Fight Finance

Question 9  DDM, NPV

For a price of $129, Joanne will sell you a share which is expected to pay a $30 dividend in one year, and a $10 dividend every year after that forever. So the stock's dividends will be $30 at t=1, $10 at t=2, $10 at t=3, and $10 forever onwards.

The required return of the stock is 10% pa.

Would you like to the share or politely ?

Question 35  bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

• 1 year zero coupon bond at a yield of 8% pa, and a
• 2 year zero coupon bond at a yield of 10% pa.

What is the company's forward rate over the second year (from t=1 to t=2)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

(a) 0.0185

(b) 0.0374

(c) 0.0604

(d) 0.1204

(e) 0.1250

Question 55  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.15	1.10	1.05	1.00	...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
• the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What will be the price of the stock in four and a half years (t = 4.5)?

(a) $5.2615

(b) $6.0386

(c) $6.3333

(d) $6.6425

(e) $11.9040

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 267  term structure of interest rates

A European company just issued two bonds, a

• 3 year zero coupon bond at a yield of 6% pa, and a
• 4 year zero coupon bond at a yield of 6.5% pa.

What is the company's forward rate over the fourth year (from t=3 to t=4)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

(a) 0.1634

(b) 0.0801

(c) 0.0704

(d) 0.07

(e) 0.0095

Question 434  Merton model of corporate debt, real option, option

A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:

##V## = Market value of assets.

##E## = Market value of (levered) equity.

##D## = Market value of zero coupon bonds.

##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.

What is the payoff to debt holders at maturity, assuming that they keep their debt until maturity?

(a) ##\max(V_1 - F_1,0)##.

(b) ##\max(F_1, V_1)##.

(c) ##\max(F_1, 0)##.

(d) ##\min(F_1, V_1)##.

(e) ##\min(V_1-F_1, F_1)##.

Question 580  price gains and returns over time, time calculation, effective rate

How many years will it take for an asset's price to quadruple (be four times as big, say from $1 to $4) if the price grows by 15% pa?

(a) 1.3685 years

(b) 3.4783 years

(c) 4.4808 years

(d) 9.919 years

(e) 11.5156 years

Question 687  option, no explanation

Which of the following statements about call options is NOT correct?

(a) Buyers of call options are required to pay an initial margin at the start.

(b) Call options are a zero-sum game in the sense that the winner gains at the expense of the loser.

(c) Buyers of call options have to pay the option price at the start.

(d) Buyers of call options do not care about the credit risk of the original call option seller since the contract is novated by the exchange.

(e) Speculators who sell call options hope that the underlying asset price falls.

Question 803  capital raising, rights issue, initial public offering, on market repurchase, no explanation

Which one of the following capital raisings or payouts involve the sale of shares to existing shareholders only?

(a) Rights issues.

(b) Private placements.

(c) Initial public offerings.

(d) Seasoned equity offerings.

(e) On-market buy backs.

Question 805  short selling

Short selling is a way to make money from falling prices. In what order must the following steps be completed to short-sell an asset? Let Tom, Dick and Harry be traders in the share market.

• Step P: Purchase the asset from Harry.
• Step G: Give the asset to Tom.
• Step W: Wait and hope that the asset price falls.
• Step B: Borrow the asset from Tom.
• Step S: Sell the asset to Dick.

Select the statement with the correct order of steps.

(a) P, G, W, B, S.

(b) B, G, W, P, S.

(c) B, W, G, P, S.

(d) P, W, S, B, G.

(e) B, S, W, P, G.