Fight Finance

Question 62  implicit interest rate in wholesale credit

A wholesale building supplies business offers credit to its customers. Customers are given 60 days to pay for their goods, but if they pay within 7 days they will get a 2% discount.

What is the effective interest rate implicit in the discount being offered?

Assume 365 days in a year and that all customers pay on either the 7th day or the 60th day. All rates given below are effective annual rates.

(a) 0.000381

(b) 0.129887

(c) 0.137736

(d) 0.149276

(e) 0.278643

Question 189  IRR

A project has the following cash flows:

Project Cash Flows
Time (yrs)	Cash flow ($)
0	-400
1	0
2	500

The required return on the project is 10%, given as an effective annual rate.

What is the Internal Rate of Return (IRR) of this project? The following choices are effective annual rates. Assume that the cash flows shown in the table are paid all at once at the given point in time.

(a) 0.2500

(b) 0.2000

(c) 0.1180

(d) 0.1000

(e) 0.1056

Question 282  expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the expected total return over the next year of shares in a mining company. The mining firm:

• Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
• Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
• Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
• Shares are traded in an active liquid market.

Your team of analysts present their findings, and everyone has different views. While there's no definitive true answer, whose calculation of the expected total return is the most plausible? Assume that:

• The analysts' source data is correct and true, but their inferences might be wrong;
• All returns and yields are given as effective annual nominal rates.

(a) Alice says 5% pa since she calculated that this was the average total yield on government bonds over the last 10 years. She says that this is also the expected total yield implied by current prices on one year government bonds.

(b) Bob says 4% pa since he calculated that this was the average total return on the mining stock over the last 10 years.

(c) Cate says 3% pa since she calculated that this was the average growth rate of the share price over the last 10 years.

(d) Dave says 6% pa since he calculated that this was the average growth rate of the share market price index (not the accumulation index) over the last 10 years.

(e) Eve says 15% pa since she calculated that this was the discount rate implied by the dividend discount model using the current share price, forecast dividend in one year and a 3% growth rate in dividends thereafter, which is the expected long term inflation rate.

Question 360  CFFA

Find Ching-A-Lings Corporation's Cash Flow From Assets (CFFA), also known as Free Cash Flow to the Firm (FCFF), over the year ending 30th June 2013.

Ching-A-Lings Corp
Income Statement for
year ending 30th June 2013
	$m
Sales	100
COGS	20
Depreciation	20
Rent expense	11
Interest expense	19
Taxable Income	30
Taxes at 30%	9
Net income	21

Ching-A-Lings Corp
Balance Sheet
as at 30th June	2013	2012
	$m	$m
Inventory	49	38
Trade debtors	14	2
Rent paid in advance	5	5
PPE	400	400
Total assets	468	445
Trade creditors	4	10
Bond liabilities	200	190
Contributed equity	145	145
Retained profits	119	100
Total L and OE	468	445

 

Note: All figures are given in millions of dollars ($m).

The cash flow from assets was:

(a) $43m

(b) $31m

(c) $23m

(d) $11m

(e) $1m

Question 526  real and nominal returns and cash flows, inflation, no explanation

How can a nominal cash flow be precisely converted into a real cash flow?

(a) ##C_\text{real, t}=C_\text{nominal,t}.(1+r_\text{inflation})^t##

(b) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{(1+r_\text{inflation})^t} ##

(c) ##C_\text{real,t}=\dfrac{C_\text{nominal,t}}{r_\text{inflation}} ##

(d) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation} ##

(e) ##C_\text{real,t}=C_\text{nominal,t}.r_\text{inflation}.t##

Question 531  bankruptcy or insolvency, capital structure, risk, limited liability

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) Alice has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $10,000 and liabilities of $3,000.

(b) Billy has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a corporate business with assets worth $3,000 and liabilities of $10,000.

(c) Carla has $6,000 cash, owes $10,000 credit card debt due immediately and 100% owns a corporate business with assets worth $10,000 and liabilities of $3,000.

(d) Darren has $10,000 cash, owes $6,000 credit card debt due immediately and 100% owns a sole tradership business with assets worth $3,000 and liabilities of $10,000.

(e) Ernie has $1,000 cash, lent $3,000 to his friend, and doesn't have any personal debt or own any businesses.

Question 564  covariance

What is the covariance of a variable X with a constant C?

The cov(X, C) or ##\sigma_{X,C}## equals:

(a) var(X) or ##\sigma_X^2##

(b) sd(X) or ##\sigma_X##

(c) 1

(d) 0

(e) Mathematically undefined

Question 594  future, continuously compounding rate

The current gold price is $700, gold storage costs are 2% pa and the risk free rate is 10% pa, both with continuous compounding.

What should be the 3 year gold futures price?

(a) $758.30

(b) $773.62

(c) $889.87

(d) $944.90

(e) $1,003.33

Question 875  omitted variable bias, systematic and idiosyncratic risk, CAPM, single factor model, two factor model

The Capital Asset Pricing Model (CAPM) and the Single Index Model (SIM) are single factor models whose only risk factor is the market portfolio’s return. Say a Solar electricity generator company and a Beach bathing chair renting company are influenced by two factors, the market portfolio return and cloud cover in the sky. When it's sunny and not cloudy, both the Solar and Beach companies’ stock prices do well. When there’s dense cloud cover and no sun, both do poorly. Assume that cloud coverage risk is a systematic risk that cannot be diversified and that cloud cover has zero correlation with the market portfolio’s returns.

Which of the following statements about these two stocks is NOT correct?

The CAPM and SIM:

(a) Betas of the Solar and Beach companies will only measure the companies’ sensitivity to the market portfolio risk factor, not the cloud coverage factor.

(b) Will under-estimate the Solar and Beach stocks’ systematic variance.

(c) Will under-estimate the Solar and Beach stocks’ diversifiable variance.

(d) Models will show positive correlations between the Solar and Beach stock’s residual (also called idiosyncratic or diversifiable) returns.

Question 905  market capitalisation of equity, PE ratio, payout ratio

The below graph shows the computer software company Microsoft's stock price (MSFT) at the market close on the NASDAQ on Friday 1 June 2018.

Based on the screenshot above, which of the following statements about MSFT is NOT correct? MSFT's:

(a) Earnings per share (EPS) is $3.60.

(b) Dividend per share is $1.68.

(c) Payout ratio is 53.27%.

(d) The market value of equity is $774.39 billion.

(e) Number of shares outstanding is 7.68 billion.