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# An easy way to understand the meaning and role of the discount rate

## The role of the discount rate

The most crucial task in valuation is to predict the future cash flows the target company will generate. You convert the estimated cash flows into present values to get the value of the target company.

The above is the basic formula for the discounted cash flow method. ‘n’ means the period you expect to earn cash flows from the target company. ‘CF^{t}‘ is the cash flows you expect the company to create at time t. r is the discount rate used to convert the cash flows into present values. In other words, the discount rate plays a role in converting expected future cash flows into present values.

## The size of the discount rate is proportional to the degree to which CF

^{t}deviates from your expectation, that is, the Volatility of CF^{t}.

For investors, it is a risk that the CF^{t} will fluctuate in the future. In other words, investment risk refers to the possibility that an investor would not receive the investment principal and its returns as expected. The discount rate reflects those risks.

## The higher the risk, the higher the discount rate, and the lower the risk, the lower the discount rate.

You need to divide an investment risk into two categories. One risk is that the cash flows could be higher than your expectations, which is called ‘upside risk’. (It is just financial terminology. Actually, it is your return.) Another risk is that the cash flows might be lower than expected, that is, ‘downside risk’.

#### Risk = Volatility of future cash flows (or expected rate of return)

Assume that you expect cash flow X and cash flow Y at time t, as shown in the figure below. Suppose the discount rate for cash flow X is r_{1}, and the one for cash flow Y is r_{2}. If you expect cash flows X to occur stably but Y to be highly volatile, r_{2} should be greater than r_{1}, given the same present value for both cash flows.

The size of discount rates

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## The meaning of the discount rate: discount rate = expected rate of return = cost of capital

Discount rate from the perspective of investors and capital consumers

In terms of the supply and demand of capital, you can better understand the meaning of the discount rate. Investors provide capital to companies and expect a return from the capital.

## From the perspective of companies consuming capital, the rate of return required by investors is the cost of capital.

The supply and demand of capital occur when the expected rate of return for investors matches the cost of capital for firms. Therefore, you can say that the expected rate of return is the same as the cost of capital. It is just the differently interpreted terms between capital consumers and investors.

For example, suppose an investor invests $100 in a company at an annual return rate of 10%. The company as a capital consumer must repay the investor $110 after one year. The $10 is a profit for the investor but a cost of capital for the company. When thinking of 10% in the cash flow discount formula, it becomes the discount rate that makes the future cash flow of $110 and the present value of $100 equal. Therefore, we can accept the following formula.

#### Discount rate = Expected rate of return = Cost of capital

The cost paid to creditors is the cost of debts, and the cost paid to shareholders is the cost of equity capital.

## Therefore, we use the cost of equity capital as the discount rate when calculating the stock value (equity holders value). And we use the WACC (Weighted Average Cost of Capital), a mixture of the cost of equity capital and debts, as the discount rate when calculating the total enterprise value (debtholders’ value + equity holders value).

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