Fight Finance

Question 60  pay back period

The required return of a project is 10%, given as an effective annual rate.

What is the payback period of the project in years?

Assume that the cash flows shown in the table are received smoothly over the year. So the $121 at time 2 is actually earned smoothly from t=1 to t=2.

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-100
1	11
2	121

(a) 2.7355

(b) 2.3596

(c) 1.7355

(d) 1.2645

(e) 0.2645

Question 195  equivalent annual cash flow

An industrial chicken farmer grows chickens for their meat. Chickens:

1. Cost $0.50 each to buy as chicks. They are bought on the day they’re born, at t=0.
2. Grow at a rate of $0.70 worth of meat per chicken per week for the first 6 weeks (t=0 to t=6).
3. Grow at a rate of $0.40 worth of meat per chicken per week for the next 4 weeks (t=6 to t=10) since they’re older and grow more slowly.
4. Feed costs are $0.30 per chicken per week for their whole life. Chicken feed is bought and fed to the chickens once per week at the beginning of the week. So the first amount of feed bought for a chicken at t=0 costs $0.30, and so on.
5. Can be slaughtered (killed for their meat) and sold at no cost at the end of the week. The price received for the chicken is their total value of meat (note that the chicken grows fast then slow, see above).

The required return of the chicken farm is 0.5% given as an effective weekly rate.

Ignore taxes and the fixed costs of the factory. Ignore the chicken’s welfare and other environmental and ethical concerns.

Find the equivalent weekly cash flow of slaughtering a chicken at 6 weeks and at 10 weeks so the farmer can figure out the best time to slaughter his chickens. The choices below are given in the same order, 6 and 10 weeks.

(a) $0.3651, $0.2374

(b) $0.3172, $0.3506

(c) $0.3065, $0.2157

(d) $0.3050, $0.2142

(e) $0.0157, $0.0491

Question 298  interest only loan

A prospective home buyer can afford to pay $2,000 per month in mortgage loan repayments. The central bank recently lowered its policy rate by 0.25%, and residential home lenders cut their mortgage loan rates from 4.74% to 4.49%.

How much more can the prospective home buyer borrow now that interest rates are 4.49% rather than 4.74%? Give your answer as a proportional increase over the original amount he could borrow (##V_\text{before}##), so:

###\text{Proportional increase} = \frac{V_\text{after}-V_\text{before}}{V_\text{before}} ###

Assume that:

• Interest rates are expected to be constant over the life of the loan.

• Loans are interest-only and have a life of 30 years.

• Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates compounding per month.

(a) 0.055679

(b) 0.029631

(c) 0.029547

(d) 0.006245

(e) 0.0025

Question 305  option, short selling, speculation

You believe that the price of a share will fall significantly very soon, but the rest of the market does not. The market thinks that the share price will remain the same. Assuming that your prediction will soon be true, which of the following trades is a bad idea? In other words, which trade will NOT make money or prevent losses?

(a) Sell all existing stock that you own.

(b) Short sell the stock.

(c) Buy put options on the stock.

(d) Sell put options on the stock.

(e) Sell call options on the stock.

Question 454  NPV, capital structure, capital budgeting

A mining firm has just discovered a new mine. So far the news has been kept a secret.

The net present value of digging the mine and selling the minerals is $250 million, but $500 million of new equity and $300 million of new bonds will need to be issued to fund the project and buy the necessary plant and equipment.

The firm will release the news of the discovery and equity and bond raising to shareholders simultaneously in the same announcement. The shares and bonds will be issued shortly after.

Once the announcement is made and the new shares and bonds are issued, what is the expected increase in the value of the firm's assets ##(\Delta V)##, market capitalisation of debt ##(\Delta D)## and market cap of equity ##(\Delta E)##? Assume that markets are semi-strong form efficient.

The triangle symbol ##\Delta## is the Greek letter capital delta which means change or increase in mathematics.

Ignore the benefit of interest tax shields from having more debt.

