Question

13) The nominal required return on XYZ stock is 14%. The nominal risk-free rate of return is 4% and the real risk-free rate of return is 2%. How much are investors requiring as compensation for risk? What is the inflation premium?

Answer 1

Values provided:

Nominal Required return = 14%

Nominal Risk-free rate of return = 4%

Real Risk-free rate of return = 2%

1) Inflation Premium:

Inflation Premium is the additional return required by an investor to compensate for inflation risk (i.e. loss in the purchasing power).

we are provided with Real and Nominal risk free rate, hence using these we can calculate the inflation premium using the below formula:

Inflation Premium =	1 + Nominal Rate	− 1
	1 + Real Rate

Inflation Premium =	1 + 0.04	− 1
	1 + 0.02

= (1.04 / 1.02) - 1

= 1.96 %

2) Compensation for risk:

Compensation for risk is the risk premium. It is the additional return required by an investor to compensate him for the additional risk of the given security. It is calculated as additional return over a risk free rate of return.

Risk premium is calculated as:

Risk Premium = Expected Nominal return - Nominal risk free return = 14% - 4 % = 10%

If you are using the real risk free rate then the risk premium is calculated as:

Risk Premium = Expected Nominal return - Real risk free return - Inflation Premium = 14% - 2% -1.96% = 10.04%

When you are using the real rate, you also need to adjust the expected return for inflation premium.