When using the dividend discount model to price a stock:

### p_{0} = \frac{d_1}{r - g} ###

The growth rate of dividends (g):

**Question 282** expected and historical returns, income and capital returns

You're the boss of an investment bank's equities research team. Your five analysts are each trying to find the **expected total return** over the next year of shares in a mining company. The mining firm:

- Is regarded as a mature company since it's quite stable in size and was floated around 30 years ago. It is not a high-growth company;
- Share price is very sensitive to changes in the price of the market portfolio, economic growth, the exchange rate and commodities prices. Due to this, its standard deviation of total returns is much higher than that of the market index;
- Experienced tough times in the last 10 years due to unexpected falls in commodity prices.
- Shares are traded in an active liquid market.

Assume that:

- The analysts' source data is correct and true, but their inferences might be wrong;
- All returns and yields are given as effective annual nominal rates.

Which of the following investable assets are **NOT** suitable for valuation using PE multiples techniques?

Over the next year, the management of an unlevered company plans to:

- Achieve firm free cash flow (FFCF or CFFA) of $1m.
- Pay dividends of $1.8m
- Complete a $1.3m share buy-back.
- Spend $0.8m on new buildings without buying or selling any other fixed assets. This capital expenditure is included in the CFFA figure quoted above.

Assume that:

- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

**Question 547** PE ratio, Multiples valuation, DDM, income and capital returns, no explanation

A firm pays out all of its earnings as dividends. Because of this, the firm has no real growth in earnings, dividends or stock price since there is no re-investment back into the firm to buy new assets and make higher earnings. The dividend discount model is suitable to value this company.

The firm's revenues and costs are expected to increase by inflation in the foreseeable future. The firm has no debt. It operates in the services industry and has few physical assets so there is negligible depreciation expense and negligible net working capital required.

Which of the following statements about this firm's PE ratio is **NOT** correct? The PE ratio should:

Note: The inverse of x is 1/x.

An Apple iPhone 6 smart phone can be bought now for $**999**. An Android Samsung Galaxy 5 smart phone can be bought now for $**599**.

If the Samsung phone lasts for **four** years, approximately how long must the Apple phone last for to have the same equivalent annual cost?

Assume that both phones have equivalent features besides their lifetimes, that both are worthless once they've outlasted their life, the discount rate is **10**% pa given as an effective annual rate, and there are no extra costs or benefits from either phone.

A **one** year European-style **call** option has a strike price of $**4**. The option's underlying stock pays no dividends and currently trades at $**5**. The risk-free interest rate is **10**% pa continuously compounded. Use a **single** step binomial tree to calculate the option price, assuming that the price could rise to $**8** ##(u = 1.6)## or fall to $**3.125** ##(d = 1/1.6)## in one year. The call option price now is:

A **one** year European-style **call** option has a strike price of $**4**.

The option's underlying stock currently trades at $**5**, pays no dividends and its standard deviation of continuously compounded returns is **47**% pa.

The risk-free interest rate is **10**% pa continuously compounded.

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