Fight Finance

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 40  DDM, perpetuity with growth

A stock is expected to pay the following dividends:

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

After year 4, the annual dividend will grow in perpetuity at 5% pa, so;

• the dividend at t=5 will be $1.15(1+0.05),
• the dividend at t=6 will be $1.15(1+0.05)^2, 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 three and a half years (t = 3.5)?

(a) $27.7567

(b) $24.1226

(c) $23.5680

(d) $22.4457

(e) $3.6341

Question 103  option

Below are 4 option graphs. Note that the y-axis is payoff at maturity (T). What options do they depict? List them in the order that they are numbered.

(a) 1: short call, 2: long call, 3: short put, 4: long put.

(b) 1: long call, 2: long put, 3: short call, 4: short put.

(c) 1: short put, 2: long put, 3: short call, 4: long call.

(d) 1: long put, 2: short put, 3: long call, 4: short call.

(e) 1: long put, 2: short call, 3: short put, 4: long call.

Question 106  CAPM

A fairly priced stock has an expected return of 15% pa. Treasury bonds yield 5% pa and the market portfolio's expected return is 10% pa. What is the beta of the stock?

(a) 0

(b) 0.5

(c) 1

(d) 1.5

(e) 2

Question 118  WACC

A company has:

• 100 million ordinary shares outstanding which are trading at a price of $5 each. Market analysts estimated that the company's ordinary stock has a beta of 1.5. The risk-free rate is 5% and the market return is 10%.
• 1 million preferred shares which have a face (or par) value of $100 and pay a constant annual dividend of 9% of par. The next dividend will be paid in one year. Assume that all preference dividends will be paid when promised. They currently trade at a price of $90 each.
• Debentures that have a total face value of $200 million and a yield to maturity of 6% per annum. They are publicly traded and their market price is equal to 110% of their face value.

The corporate tax rate is 30%. All returns and yields are given as effective annual rates.

What is the company's after-tax Weighted Average Cost of Capital (WACC)? Assume a classical tax system.

(a) 17.22%

(b) 11.47%

(c) 10.46%

(d) 10.11%

(e) 9.97%

Question 148  DDM, income and capital returns

The following equation is the Dividend Discount Model, also known as the 'Gordon Growth Model' or the 'Perpetuity with growth' equation.

### p_0 = \frac{d_1}{r - g} ###

Which expression is NOT equal to the expected dividend yield?

(a) ## r-g ##

(b) ## \dfrac{d_1}{p_0} ##

(c) ## \dfrac{d_5}{p_4} ##

(d) ## \dfrac{d_5(1+g)^2}{p_6} ##

(e) ## \dfrac{d_3}{p_0(1+r)^2} ##

Question 185  NPV, DDM, no explanation

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	2	2	2	10	3	...

After year 4, the dividend will grow in perpetuity at 4% pa. 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 5 years (t = 5), just after the dividend at that time has been paid?

(a) 61.5018

(b) 56.2432

(c) 54.0800

(d) 52.0000

(e) 48.0769

Question 362  income and capital returns, DDM, real estate

Three years ago Frederika bought a house for $400,000.

Now it's worth $600,000, based on recent similar sales in the area.

Frederika's residential property has an expected total return of 7% pa.

She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.

The present value of 12 months of rental payments is $29,089.48.

The future value of 12 months of rental payments one year ahead is $31,125.74.

What is the expected annual capital yield of the property?

(a) -0.7814%

(b) -0.2724%

(c) 1.8124%

(d) 2%

(e) 2.1518%

Question 575  inflation, real and nominal returns and cash flows

You expect a nominal payment of $100 in 5 years. The real discount rate is 10% pa and the inflation rate is 3% pa. Which of the following statements is NOT correct?

(a) The nominal cash flow of $100 in 5 years is equivalent to a real cash flow of $86.2609 in 5 years. This means that $86.2609 will buy the same amount of goods and services now as $100 will buy in 5 years.

(b) The real discount rate of 10% pa is equivalent to a nominal discount rate of 13.3333% pa.

(c) The nominal price of goods and services will increase by 3% every year.

(d) The real price of goods and services will increase by 3% every year.

(e) The present value of your payment will increase by the nominal discount rate every year.

Question 794  option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the Delta of a European call option?

(a) ##N[d_1]##

(b) ##N[d_2]##

(c) ##−N[−d_1]##

(d) ##−N[−d_2]##

(e) ##N[−d_2]##

Where:

###d_1=\dfrac{\ln⁡[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln⁡[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###