DHF Company has a beta of 1.5 and is currently in equilibrium.The required rate of return on the stock is 12.00% versus a required return on an average stock of 10.00%.Now the required return on an average stock increases by 30.0% (not percentage points).Neither betas nor the risk-free rate change.What would DHF's new required return be?
A) 14.89%
B) 15.68%
C) 16.50%
D) 17.33%
E) 18.19%

Question

Quizplus · Accepted Answer

Using the Capital Asset Pricing Model (CAPM):

rDHF = rRF + βDHF(rM - rRF)

rDHF = the required return on DHF's stock
rRF = the risk-free rate, assumed to be constant
βDHF = DHF's beta, assumed to be constant
rM = the required return on an average stock, which has increased by 30.0%

Plugging in the given values:

rDHF = 12.00% + 1.5(10.00%)
rDHF = 27.00%

rM = 10.00% + 30.0%(10.00%)
rM = 13.00%

Now we can solve for the new required return on DHF's stock:

rDHF = rRF + βDHF(rM - rRF)
rDHF = rRF + 1.5(13.00% - rRF)

We know that rDHF must be in equilibrium, so it must still equal 27.00%:

27.00% = rRF + 1.5(13.00% - rRF)

Solving for rRF:

rRF = 3.50%

Plugging back in to find rDHF:

rDHF = 3.50% + 1.5(13.00% - 3.50%)
rDHF = 16.50%

Therefore, the new required return on DHF's stock is 16.50%, or choice C).

DHF Company Has a Beta of 1