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.