Assume a company has an annual dividend of $2.00 per share. it is expected to grow that dividend at a rate of 10% p. a. over the next two years and then at a rate of 7% p. a. thereafter. assuming the market's required rate of return for this company's stock is 15% p. a.: its implied valuation using a dividend discount model is closest to:

a. $27.50
b. $28.20
c. $28.90
d. $29.70

PHASE 1

Growth rate (g) = 10% = 0.10                                                  

No of years (n) = 2 years

Cost of equity (Ke) = 15% = 0.15

Current dividend paid (Do) = $2

Dividend in 1  year’s time (D1) =  Do(1+g)n

                                               = $2(1 + 0.10)1

                                              =  $2.20  

Dividend in 2 year’s time (D2) =  Do(1+g)n

                                               = $2(1 + 0.10)2

V1 = D1            +           D2

       (1 + K)                   (1 + K)2

V1 =  $2.20     +     $2.42

        (1 + 0.15)         (1 + 0.15)2

V1 = 2.20         +       $2.42

       1.15                   1.15)2

V1 = $1.9130    +       $1.8297

V1 = $3.7427

PHASE 2    

g = 7% = 0.07

V2 = DN( 1 + g)

        (Ke –g)(1+ K)n

V2 = $2.42(1 + 0.07)

         (0.15 – 0.07)(1+ 0.15)2

V2 = $2.5894

       (0.08)(1.15)2

V2 = $2.5894

        (0.08)(1.3225)

V2 = $24.4745

Current market price = V1 + V2

                                  = $3.74 + $24.47

                                  = $28.21

The correct answer is B

Explanations:

In this case, there is need to calculate the current  market price of equity in the first growth regime of 10%. The current market price is a function of  dividend in 1 year’s time and dividend in year’s time divided by (1 + Ke)n.

In the second phase of growth, the growth rate is 7%.  We need, to determine the current market price , which is a function of dividend in 2 year’s time, subject to the new growth rate divided by the product of K-g and (1+ K)n.                                                                                                                                                                                                                                                                                                                                                                                                    

The current market price is the aggregate of market prices for the two growth regimes.        

a loan? that’s my guess, anywho.

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