Question

One year from today, investors anticipate that Gel Ltd. shares will pay a dividend of $2.10 per share. After that, investors believe that the dividends will grow at 20% per year for three years before settling down to a constant rate of 6% indefinitely. The required rate of return on Gel’s shares is 15%. What is the current value of the share? Show workings. If the market price of the share is $35, is the share over-priced, under-priced or fairly-priced. Explain your answer.

Answer 1

The value of stock is calculated using the following equation of dividend discount model

Stock value(P0) = D1/(1+r)1 + D2/(1+r)2 + D3/(1+r)3 + (D4+P4)/(1+r)4

Where, Di is the expected dividend in the ith year

r is required return

g is constant growth rate

P4 is the stock price in the 4th year

D1 = $2.10

With the growth rate of 20%, dividends in the following years are calculated below

D2 = $2.10*(1+0.20) =$2.52

D3 = $2.10*(1+0.20)2 = $3.024

D4 = $2.10*(1+0.20)3 = $3.6288

P4 = D4*(1+gc)/(r-gc)

Where, gc is the constant growth rate

P4 = $3.6288*(1+0.06)/(0.15-0.06)

= $42.7392

P0 = 2.10/(1+0.15)1 + 2.52/(1+0.15)2 + 3.024/(1+0.15)3 + (3.6288+42.7392)/(1+0.15)4

  = $32.23

Therefore, current value of share = $32.23

Since value of share is less than the market price of $35, the share is overpriced.