Fight Finance

Question 39  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 is the current price of the stock?

(a) $25.6033

(b) $20.7476

(c) $20.0000

(d) $19.8835

(e) $18.3126

Question 66  CAPM, SML

Government bonds currently have a return of 5% pa. A stock has an expected return of 6% pa and the market return is 7% pa. What is the beta of the stock?

(a) -0.5

(b) 0

(c) 0.5

(d) 1

(e) 7

Question 73  portfolio risk, standard deviation

Portfolio Details
Stock	Expected return	Standard deviation	Covariance ##(\sigma_{A,B})##	Beta	Dollars invested
A	0.2	0.4	0.12	0.5	40
B	0.3	0.8		1.5	80

What is the standard deviation (not variance) of the above portfolio? Note that the stocks' covariance is given, not correlation.

(a) 0.5497

(b) 0.5651

(c) 0.5963

(d) 0.6156

(e) 0.8165

Question 368  interest tax shield, CFFA

A method commonly seen in textbooks for calculating a levered firm's free cash flow (FFCF, or CFFA) is the following:

###\begin{aligned} FFCF &= (Rev - COGS - Depr - FC - IntExp)(1-t_c) + \\ &\space\space\space+ Depr - CapEx -\Delta NWC + IntExp(1-t_c) \\ \end{aligned}###

Does this annual FFCF or the annual interest tax shield?

Question 408  leverage, portfolio beta, portfolio risk, real estate, CAPM

You just bought a house worth $1,000,000. You financed it with an $800,000 mortgage loan and a deposit of $200,000.

You estimate that:

• The house has a beta of 1;
• The mortgage loan has a beta of 0.2.

What is the beta of the equity (the $200,000 deposit) that you have in your house?

Also, if the risk free rate is 5% pa and the market portfolio's return is 10% pa, what is the expected return on equity in your house? Ignore taxes, assume that all cash flows (interest payments and rent) were paid and received at the end of the year, and all rates are effective annual rates.

(a) The beta of equity is 5 and the expected return on equity is 30% pa.

(b) The beta of equity is 4.2 and the expected return on equity is 26% pa.

(c) The beta of equity is 0.86 and the expected return on equity is 9.3% pa.

(d) The beta of equity is 1 and the expected return on equity is 10% pa.

(e) The beta of equity is 0.6 and the expected return on equity is 8% pa.

Question 441  DDM, income and capital returns

A fairly valued share's current price is $4 and it has a total required return of 30%. Dividends are paid annually and next year's dividend is expected to be $1. After that, dividends are expected to grow by 5% pa in perpetuity. All rates are effective annual returns.

What is the expected dividend income paid at the end of the second year (t=2) and what is the expected capital gain from just after the first dividend (t=1) to just after the second dividend (t=2)? The answers are given in the same order, the dividend and then the capital gain.

(a) $1.3, $0.26

(b) $1.25, $0.25

(c) $1.1025, $0.2205

(d) $1.05, $0.21

(e) $1, $0.2

Question 666  rights issue, capital raising

A company conducts a 2 for 3 rights issue at a subscription price of $8 when the pre-announcement stock price was $9. Assume that all investors use their rights to buy those extra shares.

What is the percentage increase in the stock price and the number of shares outstanding? The answers are given in the same order.

(a) -60%,   150%

(b) -42.22%,   150%

(c) -40%,   66.67%

(d) -22.22%,   66.67%

(e) -4.44%,   66.67%

Question 790  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate, log-normal distribution, VaR, confidence interval

A risk manager has identified that their hedge fund’s continuously compounded portfolio returns are normally distributed with a mean of 10% pa and a standard deviation of 30% pa. The hedge fund’s portfolio is currently valued at $100 million. Assume that there is no estimation error in these figures and that the normal cumulative density function at 1.644853627 is 95%.

Which of the following statements is NOT correct? All answers are rounded to the nearest dollar.

(a) Future portfolio values have a log-normal distribution. The mean (expected or arithmetic average) portfolio value in one year is $115,603,957.

(b) The median (50th percentile) portfolio value in one year is $115,603,957.

(c) The 90% confidence interval of continuously compounded portfolio returns over the next year ##(r_{0 \rightarrow 1})## is ##-39.3456088\% < r_{0 \rightarrow 1} < 59.3456088\%##.

(d) The 90% confidence interval of portfolio values in one year ##(V_1)## is ##\$67,472,095 < V_1 < \$181,023,395##.

(e) The annual 95% relative VaR is $48,131,863 and the absolute VaR is $32,527,905.

Question 870  income and capital returns

An Apple (NASDAQ:AAPL) stock was purchased by an investor for $120 and one year later was sold for $150. A dividend of $4 was also collected at the end of the year just before the stock was sold.

Which of the following statements about the stock investment is NOT correct? Ignore taxes.

Over the year, the investor made a:

(a) Capital gain of $30

(b) Dividend income of $4.

(c) Capital return of 25%.

(d) Dividend yield of 2.6667%.

(e) Total return of 28.3333%.

.

Question 982  corporate financial decision theory, Lintner

In his survey paper from 1956, John Lintner stated: “A prudent foresighted management will always do its best to plan ahead in all aspects of financial policy to avoid getting into such uncomfortable situations where dividends have to be cut substantially below those which the company's previous practice would lead stockholders to expect on the basis of current earnings.”

This is a statement about which decision made by financial managers?

(a) Investment decision.

(b) Financing decision.

(c) Working capital decision.

(d) Payout policy decision.

(e) Capital or labour decision.