# Fight Finance

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Calculate the effective annual rates of the following three APR's:

• A credit card offering an interest rate of 18% pa, compounding monthly.
• A bond offering a yield of 6% pa, compounding semi-annually.
• An annual dividend-paying stock offering a return of 10% pa compounding annually.

All answers are given in the same order:

$r_\text{credit card, eff yrly}$, $r_\text{bond, eff yrly}$, $r_\text{stock, eff yrly}$

When using the dividend discount model to price a stock:

$$p_{0} = \frac{d_1}{r - g}$$

The growth rate of dividends (g):

An Australian company just issued two bonds:

• A 6-month zero coupon bond at a yield of 6% pa, and
• A 12 month zero coupon bond at a yield of 7% pa.

What is the company's forward rate from 6 to 12 months? Give your answer as an APR compounding every 6 months, which is how the above bond yields are quoted.

Find the sample standard deviation of returns using the data in the table:

 Stock Returns Year Return pa 2008 0.3 2009 0.02 2010 -0.2 2011 0.4

The returns above and standard deviations below are given in decimal form.

An investor owns an empty block of land that has local government approval to be developed into a petrol station, car wash or car park. The council will only allow a single development so the projects are mutually exclusive.

All of the development projects have the same risk and the required return of each is 10% pa. Each project has an immediate cost and once construction is finished in one year the land and development will be sold. The table below shows the estimated costs payable now, expected sale prices in one year and the internal rates of returns (IRR's).

 Mutually Exclusive Projects Project Costnow ($) Sale price inone year ($) IRR(% pa) Petrol station 9,000,000 11,000,000 22.22 Car wash 800,000 1,100,000 37.50 Car park 70,000 110,000 57.14

Which project should the investor accept?

A low-quality second-hand car can be bought now for $1,000 and will last for 1 year before it will be scrapped for nothing. A high-quality second-hand car can be bought now for$4,900 and it will last for 5 years before it will be scrapped for nothing.

What is the equivalent annual cost of each car? Assume a discount rate of 10% pa, given as an effective annual rate.

The answer choices are given as the equivalent annual cost of the low-quality car and then the high quality car.

A one year European-style call option has a strike price of $4. The option's underlying stock pays no dividends and currently trades at$5. The risk-free interest rate is 10% pa continuously compounded. Use a single step binomial tree to calculate the option price, assuming that the price could rise to $8 $(u = 1.6)$ or fall to$3.125 $(d = 1/1.6)$ in one year. The call option price now is:

Question 880  gold standard, no explanation

Under the Gold Standard (1876 to 1913), currencies were priced relative to:

Below is a graph showing the spread or difference between government bond yields in different countries compared to the US. Assume that all governments have zero credit risk. According to the principle of cross-currency interest rate parity, which country is likely to have the greatest expected currency appreciation against the USD over the next 2 years?

Question 990  Multiples valuation, EV to EBITDA ratio, enterprise value

A firm has:

2 million shares;

$200 million EBITDA expected over the next year;$100 million in cash (not included in EV);

1/3 market debt-to-assets ratio is (market assets = EV + cash);

4% pa expected dividend yield over the next year, paid annually with the next dividend expected in one year;

2% pa expected dividend growth rate;

40% expected payout ratio over the next year;

10 times EV/EBITDA ratio.

30% corporate tax rate.

The stock can be valued using the EV/EBITDA multiple, dividend discount model, Gordon growth model or PE multiple. Which of the below statements is NOT correct based on an EV/EBITDA multiple valuation?