Fight Finance

Question 1  NPV

Jan asks you for a loan. He wants $100 now and offers to pay you back $120 in 1 year. You can borrow and lend from the bank at an interest rate of 10% pa, given as an effective annual rate.

Ignore credit risk. Remember:

### V_0 = \frac{V_t}{(1+r_\text{eff})^t} ###

Will you or Jan's deal?

Question 151  income and capital returns

A share was bought for $30 (at t=0) and paid its annual dividend of $6 one year later (at t=1).

Just after the dividend was paid, the share price fell to $27 (at t=1). What were the total, capital and income returns given as effective annual rates?

The choices are given in the same order:

##r_\text{total}## , ##r_\text{capital}## , ##r_\text{dividend}##.

(a) -0.1, -0.3, 0.2.

(b) -0.1, 0.1, -0.2.

(c) 0.1, -0.1, 0.2.

(d) 0.1, 0.2, -0.1.

(e) 0.2, 0.1, -0.1.

Question 163  bond pricing, premium par and discount bonds

Bonds X and Y are issued by different companies, but they both pay a semi-annual coupon of 10% pa and they have the same face value ($100), maturity (3 years) and yield (10%) as each other.

Which of the following statements is true?

(a) Bonds X and Y are premium bonds.

(b) Bonds X and Y are discount bonds.

(c) Bond X is a discount bond but bond Y is a premium bond.

(d) Bond X is a premium bond but bond Y is a discount bond.

(e) Bonds X and Y are par bonds.

Question 267  term structure of interest rates

A European company just issued two bonds, a

• 3 year zero coupon bond at a yield of 6% pa, and a
• 4 year zero coupon bond at a yield of 6.5% pa.

What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

(a) 0.1634

(b) 0.0801

(c) 0.0704

(d) 0.07

(e) 0.0095

Question 370  capital budgeting, NPV, interest tax shield, WACC, CFFA

Project Data
Project life	2 yrs
Initial investment in equipment	$600k
Depreciation of equipment per year	$250k
Expected sale price of equipment at end of project	$200k
Revenue per job	$12k
Variable cost per job	$4k
Quantity of jobs per year	120
Fixed costs per year, paid at the end of each year	$100k
Interest expense in first year (at t=1)	$16.091k
Interest expense in second year (at t=2)	$9.711k
Tax rate	30%
Government treasury bond yield	5%
Bank loan debt yield	6%
Levered cost of equity	12.5%
Market portfolio return	10%
Beta of assets	1.24
Beta of levered equity	1.5
Firm's and project's debt-to-equity ratio	25%

Notes

1. The project will require an immediate purchase of $50k of inventory, which will all be sold at cost when the project ends. Current liabilities are negligible so they can be ignored.

Assumptions

• The debt-to-equity 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. Note that interest expense is different in each year.
• Thousands are represented by 'k' (kilo).
• 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 nominal. 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?

(a) $684.222k

(b) $690.919k

(c) $697.616k

(d) $698.713k

(e) $710.601k

Question 375  interest tax shield, CFFA

One formula for calculating a levered firm's free cash flow (FFCF, or CFFA) is to use net operating profit after tax (NOPAT).

###\begin{aligned} FFCF &= NOPAT + Depr - CapEx -\Delta NWC \\ &= (Rev - COGS - Depr - FC)(1-t_c) + Depr - CapEx -\Delta NWC \\ \end{aligned} \\###

Does this annual FFCF or the annual interest tax shield?

Question 597  future, continuously compounding rate

A stock is expected to pay a dividend of $5 per share in 1 month and $5 again in 7 months.

The stock price is $100, and the risk-free rate of interest is 10% per annum with continuous compounding. The yield curve is flat. Assume that investors are risk-neutral.

An investor has just taken a short position in a one year forward contract on the stock.

Find the forward price ##(F_1)## and value of the contract ##(V_0)## initially. Also find the value of the short futures contract in 6 months ##(V_\text{0.5, SF})## if the stock price fell to $90.

(a) ##F_1=110.5171, V_0=0, V_\text{0.5, SF}=14.7829##

(b) ##F_1=110.5171, V_0=0, V_\text{0.5, SF}=15.1271##

(c) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=14.7829##

(d) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=20.5171##

(e) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=9.9144##

Question 821  option, option profit, option payoff at maturity, no explanation

You just paid $4 for a 3 month European style call option on a stock currently priced at $47 with a strike price of $50. The stock’s next dividend will be $1 in 4 months’ time. Note that the dividend is paid after the option matures. Which of the below statements is NOT correct?

(a) You have the right to buy the underlying stock in 3 months’ time for a price of $50 if you want.

(b) If the dividend in 4 months were unexpectedly cancelled because the firm decided to re-invest its cash rather than pay it out then the 3 month call option price would be unaffected.

(c) If the stock price is $49 in 3 months then you wouldn’t exercise the ‘out of the money’ option.

(d) If the stock price is $51 in 3 months then you wouldn’t exercise or else you’ll incur a loss of $3.

(e) If the stock price is $57 in 3 months then you would exercise. Your profit would be $3 and payoff at maturity $7.

Question 844  gross domestic product deflator, consumer price index, inflation, no explanation

An Australian-owned company produces milk in New Zealand and exports all of it to China. If the price of the milk increases, which of the following would increase?

(a) Australia’s GDP deflator.

(b) Australia’s CPI.

(c) New Zealand’s CPI.

(d) China’s GDP deflator.

(e) China’s CPI.

Question 969  foreign exchange rate, no explanation

RBA analyst Adam Hamilton wrote in the December 2018 Bulletin article ‘Understanding Exchange Rates and Why They Are Important’ the following passage about bilateral exchange rates:

A bilateral exchange rate refers to the value of one currency relative to another. It is the most commonly referenced type of exchange rate. Most bilateral exchange rates are quoted against the US dollar (USD), as it is the most traded currency globally. Looking at the Australian dollar (AUD), the AUD/USD exchange rate gives you the amount of US dollars that you will receive for each Australian dollar that you convert (or sell). For example, an AUD/USD exchange rate of 0.75 means that you will get US75 cents for every 1 AUD.

An appreciation of the Australian dollar is an increase in its value compared with a foreign currency. This means that each Australian dollar buys you more foreign currency than before. Equivalently, if you are buying an item that is priced in foreign currency it will now cost you less in Australian dollars than before. If there is a depreciation of the Australian dollar, the opposite is true.

Based on this information, which of the following statements is NOT correct?

(a) 'US75 cents for every 1 AUD’ is an American terms quote of the AUD.

(b) 'US75 cents for every 1 AUD’ is equivalent to 0.75AUD per USD.

(c) The AUD would have appreciated against the USD if the quote moved from US75 to US80 cents for every 1 AUD.

(d) Importers of US goods into Australia would pay less in AUD and be happy if the exchange rate moved from US75 to US80 cents for every 1 AUD, all other things remaining equal.

(e) Exporters of Australian goods into the USA would receive less in AUD and be unhappy if the exchange rate moved from US75 to US80 cents for every 1 AUD, all other things remaining equal.