# Expected, Required and Risk Free Rates of Return

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#### Solution Summary

1) Four probable states of the economy may prevail next year. Below are the returns on stocks of A & B companies under each of the probable states & the probabilities for each state. (For this problem, assume that the economy definitely will fall within one of these 4 probable states.)

State of Economy Probability A Stock B Stock

Mild Recession 20.0% 4.00% 5.00%

Low Growth 35.0% 6.00% 7.00%

Moderate Growth 30.0% 9.00% 10.00%

Rapid Growth 15.0% 4.00% 14.00%

Given the probabilities for the 4 possible economic conditions, calculate the expected return for A stock & for B stock.

2) There are 3 new securities available in the market with 4 probable states of the economy. The table below shows the returns on these securities under each of the probable states and the probabilities for each state. (For this problem, we assume that the economy definitely will fall within one of these 4 probable states.)

State of Economy Probability Security 1 Security 2 Security 3

Mild Recession 10.0% 25.0% 4.0% -5.0%

Low Growth 40.0% 20.0% 7.0% 5.0%

Moderate Growth 40.0% 15.0% 12.0% 15.0%

Rapid Growth 10.0% 10.0% 18.0% 30.0%

Given the probabilities for the 4 possible economic conditions, calculate the expected returns for each security.

3) Using the Capital Asset Pricing Model (ks = kRF + (kM - kRF)x βs), calculate the required rate of return for the each of the stocks listed below.

Example: Truman Co. has a beta of 1.8. If the risk-free rate of return is 5% and the expected market return is 12%, what is the required rate of return for Truman Co?

Answer:

KRF MRP Beta MRP * Beta Required Rate

5.0% 7% 1.8 12.6% 17.6%

Assumptions (apply to all problems):

? The Risk-Free Rate of Return (return on long term treasure securities) is 6.5%

? The expected market rate of return is 14.5%.

A) Corp A has a beta of 1.5

B) Corp B has a beta of 1.8

C) Corp C has a beta of 0.75

D) Corp D has a beta of 1.0

E) Corp E has a beta of 2.0

F) Corp F has a beta of 1.2

G) Corp G has a beta of 0.5

H) Corp H has a beta of 1.6