Final Exam Sample Questions

Corporate Finance II, FINC2012

Semester 2, 2015

Note: This sample question should only be used as a guide to the styles of final exam

questions. The topics covered here are not exhaustive. Your revision should not be

based on these set of questions only. The level of difficulty of this sample exam is

also NOT indicative of the level of difficulty of the actual exam. The answers are in a

separate file.

FINC2012 Final Exam Sample Questions (Semester 2, 2015) Page 2 of 4

Question 1 (10 Marks) DEBT, INVESTMENTS and EQUITY

a) (5 marks) Calculate the price and duration of a 3-year 8% bond, paying semi-annual

coupons, with a current market yield of 10% p.a. Will this bond be more or less sensitive to

interest rate movements than a 3-year zero coupon bond? The face value of both bonds is

$100.

b) (5 marks) Always Expanding Ltd. has announced a rights issue and the price of the

existing shares has fallen about three percent and they are now trading at $12 per share. The

rights issue will be made at a price of $10 per share and shareholders will be entitled to buy

one new share for each share they own prior to the stock going ex-rights. Briefly explain the

likely reason for the fall in price when the rights issue was announced. Also briefly explain

what will happen to the share price on the day the stock goes ex-rights and calculate how big

the price movement is expected to be.

FINC2012 Final Exam Sample Questions (Semester 2, 2015) Page 3 of 4

Question 2 (5 Marks) COST OF CAPITAL, IMPUTATION and FORWARDS

a)(2 marks) Briefly explain how the value of debt tax shields is affected by the imputation tax

system.

b)(3 marks) You have the following information about Loosely Levered Ltd. The debt to

value (D/V) ratio is 50%, the cost of debt is 9%, and the equity beta is 1.2. The risk free rate

of interest is 7% and the market risk premium is 6%. Compute the beta of the debt, the beta of

the assets and the required return on the assets. Assume there are no taxes.

FINC2012 Final Exam Sample Questions (Semester 2, 2015) Page 4 of 4

Question 3 DEBT, TAXES, DIVIDENDS AND FUTURES

a)(5 marks) Outback Gold Ltd. pays dividends about every 6 months. The current dividend of

$1.00 has just been announced. The dividend is fully franked at the corporate tax rate of 30%.

The marginal investor has an income tax rate of 40% and a capital gains tax rate of 20%.

Calculate the grossed up value of the dividend, the amount of income tax the investor has to

pay and the expected price drop attributable to the dividend payment. Does this price drop

happen when the dividend is announced, on the record date, the ex-dividend date, or the

payment date?

b)(2 marks)Compute the present value of the tax shield according to M&M under a classical

tax system for a company that raises $1 million through the issue of perpetual debt with an

interest rate of 10%. The corporate tax rate is 30%. Now, assume the debt is callable at face

value and the company plans to exercise the call at the end of year 2, what is the present value

of the tax shield.

THIS IS THE FINAL PAGE

Extra Question

A natural gas company is considering the purchase of a gas reserve in Russia for a price of $100

million. The total amount of gas reserved is almost unlimited, but due to technological constraint

the amount of natural gas can be extracted each year is 5 million MMBtu. The current spot price

is $2.92/MMBtu, and it could rise by 20% or fall by 15% in one year’s time, after which the

price will become stable. If the company decides to extract the natural gas, an equipment cost of

$10 will be incurred. A client has approached the company and made an offer to buy all of its

natural gas at a fixed price starting from next year. Once the extraction begins, the company can

sell the gas at either the year-end market price or the price offered by the client, the first cash in-

flow is generated at the end of the year, and subsequent cash flows are generated at the end of

each year forever. The variable cost can be deemed as zero, the risk free interest rate is 5% p.a.

and the company cost of capital is 15%.

1) Calculate the NPV of this project if the extraction starts immediately after purchasing the

reserve, and there is no offer made from the client. (Assuming the probability for a rise in

natural gas price is equal to that for a fall). (3 marks)

2) Identify the real option in this situation and its specifications (maturity, strike price,

underlying asset, etc.) If you are the client and you want to encourage the company to

purchase this reserve, what is the minimum offer price you should make? Use the

binomial tree method and round your numbers to four decimal points in each step. The

final answer should be rounded to two decimal places (7 marks)

QS, fa), 5 marks

•'

1. Gr.ossed;up valtie.ofthe dlvi.dends= $1.00/{1 �o�ao) = $1.428 {1 mark)

2. Ta>q;)ayable :=;0.40{1At8) -fi.30().428) = $0.t4.Z8 (2 tna:t�s,}

3, Pric:e dmp= {1.:o:.40)/{J,-0.20){1-0,30};:;$t,071 {Z mark$}

,Sb> (Z mark$) •CQmpute t�El pres�nt va'lue of the ta� ,shield. acc:Qri:;IJi,g JQ M�M::u.ntfe.r a cia:Ssical tax

, system for a compa('ly f j,at raises $1 mill.ion ,thrciugh thefi$s\le qf r,ierpet_ual debt with an it,t¢re�t

rate .of 10% The i.orp·orate fax .rate is 30%, NciW; li$slirne·the tl�bt Is �allable adace value aodl th'.e;

company plans tb exercise the call atthe end: of yei:lt z; wh�t:is.tn� present value ofth.e tax shi.el!f.

i} Value of ta.x shie.ld ::; T,D = 0.30*$1M = $30M

iit Value of tax s.hi¢1d = (Tc{D)t:o}l{l+ r0) + (Tc(D)rp)/{l + n,f = 3/1.:.l + ;3/{;J..;J.f� 2]273. +2.4793

=$5.2.Cl 0($:s.21 depending on rounding.

A really smart student might say'it depends on what you assume ab91,.1t rollfngove·rthe debt. For

example if you assu.me perpetual rolling over you can make a t;ase for an�wer {{)�

Extra Question

A natural gas company is considering the purchase of a gas reserve in Russia for a price of $100

million. The total amount of gas reserved is almost unlimited, but due to technological constraint

the amount of natural gas can be extracted each year is 5 million MMBtu. The current spot price

is $2.92/MMBtu, and it could rise by 20% or fall by 15% in one year’s time, after which the

price will become stable. If the company decides to extract the natural gas, an equipment cost of

$10 will be incurred. A client has approached the company and made an offer to buy all of its

natural gas at a fixed price starting from next year. Once the extraction begins, the company can

sell the gas at either the year-end market price or the price offered by the client, the first cash in-

flow is generated at the end of the year, and subsequent cash flows are generated at the end of

each year forever. The variable cost can be deemed as zero, the risk free interest rate is 5% p.a.

and the company cost of capital is 15%.

1) Calculate the NPV of this project if the extraction starts immediately after purchasing the

reserve, and there is no offer made from the client. (Assuming the probability for a rise in

natural gas price is equal to that for a fall). (3 marks)

2) Identify the real option in this situation and its specifications (maturity, strike price,

underlying asset, etc.) If you are the client and you want to encourage the company to

purchase this reserve, what is the minimum offer price you should make? Use the

binomial tree method and round your numbers to four decimal points in each step. The

final answer should be rounded to two decimal places (7 marks)

Answers:

1)

NPV = Exp(C1)/(r-g) – C0

Where Exp(C1) = ((2.92* 1.2) *0.5 + (2.92 * 0.85)*0.5) * 5m = $14.965m

r = cost of capital = 0.15

g = 0

c0 = 100 + 10 = 110m

NPV = 14.965/0.15 – 110 = -$10.2333m

2)

rf 0.05

cost of capital 0.15

u 1.2

d 0.85

S0 2.92

s up 3.504

s down 2.482

q per year 5

real prob up 0.5

1-real prob up 0.5

exp(c1) 14.965

PV cash flows 99.76667

fixed cost 110

NPV -10.2333

p 0.571429

1-p 0.428571

It is a put option on the natural gas, maturing in one year, and the exercise price is the offer price.

The minimum option value should be 0 - NPV = $10.2333

Fist, if the offer price is greater than u*s0, it is simple to show that the NPV > 0. Therefore it is

not the lowest offer price. This suggests that the offer price is below Su, therefore option value if

price goes up is 0.

3.504 Payoff = max(X-3.504, 0)*5m/0.15 * 0.5714

Option Value 0

(to achieve minimum offer price, first assume if price goes

up, the option value is 0, the company will sell at market

price rather than take the option and sell at offered price)

2.92

10.23333

2.482 Payoff = max(X-2.482, 0)*5m/0.15 * 0.4286

Option Value 25.07167

Choose the offered price, how much extra can the

company make

Price – market

price

0.75215

Increase in profit per unit as a result of selling at the

offered price (this is not the profit per unit, but an increase

in the profit because you can sell at offered price instead

of the market price)

Offered Price =

increase in gross

profit + market

price

3.23415 Offered price = extra profit per unit + 2.482

Double check if offer price is smaller than 3.504,

otherwise the option value if price increases will not be 0

The minimum offer price should be $3.23415

Also note, once the company purchases the gas reserve, it will immediately start extraction (the

cost of equipment is justified by the DCFs regardless of a rise or a fall in the price, therefore the

sooner the equipment is deployed, the sooner the company can get cash inflows). Therefore, the

decision of whether the extraction should be delayed is irrelevant (because the reasonable

decision is to start extraction right away) and should not be considered as part of the real option.