Question

Question 72. Suppose a risky security pays an average cash flow of $100 in one year. The risk-free rate is 5%, and the expected return on the market index is 13%. If the returns on this security are high when the economy is strong and low when the economy is weak, but the returns vary by only half as much as the market index, then the price for this risky security is closest to: A. 88 B. 92 C. 93 D. 95 E. 105

Answer 1

In this question, we need to calculate the price of the risky security. Price can be calculated by discounting the cash flows to be received. But, Here is the thing, We don't have the discount rate. Let's follow this step by step approach:

Step 1: Find Beta

It is mentioned that returns on the security are high when the economy is strong and low when the economy is weak. This gives an indication of direction of Beta. It means that the Beta is +ve since it is moving in line with the economy.

Now, returns vary by only half as much as the market index. It means that for example if market changes by 14%, the return will change by only 7% or Our Beta is 0.5(half).

So, Beta = +0.5

Step 2: Use CAPM.

We can calculate the discount rate using CAPM like this:

Risk Free Rate + Beta (Market Return - Risk Free Rate)

= 5% + 0.5 (13% - 5%)

= 5% + 0.5 (8%)

= 5% + 4%

=9%

The discount rate is 9%

Step 3: Calculate the price by discounting the cash flow.

We are receiving $100 in one year from the security. The present value of the security is:

Cash Flow / (1+discount rate)

= 100 / ( 1+0.09)

= 100 /1.09

= 91.74

The price of the security is $91.74 or closest to $92.

The answer is Option B ($92)