Question

Consider the following table, which gives a security analyst’s expected return on two stocks in two particular scenarios for the rate of return on the market:

Market Return		Aggressive Stock		Defensive Stock
5	%	–3	%	4	%
24		36		9

a. What are the betas of the two stocks? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Agressive stock:

Defensive stock

b. What is the expected rate of return on each stock if the two scenarios for the market return are equally likely to be 5% or 24%? (Do not round intermediate calculations. Round your answers to 1 decimal place.)

Agressive stock:

Defensive stock

e. What hurdle rate should be used by the management of the aggressive firm for a project with the risk characteristics of the defensive firm’s stock if the two scenarios for the market return are equally likely? Also, assume a T-Bill rate of 4%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Hurdle rate:

Answer 1

Let the two stocks be A & D

Aggressive = A

Defensive = D

A)Beta of a stock implies the rate of change in stock return/price when the market changes by 1%. Hence, it tells us about the sensitivity between the stock return and the market return.

Above, we are provided with the details of two different rates for the markets and the two stocks.

We can find the Beta of the stocks by finding the difference in the return of stock A/D to the difference in the return of the market.

= Difference in stock return (A/D) / Difference in market return

For Aggressive stock A:

= [ 36 - (-3) ] / [ 24 - 5 ]

= 2.05

For Defensive stock D:

= [ 9 - 4 ] / [ 24 - 5 ]

= 0.26

B) If the outcome of the two scenarios mentioned above are equally likely, then the return for stocks A & D can be found by simply putting a weightage of 0.5 to both the returns of a stock under these two circumstances.

Stock A: => 0.50*36 + 0.50*(-3) = 18 + (-1.5) = 16.5%

Stock D: => 0.50*9 + 0.50*4 = 4.5 + 2 = 6.5%

C) Hurdle rate of a project is the minimum return that a project should earn for it to be beneficial for a company. Hence, the minimum the project should earn can be the cost of capital of that project atleast.

Over here the project taken up by the aggressive company is similar to risk characteristics of the defensive company. Hence, the hurdle rate should be calculated using the beta of the defensive stock such that its characteristics is represented in the rate calculated.

Formula for hurdle rate: Rf + (Rm - Rf) * B

where, Rf = T-bill rate (4%)

Rm= market rate of return

B= Beta of stock D

Market rate of return is when both conditions are equally likely:

= 0.50*5 + 0.50*24

= 14.50%

Hurdle rate = 4 + (14.50 - 4)*0.26

= 4 + 10.50*0.26

= 6.73%