*.)*

*FYI On ROI: A Guide To Return On Investment*

**TUTORIAL: Risk And Diversification****Discounting Models**

One particularly important use of the required rate of return is in discounting most types of cash flow models and some relative value techniques. Discounting different types of cash flow will use slightly different rates with the same intention - finding the net present value.

Common uses of the required rate of return include:

- Calculating the present value of dividend income for the purpose of evaluating stock prices
- Calculating the present value of free cash flow to equity
- Calculating the present value of operating free cash flow

**Equity and Debt**

In equities the required rate of return is used in various calculations. For example the dividend discount model uses the RRR to discount the periodic payments and calculate the value of the stock. Finding the required rate of return can be done by using the capital asset pricing model (CAPM).

The CAPM will require that you find certain inputs:

- the risk free rate (RFR)
- the stock's beta
- the expected market return.

Then, take the expected market risk premium for this stock. This can have a wide range of estimates. For example, it could range between 3% to 9%, based on factors such as business risk, liquidity risk, financial risk. Or, you can simply derive it from historical yearly market returns. Let's use 6%, rather than any of the extreme values. Often, the market return will be estimated by a brokerage, and you can just subtract the risk-free rate. (Learn how to calculate the risk premium and why academic studies usually estimate a low. Check out

*The Equity-Risk Premium: More Risk For Higher Returns*and

*Calculating The Equity Risk Premium*.)

Return of Stock = α + β_{stock} R_{market} |

- β
_{stock}is the beta coefficient for the stock, meaning it is the covariance between the stock and the market divided by the variance of the market. We will assume the beta is 1.25. - R
_{market}is the return expected from the market. For example, the return of the S&P 500 can be used for all stocks trading on it - and even some stocks not on the index, but related to businesses that are. - α is a constant that measures excess return for given level of risk (For more on this, see
*Calculating Beta: Portfolio Math For The Average Investor*.)

E(R) = RFR + β_{stock} (R_{market} – RFR)E(R) = 0.04 + 1.25 (6)E(R) = 11.5% |

- E(R) = the required rate of return, or expected return
- RFR = the risk free rate
- β
_{stock}= beta of the stock - R
_{market}= return of the market as a whole - (R
_{market}– RFR) = the market risk premium, or the return above the risk-free rate to accommodate additional unsystematic risk

**Dividend Discount Approach**

An investor could also use the dividend discount model, also known as the Gordon growth model. By finding the current stock price, the dividend payment and an estimate of the growth rate for dividends, you can rearrange the formula into:

k=(D/S)+g |

- k = required rate of return
- D = dividend payment (expected to be paid next year)
- S = current stock value (if using the cost of newly issued common stock you will need to minus the flotation costs)
- g = growth rate of the dividend

**Required Rate of Return in Corporate Finance**

Investment decisions are not limited to stocks; every time money is risked for something like expansion or a marketing campaign an analyst can look at the minimum return these expenditures demand. If the current project will give a lower return than other potential projects, then it will not be done. Other factors do go into these decisions, such as risk, time horizon and available resources, among others, but the required rate of return is the basis for deciding between multiple investments. When looking at an investment decision in corporate finance, the overall required rate of return will be the weighted average cost of capital (WACC). (Learn more about this metric in

*.)*

*Investors Need A Good WACC***Capital Structure**

The WACC is the cost of financing new projects based on how a company is structured. If a company is 100% debt then it would be easy: just find the interest on the issued debt and adjust for taxes (because interest is tax deductible). In reality, a corporation is much more complex. Finding the true cost of capital requires a calculation based on a combination of sources. Some would even argue that, under certain assumptions, the capital structure is irrelevant, as outlined in the Modigliani-Miller theorem.

To calculate the WACC simply take the weight of the source of financing and multiply it by the corresponding cost. There is one exception: you should multiply the debt portion by one minus the tax rate. Then sum the totals. The equation looks something like this:

WACC = W_{d} [k_{d}(1-t)] + W_{ps}(k_{ps}) + W_{ce}(k_{ce}) |

- WACC = weighted average cost of capital (firm wide required rate of return)
- W
_{d}= weight of debt - k
_{d}= cost of debt financing - t = tax rate
- W
_{ps}= weight of preferred shares - k
_{ps}= cost of preferred shares - W
_{ce}= weight of common equity - k
_{ce}= cost of common equity

*Evaluating A Company's Capital Structure*.)

**The Bottom Line**

The required rate of return is a difficult metric to pinpoint due to the various estimates and preferences from one decision maker to the next. The risk return preferences, inflation expectations and the firm's capital structure all play a role in determining the required rate. Any one of the many factors can have major effects on an asset's intrinsic value. As with many things, practice makes perfect. As you refine your preferences and dial in estimates, your investment decisions become dramatically more predictable.