1. The equation for CAPM is kj = Rf + [bj x (Rm - Rf)] where, kj = required retu
ID: 2668188 • Letter: 1
Question
1. The equation for CAPM is kj = Rf + [bj x (Rm - Rf)]
where,
kj = required return on asset j,
Rf = risk-free rate of return, (6%)
bj = beta coefficient for asset j, (1.75)
Rm = market return. (10%)
kj = Solve for required return on asset j
The equation for the Gordon Growth Model is,
2. Gordon Growth Model equation
where,
P0 = price of the common stock,
D1 = per share dividend expected at the end of year 1,
D0 = most recently paid dividend,
Ks = required return on common stock,
g = growth rate in dividends.
To calculate g, we have to assume that future dividend payments will grow at a constant rate into the future forever. This constant rate can be estimated by examining the average growth rate in the past. On a calculator,
Let,
PV = $ .86,
FV = $2.00,
n = 8.
Solve for i. i = the average growth rate. In this case i = g = Solve for this unknown
Plugging this growth rate into the Gordon Growth Model,
P0 = FV(1 + i) = Solve for this stock price
kj - i
3. This time,
Let,
PV = $1.42,
FV = $2.00,
n = 5.
Solve for i. i = g = Solve for this growth rate
Plugging this growth rate into the Gordon Growth Model,
P0 = FV(1 + i) / kj - i = Solve for this stock price
Please use Apple as the stock to do calculation.
Explanation / Answer
1. From CAPM, Required rate of return = 6% + (10% - 6%)*1.75 = 6% + 4%*1.75 =6% + 7% =13% Required rate of return Kj is 13%. 2. Calculation of Growth rate: Future dividend = Current dividend(1 + g) $2.00 = 0.86(1 + g)^8 (1+g)^8 = 2.00/0.86 =2.235 1+g = 1.1057 g = 10.57% Stock price = FV(1+i)/(Kj - i) = 2(1+10.57%)/(13% - 10.57%) =2(1.1057)/0.0243 = 2.2114/0.0243 =91 Stock price is $91. 3. Calcultion of Growth rate: 2.00 = $1.42(1+g)^5 (1+g)^5 = 2.00/1.42 =1.4084 1+g =1.0709 g =0.709 Growth rate is 7.09%. Stock price = 2(1+7.09%)/(13% - 7.09%) = 2(1.0709)/0.0591 =2.1418/0.0591 =36.24 Stock price is $36.24Related Questions
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