1. The equation for CAPM is kj = Rf + [bj x (Rm - Rf)] where, kj = required retu

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 $36.24

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