Fight Finance

Question 37  IRR

If a project's net present value (NPV) is zero, then its internal rate of return (IRR) will be:

(a) Positive infinity (##+\infty##)

(b) Zero (0).

(c) Less than the project's required return.

(d) More than the project's required return.

(e) Equal to the project's required return.

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 122  option

You have just sold an 'in the money' 6 month European put option on the mining company BHP at an exercise price of $40 for a premium of $3.

Which of the following statements best describes your situation?

(a) You have bought the right to buy a BHP share for $40 in 6 months.

(b) You have bought the right to sell a BHP share for $40 in 6 months.

(c) You have bought the obligation to sell a BHP share for $40 in 6 months.

(d) You have sold the right that allows your counterparty to buy a BHP share from you for $40 in 6 months. This means that you have the obligation to sell a BHP share to your counterparty for $40 in 6 months if he wants to buy it.

(e) You have sold the right that allows your counterparty to sell a BHP share to you for $40 in 6 months. This means that you have the obligation to buy a BHP share from your counterparty for $40 in 6 months if he wants to sell it.

Question 194  bond pricing, capital raising

A firm wishes to raise $8 million now. They will issue 7% pa semi-annual coupon bonds that will mature in 10 years and have a face value of $100 each. Bond yields are 10% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 107,441

(b) 98,393

(c) 90,480

(d) 80,000

(e) 64,039

Question 274  derivative terminology, option

The 'option price' in an option contract is paid at the start when the option contract is agreed to. or ?

Question 345  capital budgeting, break even, NPV

Project Data
Project life	10 yrs
Initial investment in factory	$10m
Depreciation of factory per year	$1m
Expected scrap value of factory at end of project	$0
Sale price per unit	$10
Variable cost per unit	$6
Fixed costs per year, paid at the end of each year	$2m
Interest expense per year	0
Tax rate	30%
Cost of capital per annum	10%

Notes

1. The firm's current liabilities are forecast to stay at $0.5m. The firm's current assets (mostly inventory) is currently $1m, but is forecast to grow by $0.1m at the end of each year due to the project.
   At the end of the project, the current assets accumulated due to the project can be sold for the same price that they were bought.
2. A marketing survey was used to forecast sales. It cost $1.4m which was just paid. The cost has been capitalised by the accountants and is tax-deductible over the life of the project, regardless of whether the project goes ahead or not. This amortisation expense is not included in the depreciation expense listed in the table above.

Assumptions

• 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 real. The inflation rate is 3% pa.
• All rates are given as effective annual rates.

Find the break even unit production (Q) per year to achieve a zero Net Income (NI) and Net Present Value (NPV), respectively. The answers below are listed in the same order.

(a) 750,000 and 750,000.

(b) 750,000 and 951,682.

(c) 750,000 and 987,396.

(d) 750,000 and 1,009,805.

(e) 750,000 and 1,024,807.

Question 384  option, real option

Which of the following is the least useful method or model to calculate the value of a real option in a project?

(a) Project value with the option less project value without the option.

(b) No-arbitrage binomial option pricing model.

(c) Risk-neutral binomial option pricing model.

(d) Gordon growth model.

(e) Black-Sholes option pricing model.

Question 712  effective rate conversion

An effective monthly return of 1% ##(r_\text{eff monthly})## is equivalent to an effective annual return ##(r_\text{eff annual})## of:

(a) 12.682503% pa

(b) 12.060201% pa

(c) 12% pa

(d) 11.940397% pa

(e) 3.464102% pa

Question 900  Basel accord

Which of the following statements about the Basel 3 minimum capital requirements is NOT correct? Common equity tier 1 (CET1) comprises the highest quality components of capital that fully satisfy all of the following characteristics:

(a) Provide a permanent and unrestricted commitment of funds;

(b) Are freely available to absorb losses;

(c) Impose unavoidable servicing charges against earnings;

(d) Rank behind the claims of depositors and other creditors in the event of winding-up of the issuer.

Question 904  option, Black-Scholes-Merton option pricing, option on future on stock index

A six month European-style call option on six month S&P500 index futures has a strike price of 2800 points.

The six month futures price on the S&P500 index is currently at 2740.805274 points. The futures underlie the call option.

The S&P500 stock index currently trades at 2700 points. The stock index underlies the futures. The stock index's standard deviation of continuously compounded returns is 25% pa.

The risk-free interest rate is 5% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is:

(a) 226.43 points

(b) 220.56 points

(c) 176.21 points

(d) 162.83 points

(e) 128.92 points