# Fight Finance

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Your friend just bought a house for $400,000. He financed it using a$320,000 mortgage loan and a deposit of $80,000. In the context of residential housing and mortgages, the 'equity' tied up in the value of a person's house is the value of the house less the value of the mortgage. So the initial equity your friend has in his house is$80,000. Let this amount be E, let the value of the mortgage be D and the value of the house be V. So $V=D+E$.

If house prices suddenly fall by 10%, what would be your friend's percentage change in equity (E)? Assume that the value of the mortgage is unchanged and that no income (rent) was received from the house during the short time over which house prices fell.

Remember:

$$r_{0\rightarrow1}=\frac{p_1-p_0+c_1}{p_0}$$

where $r_{0-1}$ is the return (percentage change) of an asset with price $p_0$ initially, $p_1$ one period later, and paying a cash flow of $c_1$ at time $t=1$.

A project has an internal rate of return (IRR) which is greater than its required return. Select the most correct statement.

The following is the Dividend Discount Model used to price stocks:

$$p_0=\frac{d_1}{r-g}$$

All rates are effective annual rates and the cash flows ($d_1$) are received every year. Note that the r and g terms in the above DDM could also be labelled as below: $$r = r_{\text{total, 0}\rightarrow\text{1yr, eff 1yr}}$$ $$g = r_{\text{capital, 0}\rightarrow\text{1yr, eff 1yr}}$$ Which of the following statements is NOT correct?

When someone says that they're "buying American dollars" (USD), what type of asset are they probably buying? They're probably buying:

One year ago you bought $100,000 of shares partly funded using a margin loan. The margin loan size was$70,000 and the other $30,000 was your own wealth or 'equity' in the share assets. The interest rate on the margin loan was 7.84% pa. Over the year, the shares produced a dividend yield of 4% pa and a capital gain of 5% pa. What was the total return on your wealth? Ignore taxes, assume that all cash flows (interest payments and dividends) were paid and received at the end of the year, and all rates above are effective annual rates. Hint: Remember that wealth in this context is your equity (E) in the house asset (V = D+E) which is funded by the loan (D) and your deposit or equity (E).  Project Data Project life 1 year Initial investment in equipment$6m Depreciation of equipment per year $6m Expected sale price of equipment at end of project 0 Unit sales per year 9m Sale price per unit$8 Variable cost per unit $6 Fixed costs per year, paid at the end of each year$1m Interest expense in first year (at t=1) $0.53m Tax rate 30% Government treasury bond yield 5% Bank loan debt yield 6% Market portfolio return 10% Covariance of levered equity returns with market 0.08 Variance of market portfolio returns 0.16 Firm's and project's debt-to-assets ratio 50% Notes 1. Due to the project, current assets will increase by$5m now (t=0) and fall by $5m at the end (t=1). Current liabilities will not be affected. Assumptions • The debt-to-assets ratio will be kept constant throughout the life of the project. The amount of interest expense at the end of each period has been correctly calculated to maintain this constant debt-to-equity ratio. • Millions are represented by 'm'. • All cash flows occur at the start or end of the year as appropriate, not in the middle or throughout the year. • All rates and cash flows are real. The inflation rate is 2% pa. • All rates are given as effective annual rates. • The 50% capital gains tax discount is not available since the project is undertaken by a firm, not an individual. What is the net present value (NPV) of the project? An Apple iPhone 6 smart phone can be bought now for$999. An Android Kogan Agora 4G+ smart phone can be bought now for $240. If the Kogan phone lasts for one year, approximately how long must the Apple phone last for to have the same equivalent annual cost? Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is 10% pa given as an effective annual rate, and there are no extra costs or benefits from either phone. Which of the following statements about an option (either a call or put) and its underlying stock is NOT correct?  European Call Option on a non-dividend paying stock Description Symbol Quantity Spot price ($) $S_0$ 20 Strike price ($) $K_T$ 18 Risk free cont. comp. rate (pa) $r$ 0.05 Standard deviation of the stock's cont. comp. returns (pa) $\sigma$ 0.3 Option maturity (years) $T$ 1 Call option price ($) $c_0$ 3.939488 Delta $\Delta = N[d_1]$ 0.747891 $N[d_2]$ $N[d_2]$ 0.643514 Gamma $\Gamma$ 0.053199 Theta ($/year) $\Theta = \partial c / \partial T$ 1.566433 Question 860 idiom, hedging, speculation, arbitrage, market making, insider trading, no explanation Which class of derivatives market trader is NOT principally focused on ‘buying low and selling high’? A one year European-style call option has a strike price of$4.

The option's underlying stock currently trades at \$5, pays no dividends and its standard deviation of continuously compounded returns is 47% pa.

The risk-free interest rate is 10% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is: