HR Industries (HRI) has a beta of 2.4, while LR Industries\' (LRI) beta is 0.9.

Question

HR Industries (HRI) has a beta of 2.4, while LR Industries' (LRI) beta is 0.9. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. The expected rate of inflation built into rRF falls by 1.5 percentage points, the real risk-free rate remains constant, the required return on the market falls to 10.5%, and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI? (Round your answer to two decimal places.)

Explanation / Answer

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HR Industries (HRI) has a beta of 1.2, while LR Industries' beta is 0.6. The risk-free rate is 6%, and the required rate of return on an average stock is 13%. Now the expected rate of inflation built into rRF falls by 1.5 percentage points, the real risk-free rate remains constant, the required return on the market falls to 10.5%, and all betas remain constant. After all of these changes, what will be the difference in the required returns for HRI and LRI? Round your answer to two decimal places.

solution

Initial values:
bHRI = 1.8
bLRI = 0.6
rRF = 6%
rM = 13%
After the change:
IP’ = IP - 1.5%
r*’ = r*
rM’ = 10.5%
So, after the change the risk free rate will fall by
1.5%.
rRF’ = 6% - 1.5% = 4.5%
The market risk premium after the change is:
(rM’ – rRF’) = 10.5% - 4.5% = 6%
Now SML: ri = rRF + bi x Market Risk Premium
rHRI= 4.5% + 1.8 x 6% = 15.3%
rLRI = 4.5% + 0.6 x 6% = 8.1%
Difference: 15.3% - 8.1% = 7.2

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