Remember: ##\Delta V = \Delta D+ \Delta E##

(a) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 250##

(b) ##\Delta V = 250m##, ##ΔD = 300m##, ##ΔE= 750##

(c) ##\Delta V = 400m##, ##ΔD = 300m##, ##ΔE= -250##

(d) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 750##

(e) ##\Delta V = 1,050m##, ##ΔD = 300m##, ##ΔE= 250##

Question 709  continuously compounding rate, APR

Which of the following interest rate quotes is NOT equivalent to a 10% effective annual rate of return? Assume that each year has 12 months, each month has 30 days, each day has 24 hours, each hour has 60 minutes and each minute has 60 seconds. APR stands for Annualised Percentage Rate.

(a) 9.7617696% is the APR compounding semi-annually ##(r_\text{apr comp 6mth})##

(b) 9.5689685% is the APR compounding monthly ##(r_\text{apr comp monthly})##

(c) 9.6454756% is the APR compounding daily ##(r_\text{apr comp daily})##

(d) 9.5310182% is the APR compounding per second ##(r_\text{apr comp per second})##

(e) 9.5310180% is the continuously compounded rate per annum ##(r_\text{cc annual})##

Question 723  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Here is a table of stock prices and returns. Which of the statements below the table is NOT correct?

Price and Return Population Statistics
Time	Prices	LGDR	GDR	NDR
0	100
1	99	-0.010050	0.990000	-0.010000
2	180.40	0.600057	1.822222	0.822222
3	112.73	0.470181	0.624889	0.375111
Arithmetic average		0.0399	1.1457	0.1457
Arithmetic standard deviation		0.4384	0.5011	0.5011

 

(a) The geometric average of the gross discrete returns (GAGDR) equals 1.04075 which is 104.075%.

(b) ##\exp \left( \text{GAGDR} \right) = \text{AALGDR}##. The natural exponent of the GAGDR equals the arithmetic average of the logarithms of the gross discrete returns (AALGDR).

(c) ##\text{GAGDR}^T = \left( P_T/P_0 \right)##. The GAGDR raised to the power of the number of time period that it's measured over equals the ratio of the first and last prices.

(d) ##\text{GAGDR} = \exp \left( \text{AALGDR} \right)##. This is always true, regardless of the distribution of the prices or returns. The logarithm of the geometric average of the gross discrete returns (LGAGDR) is always equal to the arithmetic average of the logarithm of the gross discrete returns (AALGDR).

(e) ##\text{AAGDR} \approx \exp \left( \text{AALGDR} + \text{SDLGDR}^2/2 \right)##. This is only approximately true and depends on the distribution of the prices and returns. It's asymptotically true as the time period that the returns are measured over reaches infinity.

Question 762  equivalent annual cash flow, no explanation

Radio-Rentals.com offers the Apple iphone 5S smart phone for rent at $12.95 per week paid in advance on a 2 year contract. After renting the phone, you must return it to Radio-Rentals.

Kogan.com offers the Apple iphone 5S smart phone for sale at $699. You estimate that the phone will last for 3 years before it will break and be worthless.

Currently, the effective annual interest rate is 11.351%, the effective monthly interest rate 0.9% and the effective weekly interest rate is 0.207%. Assume that there are exactly 52 weeks per year and 12 months per year.

Find the equivalent annual cost of renting the phone and also buying the phone. The answers below are listed in the same order.

(a) $362.33,   $287.79

(b) $362.33,   $506.29

(c) $516.29,   $506.29

(d) $673.40,   $233.00

(e) $711.67,   $287.79

Question 886  foreign exchange rate, no explanation

A British man wants to calculate how many British pounds (GBP) he needs to buy a 1 million euro (EUR) apartment in Germany. The exchange rate is 1.42 USD per GBP and 1.23 USD per EUR. What is the EUR 1 million equivalent to in GBP?

(a) GBP 1,746,600

(b) GBP 1,727,012

(c) GBP 1,154,472

(d) GBP 866,197

(e) GBP 572,541

Question 919  duration, bond convexity

Which of the following statements about bond convexity is NOT correct?

(a) Bond holders like convexity, it’s good for them.

(b) Bond issuers like convexity, it’s good for them.

(c) If yields rise, convex bonds lose less value than non-convex bonds of equal duration.

(d) If yields fall, convex bonds gain more value than non-convex bonds of equal duration.