, N, whose weightings in the

portfolio are x1, x2, x3, …, xN and whose returns are r1, r2, r3,…, rN, respectively, is 𝑟𝑃 ≡ 𝑥1𝑟1 + 𝑥2𝑟2 + 𝑥3𝑟3 … 𝑥𝑁 𝑟𝑁, and the expected return is here μ1, μ2, μ3, …, μN are the expected returns of stocks 1, 2, 3, …, N, respectively.

Variance and standard deviation of returns. If an investment has possible returns R1, R2,…, RN, with

respective probabilities p1, p2,…, pN, its variance of

returns is:

𝑁

𝜎2 = ∑ 𝑝𝑖(𝑅𝑖 − 𝜇)2

i=1

where μ is the investment’s expected return. The investment’s standard deviation of returns is the square root of the variance of those returns.

Hetta is sportswear chain. It generates annual EBIT of $1,000,000, and this figure is not expected to change. It makes capital investments of $200,000 each year,

and its annual depreciation charge is $200,000; its working capital balances are constant. Hetta is entirely equity financed, and has 2,000,000 shares outstanding.

Hetta has an equity beta of 1.2, the risk-free rate is 2%, the market risk premium is 5%, and the corporate tax rate is 40%.

i. What is the Hetta’s share price? [5 marks]

ii. Suppose that Hetta now borrows $3,000,000 of perpetual debt that pays a coupon of 4%, and that it uses the debt to buy back shares at a price that

renders shareholders indifferent between selling and not selling. How many shares remain after the buy-back and what is the market price per share

at that point? [5 marks]

i. Annual Free Cash Flow:

FCF = EBIT 1 − 𝜏) + Depreciation - Capex - ChWC

= 1,000,000(1 − 0.4) + 200,000 − 200,000 − 0 = 600,000

Formula = Free Cash Flow

Cost of capital: 2% + 1.2 × 5% = 8%. Hence the business is worth 600,000 / 0.08 = 7,500,000

and the share price is

7,500,000 / 2,000,000 = 3.75

Formula = WACC

ii. The value of the company before the buyback is 7,500,000 + 3,000,000 × 40% = 8,700,000 and the share price is 8,700,000 / 2,000,000 = 4.35.

The number of shares after the buyback

is2,000,000 − (3,000,000/4.35) = 1,310,344.828.

The value of equity after the

buyback is 8,700,000 − 3,000,000 = 5,700,000. We can confirm that the share price

after the buyback is 5,700,000 / 1,310,344.828 = 4.35.

Firm F is in default but will be worth 100 or 20 with equal probability after one period, and the interest rate is zero. The liquidation value of F now is 40. The senior creditors are owed 50 and the junior creditors are owed 10. Explain how in this case an economically viable company may be inefficiently liquidated if absolute priority is respected.

Value of F now = (100 + 20)/2 = 60 > liquidation value of 40. Payoff to Cs afterone period = 0.5(50+20)=35<40, so they will liquidate.

Suppose you were to receive a monthly payment of 200 for 36 months, and the monthly cost of capital was 0.3%. What is the present value of this stream of payments? [4 marks]

200/0.003 - ((200/0.003)*(1/1.003^36)) = 6815.15

In initial public offerings, stabilization:

(a) Is the tendency for investors in IPOs to keep their shares for the long term.

(b) Is the tendency for IPO fees to remain stable over time.

(c) Guarantees the issuer a minimum price for an IPO.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(h) None of the above

Explain how you would create a volatility spread trading strategy using options, and draw the payoff diagram for such a strategy. Why would a trader use this strategy? [6 marks]

Buy a straddle and sell a strangle. It looks like a V with horizontal lines sticking out at the sides. Traders buy them when they anticipate moderate volatility. We will

allow students to describe a reverse volatility spread: sell straddle, buy strangle; picture flipped. and short volatility but with protection against big swings. Of course, there are other ways to create a volatility spread: Buy low strike call, sell two mid-strike calls, buy high-strike call, for example. Any of those will do just as well.

Credit rating agencies:

(a) Own a fraction of structured finance products that they rate.

(b) Ignore pension liabilities of a corporation when conducting their analysis on a

corporate bond.

