HR Industries (HRI) has a beta of l 8, while LR Industries (LRI) beta is 0.6. Th
ID: 2801879 • Letter: H
Question
HR Industries (HRI) has a beta of l 8, while LR Industries (LRI) beta is 0.6. The risk-free rate is 55%, and the required rate of return on a stock with a beta of 1 is 12.5%. The expected rte 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 percentage points) in the required 13) returns for HRI and LRI? A. 3.8% B. 0.9% C. 1.5% D. 2.4% E. 3.5%Explanation / Answer
Calculation of required rate of return = Risk free rate + Beta( Market return - risk free rate)
Old RRR of HRI = 5.5 + 1.8 (12.5 - 5.5)
= 5.5 + 1.8*7
= 5.5 + 12.6 = 18.1%
Old RRR of LRI = 5.5 + 0.6 (12.5 - 5.5)
= 5.5 + 0.6*7
= 5.5 + 4.2 = 9.7%
The formula for finding out change in nominal risk free rate is:
1 + nominal = (1 + real) * (1 + inflation)
here change in real rate is 0 and inflation rate is 1.5%
1 + n = (1 + 0) * (1 + -0.015)
= 0.985
n = 0.985 - 1 = -0.015 = -1.5%
The nominal rate also falls by 1.5%
New nominal rate = 5.5 - 1.5 = 4%
Required return on beta of 1 = market return
New Required return for HRI = Rf + Beta (Rm - Rf)
= 4 + 1.8 (10.5-4)
= 4 + 1.8*6.5
= 4 + 11.7
= 15.7%
New required return for LRI = 4 + 0.6 (10.5-4)
= 4 + 0.6 * 6.5
= 4 + 3.9
= 7.9%
The difference in the required return for HRI = 18.1 - 15.7 = 2.4%
The difference in the required return for LRI = 9.7 - 7.9 = 1.8%
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