**Question 56** income and capital returns, bond pricing, premium par and discount bonds

Which of the following statements about risk free government bonds is **NOT** correct?

**Hint:** Total return can be broken into income and capital returns as follows:

###\begin{aligned} r_\text{total} &= \frac{c_1}{p_0} + \frac{p_1-p_0}{p_0} \\ &= r_\text{income} + r_\text{capital} \end{aligned} ###

The capital return is the growth rate of the price.

The income return is the periodic cash flow. For a bond this is the coupon payment.

The following cash flows are expected:

- 10 yearly payments of $60, with the first payment in 3 years from now (first payment at t=3).
- 1 payment of $400 in 5 years and 6 months (t=5.5) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

All things remaining equal, the higher the correlation of returns between two stocks:

The following cash flows are expected:

- Constant perpetual yearly payments of $70, with the first payment in 2.5 years from now (first payment at t=2.5).
- A single payment of $600 in 3 years and 9 months (t=3.75) from now.

What is the NPV of the cash flows if the discount rate is 10% given as an effective annual rate?

An investor bought a **10** year **2.5**% pa fixed coupon government bond priced at **par**. The face value is $**100**. Coupons are paid **semi-annually** and the next one is in 6 months.

**Six months later**, just **after** the coupon at that time was paid, yields suddenly and unexpectedly fell to **2**% pa. Note that all yields above are given as APR's compounding semi-annually.

What was the bond investors' historical total return over that first 6 month period, given as an effective semi-annual rate?

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. Of the **15**% pa total expected return, the dividend yield is expected to always be **7**% pa and rest is the capital yield.

Assuming that the company's statements are correct, what is the NPV of buying the investment if the **15**% total return lasts for the next 100 years (t=0 to 100), then reverts to **10**% 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, the dividends can only be re-invested at **10**% pa and 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 767** idiom, corporate financial decision theory, no explanation

The sayings "Don't cry over spilt milk", "Don't regret the things that you can't change" and "What's done is done" are most closely related to which financial concept?

Which one of the following businesses is likely to be a **public** company, judging by its name?

**Question 880** gold standard, no explanation

Under the Gold Standard (1876 to 1913), currencies were priced relative to:

**Question 903** option, Black-Scholes-Merton option pricing, option on stock index

A **six** month European-style **call** option on the S&P500 stock index has a strike price of **2800** points.

The underlying S&P500 stock index currently trades at **2700** points, has a continuously compounded dividend yield of **2**% pa and a standard deviation of continuously compounded returns of **25**% pa.

The risk-free interest rate is **5**% pa continuously compounded.

Use the Black-Scholes-Merton formula to calculate the option price. The call option price now is: