# Fight Finance

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The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

$$P_{0} = \frac{C_1}{r_{\text{eff}} - g_{\text{eff}}}$$

What would you call the expression $C_1/P_0$?

Suppose that the US government recently announced that subsidies for fresh milk producers will be gradually phased out over the next year. Newspapers say that there are expectations of a 40% increase in the spot price of fresh milk over the next year.

Option prices on fresh milk trading on the Chicago Mercantile Exchange (CME) reflect expectations of this 40% increase in spot prices over the next year. Similarly to the rest of the market, you believe that prices will rise by 40% over the next year.

What option trades are likely to be profitable, or to be more specific, result in a positive Net Present Value (NPV)?

Assume that:

• Only the spot price is expected to increase and there is no change in expected volatility or other variables that affect option prices.
• No taxes, transaction costs, information asymmetry, bid-ask spreads or other market frictions.

A wholesale shop offers credit to its customers. The customers are given 21 days to pay for their goods. But if they pay straight away (now) they get a 1% discount.

What is the effective interest rate given to customers who pay in 21 days? All rates given below are effective annual rates. Assume 365 days in a year.

A firm has forecast its Cash Flow From Assets (CFFA) for this year and management is worried that it is too low. Which one of the following actions will lead to a higher CFFA for this year (t=0 to 1)? Only consider cash flows this year. Do not consider cash flows after one year, or the change in the NPV of the firm. Consider each action in isolation.

A 10 year bond has a face value of $100, a yield of 6% pa and a fixed coupon rate of 8% pa, paid semi-annually. What is its price? The 'futures price' in a futures contract is paid at the start when the futures contract is agreed to. or ? Estimate Microsoft's (MSFT) share price using a price earnings (PE) multiples approach with the following assumptions and figures only: • Apple, Google and Microsoft are comparable companies, • Apple's (AAPL) share price is$526.24 and historical EPS is $40.32. • Google's (GOOG) share price is$1,215.65 and historical EPS is $36.23. • Micrsoft's (MSFT) historical earnings per share (EPS) is$2.71.

Source: Google Finance 28 Feb 2014.

In a takeover deal where the offer is 100% scrip (shares), the merged firm's number of shares will be equal to the sum of the acquirer and target firms' original number of shares. or ?

Who is most in danger of being personally bankrupt? Assume that all of their businesses' assets are highly liquid and can therefore be sold immediately.

A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.

 Delta Hedging a Short Call using Stocks and Debt Description Symbol Days to maturity (T in days) 60 59 58 57 56 55 Spot price ($) S 10000 10125 9800 9675 10000 10000 Strike price ($) K 10000 10000 10000 10000 10000 10000 Risk free cont. comp. rate (pa) r 0.05 0.05 0.05 0.05 0.05 0.05 Standard deviation of the stock's cont. comp. returns (pa) σ 0.4 0.4 0.4 0.4 0.4 0.4 Option maturity (years) T 0.164384 0.161644 0.158904 0.156164 0.153425 0.150685 Delta N[d1] = dc/dS 0.552416 0.582351 0.501138 0.467885 0.550649 0.550197 Probability that S > K at maturity in risk neutral world N[d2] 0.487871 0.51878 0.437781 0.405685 0.488282 0.488387 Call option price ($) c 685.391158 750.26411 567.990995 501.487157 660.982878 ? Stock investment value ($) N[d1]*S 5524.164129 5896.301781 4911.152036 4526.788065 5506.488143 ? Borrowing which partly funds stock investment ($) N[d2]*K/e^(r*T) 4838.772971 5146.037671 4343.161041 4025.300909 4845.505265 ? Interest expense from borrowing paid in arrears ($) r*N[d2]*K/e^(r*T) 0.662891 0.704985 0.594994 0.551449 ? Gain on stock ($) N[d1]*(SNew - SOld) 69.052052 -189.264008 -62.642245 152.062648 ? Gain on short call option ($) -1*(cNew - cOld) -64.872952 182.273114 66.503839 -159.495721 ? Net gain (\$) Gains - InterestExpense 3.516209 -7.695878 3.266599 -7.984522 ? Gamma Γ = d^2c/dS^2 0.000244 0.00024 0.000255 0.00026 0.000253 0.000255 Theta θ = dc/dT 2196.873429 2227.881353 2182.174706 2151.539751 2266.589184 2285.1895

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is NOT correct?