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)?

**Question 308** risk, standard deviation, variance, no explanation

A stock's standard deviation of returns is expected to be:

- 0.09 per
**month**for the first 5 months; - 0.14 per
**month**for the next 7 months.

What is the expected standard deviation of the stock per **year** ##(\sigma_\text{annual})##?

Assume that returns are independently and identically distributed (iid) and therefore have zero auto-correlation.

**Question 433** Merton model of corporate debt, real option, option, no explanation

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 equity holders at maturity, assuming that they keep their shares until maturity?

**Question 498** NPV, Annuity, perpetuity with growth, multi stage growth model

A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will **NOT** give the correct net present value of the project?

**Question 546** income and capital returns, interest only loan, no explanation

Which of the following statements about the capital and income returns of an **interest-only** loan is correct?

Assume that the yield curve (which shows total returns over different maturities) is flat and is not expected to change.

An interest-only loan's expected:

A semi-annual coupon bond has a yield of 3% pa. Which of the following statements about the yield is **NOT** correct? All rates are given to four decimal places.

**Question 664** real and nominal returns and cash flows, inflation, no explanation

What is the present value of **real** payments of $100 every year forever, with the first payment in one year? The **nominal** discount rate is 7% pa and the inflation rate is 4% pa.

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

**Question 928** mean and median returns, mode return, return distribution, arithmetic and geometric averages, continuously compounding rate, no explanation

The arithmetic average continuously compounded or log gross discrete return (AALGDR) on the ASX200 accumulation index over the 24 years from 31 Dec 1992 to 31 Dec 2016 is **9.49**% pa.

The arithmetic standard deviation (SDLGDR) is **16.92** percentage points pa.

Assume that the log gross discrete returns are normally distributed and that the above estimates are true population statistics, not sample statistics, so there is no standard error in the sample mean or standard deviation estimates. Also assume that the standardised normal Z-statistic corresponding to a one-tail probability of **2.5**% is exactly **-1.96**.

If you had a $1 million fund that replicated the ASX200 accumulation index, in how many years would the **mode** dollar value of your fund first be expected to lie outside the **95**% confidence interval forecast?

Note that the mode of a log-normally distributed future price is: ##P_{T \text{ mode}} = P_0.e^{(\text{AALGDR} - \text{SDLGDR}^2 ).T} ##