(c) Ignore the governance of a corporation when conducting their analysis on a corporate

bond.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(h) None of the above

If you short a call option:

(a) You have unlimited downside.

(b) This will be a hedge if the only other asset in your portfolio is a long put option with

the same strike price.

(c) …and are long a put option with the same strike price, you are creating a straddle.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(a) You have unlimited downside.

Consider an individual portfolio of stocks X and Y.

(a) What happens to the risk of the portfolio as we decrease the correlation between X

and Y? Explain briefly.

(b) What happens to the return of the portfolio as we decrease the correlation between X

and Y? Explain briefly.

(c) Is it possible to have a portfolio of X and Y that has zero risk? Explain briefly.

a) The risk decreases as the portfolio becomes more diversified.

b) There is no effect on the return.

c) Yes it is possible. The stocks must be perfectly negatively correlated and the weights must

be adjusted perfectly to match their variances.

The IRR investment rule states that you should accept a project if its IRR (internal rate

of return) is higher than the cost of capital. Explain why this rule is equivalent to saying

that the project has a positive NPV (net present value).

The IRR is the discount rate at which the NPV of the cashflows is zero. The cost of capital

is the correct rate to discount the cashflows. If the cost of capital is lower than the IRR the

NPV of the cashflows will be therefore be positive.

Give three reasons why IRR can be a misleading approach to project appraisal.

- If positive cashflows come first, the IRR rule doesn’t work.
- If there is more than one

change of sign in the cashflows, there can be more than one IRR. - IRR can be rigged by

changing the timing of the cashflows.

Define the payback method of project appraisal and state one of its disadvantages.

The payback period is the time it takes for the cumulative earnings of a project to become

positive. It does not discount the cashflows to the present.

In initial public offerings, underpricing:

(a) Is the banks’ method of guaranteeing the proceeds of the offering to the issuer.

(b) Means the same as the ‘gross spread’.

(c) Can be negative.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Can be negative.

Regarding the Capital Asset Pricing Model:

(a) The Capital Market Line plots a stock’s idiosyncratic risk against its expected return.

(b) If prices are perfectly efficient, all stocks should lie on the Security Market Line.

(c) The returns on small-cap stocks in fact tend to be above the Security Market Line.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(e) (b) and (c)

Regarding Credit Rating Agencies’ relationships with issuers:

(a) Longer relationships result on average in higher ratings.

(b) Longer relationships imply that the firm is riskier.

(c) Longer relationships facilitate the transmission of information between the CRA and

the issuer.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(f) (a) and (c)

If you short a put option:

(a) You have unlimited downside.

(b) This will be a hedge if the only other asset in your portfolio is a long call option.

(c) And are long a call option with the same strike price, you replicate a forward/future.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) And are long a call option with the same strike price, you replicate a forward/future.

Firm F is in default but will be worth 200 or 80 with equal probability after one period, and the interest rate is zero. The liquidation value of F now is 120. The senior

creditors are owed 150 and the junior creditors are owed 50. Explain how in this case an economically viable company may be inefficiently liquidated.

Value of F now = (200 + 80)/2 = 140 > liquidation value of 120. PV of expected payoff to Cs after one period=0.5(150+80)=115<120, so they will liquidate.

Suppose Jupiter Co.’s stock price is currently 42. At the end of 1 year, Jupiter Co.’s stock price will either be 50 or 40. The risk free rate for one year is 5%.

(a) What is the current value of a call option with a strike price of 45 with an expiry date

in 1 year on Jupiter Co.?

(b) Describe what financial instruments would replicate the payoff in one year of a call

option on Jupiter with a strike price of 45 minus a share of Jupiter stock. You may

assume the stock pays no dividends.

(a) 50Δ + 1.05B = 5 and 40 Δ + 1.05B = 0 imply that Δ=.5 and B=-19.05. The value of the

call option is 42(.5) – 19.05 = 1.95

(b) From put-call parity, a call with strike price 45 - share = put with strike price 45 – zero coupon risk free bond with face value 45.

Teleco’s WACC is 9%. The risk free rate is 3%.

If Teleco had 10% debt (and that debt was riskless) and 90% equity, what would its

equity cost of capital be?

[

.09 = .1(.03) + .9rE gives us rE=.0967

Teleco’s WACC is 9%. The risk free rate is 3%.

If the Modigliani Miller assumptions hold, would Teleco prefer to be 100% equity financed or 90% equity financed? Explain briefly.

If the Modigliani Miller assumptions hold, Teleco doesn’t have a preference over how its capital structure is set as it doesn’t change the value of the firm.

Suppose Firm XYZ uses copper as a primary input. Describe Firm XYZ’s risk and four ways it could hedge that risk.

Firm XYZ faces the risk that the copper price rises, and can hedge that risk by buying copper and storing it, buying a copper mine, buying a forward/future, or buying a call option on copper.

You plan to undertake a project for which the standard deviation of returns is expected to be 40%. The expected return of the market portfolio is 10%, the standard deviation of the market portfolio is 20%, the risk-free rate is 2%, and the correlation of returns between your project and those of the market portfolio is expected to be

0.75. Assuming that the Capital Asset Pricing Model holds, what is the expected return on the project?

𝛽 = 0.4 / 0.2 × 0.75 = 1.5; 𝐸(𝑟) = 0.02 + 1.5 × 0.08 = 0.14 = 14%

An internet company that is publicly listed has a capital structure with only 2% debt.

Define the tradeoff theory and use it to explain why the company has so little debt.

The tradeoff theory states that firms have an optimal amount of leverage that trades off the tax shield of debt and the cost of bankruptcy. The internet company’s value is tied to its human capital, if it enters financial distress, its employees will leave and destroy a lot of the firm’s value.

The current price of silver is £20 per troy ounce. It costs 40 pence to safely store a troy ounce of silver per year and the convenience of having a troy ounce of silver per

year is worth 20 pence. The risk free rate for 1 year is 2%. What is the futures price of a troy ounce of silver one year from now?

F=S0(1 + r + storage - convenience yield)t

F=20(1 + .02 + (.4/20) - (.2/20)) = 20.6 or 20(1+.02) +.4-.2 =20.6

Suppose stock Hec has a current share price of £25. The share price can go up or down 1 period from now. If it goes up, it will go to £35 for sure, and if it goes down it

will go to £20 for sure. The risk free interest rate is 5% annualized. How much will a European put option with a strike price of £30 cost now?

35Δ + 1.05B =0, 20Δ + 1.05B = 10 implies Δ=-.66 and B = 22. The put price is then 25(-.66) +22 = 5.5

Explain how you would create a volatility spread trading strategy using options, and draw the payoff diagram for such a strategy. Why would a trader use this strategy?

Buy a straddle and sell a strangle. It looks like a V with horizontal lines sticking out at the sides.

Traders buy them when they anticipate moderate volatility. We will allow students to describe a reverse volatility spread: sell straddle, buy strangle; picture

flipped. and short volatility but with protection against big swings.

Of course, there areother ways to create a volatility spread: Buy low strike call, sell two mid-strike calls,

buy high-strike call, for example. Any of those will do just as well.

Suppose you were to receive a monthly payment of 200 for 36 months, and the monthly cost of capital was 0.3%.

What is the present value of this stream of payments?

200/0.003 - ((200/0.003)*(1/1.003^36)) = 6815.15

The Credit Rating industry is very concentrated (there are very few important firms) because of:

(a) An artificial barrier to entry from regulation

(b) A natural barrier to entry due to technology costs

(c) Lack of demand for ratings

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(a) An artificial barrier to entry from regulation

In bookbuilt IPOs

(a) Shares are allocated to all investors at the price at which they bid

(b) Investors may state a maximum price limit at which they will buy shares

(c) Investors bid anonymously for shares

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(b) Investors may state a maximum price limit at which they will buy shares

A commodity futures contract

(a) Gives the owner of the contract the option to buy the commodity at an agreed date

(b) Can never be loss making for the owner of the contract

(c) Can be used by the owner of the contract to hedge commodity price risk

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Can be used by the owner of the contract to hedge commodity price risk

A stock pays a 3% dividend per year and has a current price of 150, while the yearly interest rate is 5%. What is the current futures price for delivery of the stock in 2 years?

F = 150(1 + .05 - .03)2 = 156.06

Briefly discuss how a mortgage backed security can transform risky mortgages into low risk securities.

The mortgage backed security changes the priority structure of the mortgages, creating safe securities which only default if multiple underlying mortgages default.

Credit Ratings

(a) Translate directly into a projected probability that a bond will default

(b) Can be investment grade for mortgage backed securities where all of the underlying mortgages are

subprime

(c) May be inflated due to competition between rating agencies

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(a) Translate directly into a projected probability that a bond will default

In initial public offerings (in general):

(a) US banks charge higher fees than European banks in both the US and Europe.

(b) Banks charge higher fees in Europe than in the US.

(c) Banks charge higher fees in the US than in Europe.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Banks charge higher fees in Europe than in the US.

Being short a call option on stock X:

(a) Is in all situations a hedge.

(b) Has potential unlimited downside.

(c) Is a hedge if you are long a put option on stock X.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Is a hedge if you are long a put option on stock X.

In initial public offerings

(a) The bookbuilding technique is used in the US, but rarely elsewhere.

(b) Fees to syndicate banks are generally paid by investors, not issuers.

(c) First-day returns are usually positive.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) First-day returns are usually positive.

In a semi-strong efficient market, the current price of a security

(a) Reflects all publicly available information except information about past prices.

(b) Reflects all publicly available information.

(c) Allows traders without private information to predict share price movements.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(b) Reflects all publicly available information.

All Residential Mortgage Backed Securities

(a) Are always rated AAA.

(b) Only have subprime loans in the underlying asset pool.

(c) Will default if any of the loans in the underlying asset pool default.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(h) None of the above

Firm F is in default but will be worth 100 or 20 with equal probability after one period, and the interest rate is zero. The liquidation value of F now is 40. The senior creditors are owed 50 and the junior creditors are owed 10.

(a) Explain how in this case an economically viable company may be inefficiently liquidated.

Now suppose that the senior creditors convert 10 of their debt into a 50% equity stake in F, and

that the junior creditors convert all their debt into the other 50% of the equity.

(b) Will the company be liquidated? Why or why not?

a. Value of F now = (100 + 20)/2 = 60 > liquidation value of 40. PV of expected payoff to Cs after one period=0.5(50+20)=35<40, so they will liquidate.

b. Now Cs are owed 40 and Cj write off their debt. PV of expected payoff to Cs after one period=0.5(40+30)+(0.5)20=45; PV of expected payoff to Cj=(0.5)30+(0.5)0=15

Total=60>40

Company ABC has a market capitalization of 60 million and it is entirely equity financed. The equity beta of ABC is 1.2, the risk-free rate is 5% and the market risk premium is 6%. The corporate tax rate is 35%.

a) What is the ABC’s cost of capital?

b) Suppose that ABC will generate a free cash flow (FCF) of 1 million in one year, which is then expected to grow at a constant rate g forever.

i. Which rate of growth g would justify the current valuation of the company?

ii. Assuming that annual depreciation is 100,000 and the working capital balance is constant, what will be the earnings before interest and taxes (EBIT) of ABC next year?

a) The cost of capital, using the CAPM, is: 5%+1.2*6%=12.2%

b)

i. 60,000,000=1,000,000/(0.122-g) g=10.53%

ii. FCF=EBIT(1-t)+depreciation

1,000,000=EBIT(1-0.35)+100,000 → EBIT=1,384,615.38

Net Working Capital - briefly define

Is the difference between current assets and current liabilities. It is important for capital budgeting calculations because the EBIT calculation on which the NPV is based assumes that raw materials are paid for precisely when they are used, and that they are sold and paid for as soon as they are manufactured. Incorporating changes to the working capital into the NPV calculation corrects for this assumption.

Systemic Risk - briefly define

The part of the risk of an investment which derives from exposure to the

market portfolio. This is the risk which cannot be diversified away.

Capital Structure - briefly define

Is the mix of debt and equity that the company uses to finance itself.

Is it correct to interpret the Modigliani-Miller propositions as saying that capital structure is irrelevant? Why?

The first Modigliani Miller (MM) Proposition states that, in a Modigliani Miller world, the way that a corporation’s value is unaffected by its capital structure; the second MM Proposition says that the corporate cost of capital is unaffected by capital structure.

It is wrong to interpret the MM propositions as saying that capital structure is irrelevant in the real world; rather, you should interpret them as statements about under what circumstances capital structure is important.

If the forward price of the dollars to euro exchange rate for two years from now is 1.5 $/€, the interest rate in the eurozone is 1% per year, and the interest rate in the U.S. is 2% per year, what is the current exchange rate of dollars for euros?

1.5= (current spot exchange price)( 1.02/1.01)2

This gives us a current spot exchange rate of 1.47$/€.

Name two real-world factors that are assumed away in a Modigliani-Miller world and describe how they can provide a motivation for risk management by a firm.

Possible answers: asymmetric information (firm knows more than investors about what risks to hedge); transaction costs/scale (firm can hedge more efficiently than investors), Bankruptcy costs (can avoid inefficiently costly bankruptcy); agency costs (may make performance more transparent and easier to provide incentives); tax (can reduce tax costs if there is a convex tax schedule).

Suppose silver is an input to your production process. Describe four ways you could hedge silver price risk.

Possible answers: buying now and storing, purchasing a silver mine or part of a silver company, writing a contract with someone to deliver silver at a fixed price in the future (can be a repeated contract), a forward or futures contract, or call options.

Credit Ratings

(a) Predict the expected return on the asset they are rating.

(b) From S&P, Moody’s, and Fitch are paid for by investors.

(c) Will not be reported to the market by Credit Rating Agencies if an issuer does not want them to be.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Will not be reported to the market by Credit Rating Agencies if an issuer does not want them to be.

A futures contract

(a) Is a security issued by a firm to raise capital.

(b) Tells you what the market price of the underlying asset will be on the date when it is due

for delivery.

(c) Allows the buyer of the contract to fix the price now at which to buy the underlying asset in the future.

(d) (a) and (b)

(e) (b) and (c)

(f) (a) and (c)

(g) (a), (b), and (c)

(h) None of the above

(c) Allows the buyer of the contract to fix the price now at which to buy the underlying asset in the future.

Firm F is in default but will be worth 80 or 40 with equal probability after one period, and the interest rate is zero. The liquidation value of F today is 65. The senior

creditors are owed 70 and the junior creditors are owed 50.

Show how, in a bankruptcy regime with structured bargaining, this firm might be inefficiently allowed to continue.

F should be liquidated now because E(F) =0.5(80) + 0.5(40) = 60 < 65. If strict priority were respected liquidation would happen, because the senior

creditors would choose that, given that the liquidation value to them = 65 > their expected value from continuation = E(Cs) = 0.5(70) + 0.5(40) = 55.

With structured bargaining the junior creditors have a say. For them the value on liquidation = 0 < their expected value from continuation = E(Cj) = 0.5(10) + 0.5(0) = 5, so they opt to continue.

When a firm is in financial distress, what is the difficulty with attracting new creditors and how is this resolved in Chapter 11?

With debt overhang the value of a firm would be increased if a new creditor lent it money (e.g. by allowing it to invest in positive NPV projects), but the

existing senior creditors refuse to give that new creditor priority over themselves, so the opportunity to increase value is foregone.

Under Chapter 11, senior creditors to a firm are forced to accept new lenders ranking above them (‘super-senior’ creditors offering ‘debtor-in-possession’ financing), removing the debt overhang problem.

A stock pays a 3% dividend per year and has a current price of 25, while the yearly risk free interest rate is 4%. What is the current price per share of a four year futures contract on the stock?

F = 25(1 + .04 – .03)4 = 26.015

What is the standard reason for why firms should not hedge their risks?

Firms do not need to hedge risks if their shareholders can hedge themselves.

Buying a Put Option gives the holder the right to…

Sell a stock at a certain price

Buying a Call Option gives the holder the right to…

Buy a stock at a certain price

Alpha definition:

Alpha is the excess return (also known as the active return), an investment or portfolio achieves, above and beyond a market index or benchmark that represent the market’s broader movements.

Beta defition:

Beta is a measurement of the volatility, or systematic risk of a security or portfolio, compared to the market as a whole.

Often referred to as the beta coefficient, beta is a key component in the capital asset pricing mode (CAPM), which calculates the theoretically appropriate required rate of return of an asset, to make it worth incorporating into an investment portfolio.