Fight Finance

Alice is wrong because a risky mining company that's highly sensitive to changes in the market portfolio should have a higher expected return than risk-free government bonds.

Bob is wrong for the same reason as above. A risky stock which is highly correlated and sensitive to the market portfolio should have a higher expected return than risk-free government bonds. Also, while the average historical return is often a good estimate of the future expected return, in this case commodity prices unexpectedly fell over the past 10 years leading to lower than expected historical stock returns. But unexpected commodity future price falls by definition can't be expected, and are just as likely as unexpected rises, so using the stock's historical average return is not a good proxy for the expected future return which we expect should be higher.

Cate is also wrong since the expected return should be at least as high as the risk free rate. What's more, she has found the average price growth or 'capital return'. It is only a part of the total return which also includes the dividend return.

Dave is wrong for the same reason as Cate. He has found the market index's average price growth which is only the capital return, it is not the total total return since it excludes dividends. If he used the accumulation index (rather than the price index) which re-invests dividends then the historical average return would be higher. Another problem is that the mining stock is highly sensitive to the market index, meaning it is more risky, so it should have a higher expected total return than the market index. But at least Dave forecasts a return higher than the risk free rate.

Eve's answer is the most plausible. She is the only person who has tried to find the expected future return rather than the historical average return. Since she used the dividend discount model (DDM) to find the expected return, her forecast total expected return depends on all of the DDM's assumptions such as a constant perpetual growth rate of dividends and a constant level of risk. But her inputs into the model appear reasonable. Using next year's forecast dividend is correct. Since the firm is mature and is not fast-growing it is suited to DDM valuation. Using the inflation rate as the dividend growth rate, which is also the capital return, is a plausible assumption.

Eve should check that the forecast dividend is not a one-off dividend higher than the others and that it is expected to be paid every year into the future. Constructing pro-forma income statements and balance sheets 10 years into the future would also be beneficial since she could see what level of capital expenditure on new assets would be required to sustain the 3% growth rate and if there will be any cash flow shortfalls that will make the 3% growth rate unsustainable. She could also cross-check the expected return predicted by the DDM with the expected return given by the capital asset pricing model (CAPM) to see if they are approximately the same which would be re-assuring. Doing all of the above for other similar mining firms would also give an idea about whether the valuation and expected return of this mining firm is reasonable and consistent with its peers.

Future cash flows and returns are important.

Owners of assets such as shares are entitled to the future cash flows only, not the past cash flows which have already been paid. This is why asset prices are the present value of future cash flows.

To calculate the present value of future dividends, the dividend discount model must use the future expected return ##r## and growth rate ##g## of the market price of equity.

Of course the future is impossible to predict. Often the best guide to the future is the past, so in practice the actual historical return and growth rate are used as a proxy for what's expected in the future.

Market prices are important.

In finance, current market prices are always more important and relevant than old historical cost book prices. The market price of a share is the price that it trades for every day on the stock exchange. It's the price that a buyer will actually pay to buy the share.

When the share was first bought, the market price and book price were the same. But after that, the book price never changes while the market price goes up and down every day. Therefore the book price is old and out of date. Generally it is not the same as the current market price, unless by coincidence.

Owners equity recorded by an accountant in the firm's balance sheet is the sum of the shareholders' equity (also called contributed equity), retained profits and reserves such as asset revaluation reserve. This is often very different to the market price of equity. If the firm has been successful in the past, usually the market price of equity will be much higher than the book price.

Equity returns calculated from book prices are also therefore not very useful to determine value. They reflect the past, not the future. Therefore accounting ratios such as ROE (Net Income/Owners Equity) and ROA (Net Income/Total Assets) are not very useful for pricing stocks. But they are a reasonable guide to past performance.

Future cash flows and returns are important.

Owners of assets such as shares are entitled to the future cash flows only, not the past cash flows which have already been paid. This is why asset prices are the present value of future cash flows.

To calculate the present value of future dividends, the dividend discount model must use the future expected growth rate ##g## of the dividend (which is also the expected future capital return).

Of course the future is impossible to predict. Often the best guide to the future is the past, so in practice the actual historical growth rate is often used as a proxy for what's expected in the future. But care must be taken because the growth rate of the dividend cannot be larger than the nominal GDP growth of the country where it does business, or else the company is forecast to take over the country. See question 3 and 333.

Stocks are more risky than debt because in the event of bankruptcy, stock holders have a residual claim on the firm's assets and are only paid out if there's anything left over after the debt holders are paid. Debt holders have first claim on the firm's assets so in the event of bankruptcy they're paid out first and thus have a higher chance of being paid when the firm's assets are liquidated.

Firms' expected future stock returns are always higher than their expected future debt returns since stocks are more risky than debt and deserve a higher return.

However, firms' past realised stock returns can be higher or lower than their past realised debt returns. This is because the firm may have had a few bad years where profits were lower than expected and the share price fell, but the debt can still be repaid so its price stayed the same. In this case the past realised returns on the shares were negative, but the returns on debt were zero.

When required returns rise and cash flows remain the same, prices will fall. For example, if cash flows are a constant perpetuity ##C_1##, required returns are ##r## and prices are ##P_0##, then:

When the required return rises, because it's in the denominator, the price must fall.

When required returns fall and cash flows remain the same, prices will rise. For example, if cash flows are a constant perpetuity ##C_1##, required returns are ##r## and prices are ##P_0##, then:

When the required return falls, because it's in the denominator, the price must rise.

When future expected cash flows rise and required returns remain the same, prices will rise. For example, if cash flows are a constant perpetuity ##C_1##, required returns are ##r## and prices are ##P_0##, then:

When the cash flow rises, because it's in the numerator, the price must rise.

The historical dividend yield would still be positive since the dividend ##(C_0)## is positive and the past dividend yield is not affected by the price now ##(P_0)##, it's affected by the price at the start of last year ##(P_{-1})##: