Fight Finance

Question 50  DDM, stock pricing, inflation, real and nominal returns and cash flows

Most listed Australian companies pay dividends twice per year, the 'interim' and 'final' dividends, which are roughly 6 months apart.

You are an equities analyst trying to value the company BHP. You decide to use the Dividend Discount Model (DDM) as a starting point, so you study BHP's dividend history and you find that BHP tends to pay the same interim and final dividend each year, and that both grow by the same rate.

You expect BHP will pay a $0.55 interim dividend in six months and a $0.55 final dividend in one year. You expect each to grow by 4% next year and forever, so the interim and final dividends next year will be $0.572 each, and so on in perpetuity.

Assume BHP's cost of equity is 8% pa. All rates are quoted as nominal effective rates. The dividends are nominal cash flows and the inflation rate is 2.5% pa.

What is the current price of a BHP share?

(a) $57.1734

(b) $28.0394

(c) $27.7723

(d) $27.5000

(e) $27.2330

Question 65  annuity with growth, needs refinement

Which of the below formulas gives the present value of an annuity with growth?

(a) ##\dfrac{C_1}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

(b) ##\dfrac{C_1(1+g)^T}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

(c) ##\dfrac{C_1}{r-g}\left(1-\dfrac{1+g}{(1+r)^T}\right)##

(d) ##\dfrac{C_1}{r-g}\left(1-\left(\dfrac{1+g}{1+r}\right)^T \right)##

(e) ##\dfrac{C_1(1+g)}{r-g}\left(1-\dfrac{1}{(1+r)^T}\right)##

Hint: The equation of a perpetuity without growth is: ###V_\text{0, perp without growth} = \frac{C_\text{1}}{r}###

The formula for the present value of an annuity without growth is derived from the formula for a perpetuity without growth.

The idea is than an annuity with T payments from t=1 to T inclusive is equivalent to a perpetuity starting at t=1 with fixed positive cash flows, plus a perpetuity starting T periods later (t=T+1) with fixed negative cash flows. The positive and negative cash flows after time period T cancel each other out, leaving the positive cash flows between t=1 to T, which is the annuity.

###\begin{aligned} V_\text{0, annuity} &= V_\text{0, perp without growth from t=1} - V_\text{0, perp without growth from t=T+1} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{T+1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r} - \dfrac{ \left( \dfrac{C_\text{1}}{r} \right) }{(1+r)^T} \\ &= \dfrac{C_\text{1}}{r}\left(1 - \dfrac{1}{(1+r)^T}\right) \\ \end{aligned}###

The equation of a perpetuity with growth is:

###V_\text{0, perp with growth} = \dfrac{C_\text{1}}{r-g}###

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 432  option, option intrinsic value, no explanation

An American style call option with a strike price of ##K## dollars will mature in ##T## years. The underlying asset has a price of ##S## dollars.

What is an expression for the current intrinsic value in dollars from owning (being long) the American style call option? Note that the intrinsic value of an option does not subtract the premium paid to buy the option.

(a) ##\min(S_0 - K, 0)##.

(b) ##\min(K-S_0, 0)##.

(c) ##\max(S_0-K, 0)##.

(d) ##\max(K-S_0, 0)##.

(e) ##\max(K, S_0)##.

Question 679  option, no explanation

A trader sells one crude oil European style call option contract on the CME expiring in one year with an exercise price of $44 per barrel for a price of $6.64. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before maturity, then at maturity she will have the:

(a) Obligation to buy the underlying oil at $44 per barrel.

(b) Obligation to sell the underlying oil at $44 per barrel.

(c) Right to sell the underlying oil at $44 per barrel if she wants.

(d) Obligation to buy the underlying oil $44 per barrel if the counterparty chooses to sell it.

(e) Obligation to sell the underlying oil at $44 per barrel if the counterparty chooses to buy it.

Question 768  accounting terminology, book and market values, no explanation

Accountants and finance professionals have lots of names for the same things which can be quite confusing.

Which of the following groups of items are NOT synonyms?

(a) Revenue, sales, turn over.

(b) Paid up capital, contributed equity.

(c) Shares, stock, equity.

(d) Net income, earnings, net profit after tax, the bottom line.

(e) Market capitalisation of equity, book value of equity.

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

Question 801  negative gearing, leverage, capital structure

The following steps outline the process of ‘negative gearing’ an investment property in Australia. Which of these steps or statements is NOT correct? To successfully achieve negative gearing on an investment property:

(a) Buy an investment property with low expected future capital gains and high rental income, funded using a low proportion of debt (mortgage loan).

(b) Rent the investment property to a tenant;

(c) Negative gearing is achieved when the property investment’s annual taxable profit is negative, due to the loan’s interest expense being greater than the net rent (rental revenue less the renting expenses such as maintenance);

(d) Deduct the property’s income loss from the investor’s separate personal wage from labour. This means that the investor will pay less personal income tax than if they didn’t make the levered property investment;

(e) The investment property will be a positive-NPV investment if the capital gains are greater than the income losses on an after-tax, risk-adjusted, present-value basis.

Question 826  future, basis risk, hedging

On 1 February 2016 you were told that your refinery company will need to purchase oil on 1 July 2016. You were afraid of the oil price rising between now and then so you bought some August 2016 futures contracts on 1 February 2016 to hedge against changes in the oil price. On 1 February 2016 the oil price was $40 and the August 2016 futures price was $43.

It's now 1 July 2016 and oil price is $45 and the August 2016 futures price is $46. You bought the spot oil and closed out your futures position on 1 July 2016.

What was the effective price paid for the oil, taking into account basis risk? All spot and futures oil prices quoted above and below are per barrel.

(a) $37

(b) $42

(c) $44

(d) $45

(e) $48

Question 934  standard deviation, risk

Which of the following statements about an asset’s standard deviation of returns is NOT correct? All other things remaining equal, the higher the asset’s standard deviation of returns:

(a) The more risky the asset is from a financial analyst’s perspective.

(b) The higher the chance of a large loss.

(c) The higher the chance of a large gain.

(d) The more predictable the asset’s future price is.

(e) The higher the variance of returns.