You want to buy an apartment priced at $300,000. You have saved a deposit of $30,000. The bank has agreed to lend you the $270,000 as a **fully amortising** loan with a term of 25 years. The interest rate is 12% pa and is not expected to change.

What will be your monthly payments? Remember that mortgage loan payments are paid in arrears (at the end of the month).

**Question 25** bond pricing, zero coupon bond, term structure of interest rates, forward interest rate

A European company just issued two bonds, a

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

What is the company's forward rate over the third year (from t=2 to t=3)? Give your answer as an effective annual rate, which is how the above bond yields are quoted.

The following is the Dividend Discount Model (DDM) used to price stocks:

### P_0 = \frac{d_1}{r-g} ###Assume that the assumptions of the DDM hold and that the time period is measured in years.

Which of the following is equal to the expected dividend in 3 years, ## d_3 ##?

**Question 155** inflation, real and nominal returns and cash flows, Loan, effective rate conversion

You are a banker about to grant a 2 year loan to a customer. The loan's principal and interest will be repaid in a single payment at maturity, sometimes called a zero-coupon loan, discount loan or bullet loan.

You require a **real** return of **6**% pa over the two years, given as an effective annual rate. Inflation is expected to be **2**% this year and **4**% next year, both given as effective annual rates.

You judge that the customer can afford to pay back $**1,000,000** in **2** years, given as a **nominal** cash flow. How much should you lend to her right now?

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?

**Question 207** income and capital returns, bond pricing, coupon rate, no explanation

For a bond that pays fixed semi-annual coupons, how is the annual coupon rate defined, and how is the bond's annual income yield from time 0 to 1 defined mathematically?

Let: ##P_0## be the bond price now,

##F_T## be the bond's face value,

##T## be the bond's maturity in years,

##r_\text{total}## be the bond's total yield,

##r_\text{income}## be the bond's income yield,

##r_\text{capital}## be the bond's capital yield, and

##C_t## be the bond's coupon at time t in years. So ##C_{0.5}## is the coupon in 6 months, ##C_1## is the coupon in 1 year, and so on.

A company advertises an investment costing $**1,000** which they say is underpriced. They say that it has an expected total return of **15**% pa, but a required return of only **10**% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.

Assuming that the company's statements are correct, what is the **NPV** of buying the investment if the 15% return lasts for the next **100** years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?

In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.

The answer choices below are given in the same order (15% for 100 years, and 15% forever):

**Question 699** utility, risk aversion, utility function, gamble

Mr Blue, Miss Red and Mrs Green are people with different utility functions.

Each person has $50 of initial wealth. A coin toss game is offered to each person at a casino where the player can win or lose $50. Each player can flip a coin and if they flip heads, they receive $50. If they flip tails then they will lose $50. Which of the following statements is **NOT** correct?