As an equity analyst you are concerned with what will happen to the required ret
ID: 2779327 • Letter: A
Question
As an equity analyst you are concerned with what will happen to the required return to Universal Toddler Industries's stoc as market conditions change. Suppose rFR=5%, rM=12%, and bUTI=1.4.
a) Under current conditions, what is the rUTI, the required rate of return on UTI stock?
b) Now suppose rFR (1) increase to 6% or (2) decreases to 4%. The slope of the SML remains constant. How would this affect rM and rUTI?
c) Now assume rFR remains at 5% but rM (1) increases to 14% or (2) falls to 11%. The slope of the SML does not remain constant. How would these changes affect rUTI?
Explanation / Answer
Answer (a)
Required rate of return on UTI stock = 14.8%
Answer (b) (1)
If r(FR) increases to 6% but slope of SML remains constant, then r(M) = 13% and r(UTI) = 15.8%
Answer (b) (2)
If r(FR) increases to 4% but slope of SML remains constant, then r(M) = 11% and r(UTI) = 13.8%
Answer (c) (1)
If r(FR) remains constant, r(M) increases to 14% and slope of SML is not constant, r(UTI) = 17.6%
If r(FR) remains constant, r(M) falls to 11% and slope of SML is not constant, r(UTI) = 13.4%
working
Risk Free rate r(FR) = 5%
Return on Market r(M) = 12%
Beta of Stock b(UTI) = 1.4
Expected Return on stock r(UTI) = r(FR) + b(UTI) * (r(M) – r(FR))
= 5% + 1.4 (12% - 5%)
= 5% + 1.4 * 7%
= 5% + 9.8% = 14.8%
Slope of SML is Treynor Ratio which is equal to
r(UTI) – r(FR)/b(UTI) = r(M) – r(FR)
(14.8% - 5%)/1.4 = 12% - 5% = 7%
The above equation can be rearranged as
r(UTI) – r(FR) = b(UTI) * (r(M) – r(FR))
which is the second part of the expected return calculation
If r(FR) increases to 6% but slope remains same at 7%
r(M) - r(FR) = 7% ==> r(M) – 6% = 7% ==> r(M) = 7% + 6% = 13%
r(UTI) = r(FR) + 1.4 (r(M) – r(FR) = 6% + 1.4 * 7% = 6% + 9.8% = 15.8%
If r(FR) decreases to 4%
r(M) - r(FR) = 7% ==> r(M) – 4% = 7% ==> r(M) = 7% + 4% = 11%
r(UTI) = r(FR) + 1.4 (r(M) – r(FR) = 4% + 1.4 * 7% = 4% + 9.8% = 13.8%
r(FR) remains constant at 5%, r(M) increase to 14% and Slope of SML is not constant
Slope = r(M) – r(FR) = 14% - 5% = 9%
r(UTI) = 5% + 1.4 * 9% = 5% + 12.6% = 17.6%
r(FR) remains constant at 5%, r(M) falls to 11% and Slope of SML is not constant
Slope = r(M) – r(FR) = 11% - 5% = 6%
r(UTI) = 5% + 1.4 * 6% = 5% + 8.4% = 13.4%
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