$11.$ Calculating a potential investment return $-$ Five steps

Calculating a stock$$s potential rate of return takes five steps:

Step $1-$ Use the Stock$$s Beta Value to Estimate the Risk of the Investment

A stock$$s beta value is a measure of the stock$$s volatility$$that is$,$ how much the stock price varies relative to the rest of the market as a whole. A stock$$s beta value can help you to estimate the amount of risk in an investment portfolio.

For example, suppose you have just purchased stock in Gems & More Jewelers that has a beta value of $1\mathrm{.}6.$ If the average price of all stocks rises by $20\%$ over a period of time, then you would expect the price of Gems & More Jewelers stock to rise by

$\%.$ However, if the average price of all stocks falls by $10\%$ over a period of time, then you would expect the price of Gems & More Jewelers stock to fall by

$\%.$

In general, a stock with a higher beta value is risky than a stock with a lower beta value.

Step $2-$ Estimate the Market Risk

To estimate the required rate of return on an investment, you must first estimate and quantify the market risk. Market risk $($also known as systematic risk$)$ is the risk associated with the effects of the overall market on securities markets. Market risk often causes the market price of a particular stock or bond to change, even though nothing has changed in the fundamental values underlying that investment.

Historical records indicate that $\%$ represents a realistic estimate of market risk for U$.$S$.$ stocks. However, in the short term or in times of economic turbulence, the market risk may be significantly $.$

Step $3-$ Calculate your Required Rate of Return

The return on short$-$term U$.$S$.$ Treasury bills $($T$-$bills$)$ has historically exceeded the rate of inflation by a slight degree. For example, when T$-$bills pay $2\%$ interest, the inflation rate might be around $1\mathrm{.}7\%.$ In this case, T$-$bills provide almost no gain for the investor, because inflation and income taxes reduce the return to about zero. Therefore, investors often use the yield on Treasury bills as a base number that provides a zero real rate of return, that is a zero return on an investment after inflation and income taxes.

To calculate your required rate of return on an investment, multiply the investment$$s beta value by the estimated market risk and then add the risk$-$free T$-$bill rate as shown in the following equation:

Estimate of the Required Rate of Return on an Investment$=$T$-$bill Rate$+($Beta$\backslash$times Market Risk$)$

For example, suppose that the stock for Gems & More Jewelers has a beta value of $1\mathrm{.}6.$ If you assume a market risk of $8\%$ and the current T$-$bill rate is $2\mathrm{.}0\%,$ the total rate of return you will require on this investment is

$\%.($Hint: Round your answer to one decimal place.$)$ In other words, you would need a promise of a higher rate of return than this percentage in order to justify putting your money at risk in this investment.

Step $4-$ Calculate the Stock$$s Potential Rate of Return

The potential rate of return for an investment over a period of years can be determined by adding the anticipated income $($from dividends, interest, rent, or other sources$)$ to the future value of the investment and then subtracting the investment$$s original cost.

Suppose that you have determined that Gems & More Jewelers is currently trading at $$35$ per share, its most recent $12-$month earnings amounted to $$7\mathrm{.}00$ per share, and the cash dividend for the same period was $$1\mathrm{.}50$ per share.

Begin by projecting the future value of one share of stock by using the earnings per share $($EPS information$).$ In this case, the price$-$to$-$earnings ratio is $5\mathrm{.}0($$$35$ price per share$$7\mathrm{.}00$ earnings$=5\mathrm{.}0$

$).$

Next, apply an assumed $12\mathrm{.}0\%$ rate of growth estimate $($the same rate as occurred in previous years, according to the company$$s annual report$)$ to calculate the earnings per share $($EPS$)$ for each year. The following table lists the estimated projections of earnings and dividends for one share of Gems & More Jewelers if you assume a $12\mathrm{.}0\%$ rate of growth over the next five years:

End of Year

Earnings

Dividend Income

$($Dollars$)$

$($Dollars$)$

$1$ $$7\mathrm{.}84$ $$1\mathrm{.}68$

$28\mathrm{.}781\mathrm{.}88$

$39\mathrm{.}832\mathrm{.}11$

$411\mathrm{.}012\mathrm{.}36$

$512\mathrm{.}332\mathrm{.}64$

Total dividends: $$10\mathrm{.}67$

Average annual dividend $(10\mathrm{.}675$

$)$: $$2\mathrm{.}13$

Using an assumed price$/$earnings ratio of $5\mathrm{.}0($the same as the current ratio$),$ you can estimate the market price of the stock after five years to be $

per share. $($Note: Round your answer to two decimal places.$)$

Once you have determined the projected stock price and the average annual dividend $($as shown in the previous table$),$ you can convert those figures into a potential rate of return by calculating the approximate compound yield $($ACY$)$ with the following equation: $($Note: Do not round intermediate calculations. Round your final answer to one decimal place.$)$

ACY $=$ Average Annual Dividend$+$Projected Price of Stock $$ Current Price of StockNumber of Years ProjectedProjected Price of Stock $+$ Current Price of Stock$2$

$=$

$\%$

Step $5-$ Compare the Requ