Question

Shell is experiencing rapid growth. Earnings and dividends are expected to grow at a rate of 15% during the next 2 years, at 13% the following year, and at a constant rate of 6% during Year 4 and thereafter. Its last dividend was $1.15, and its required rate of return is 12%.

b) Find the PV of the firm’s stock price at the end of Year 3.

f) Calculate the dividend and capital gains yields for Years 1, 2, and 3.

Dividend Yield Year 1 =   %

Capital Gains Yield Year 1 =   %

Dividend Yield Year 2 =   %

Capital Gains Yield Year 2 =   %

Dividend Yield Year 3 =   %

Capital Gains Yield Year 3 =   %

Answer 1

D0 = 1.15

Growth rate for first 2 years is 15%, for next year is 13% and a constant growth rate (g) of 6%

D1 = 1.15 * 1.15 = 1.3225

D2 = 1.3225 * 1.15 = 1.5209

D3 = 1.5209 * 1.13 = 1.7186

D4 = 1.7186 * 1.06 = 1.8217

Required return = 12%

P3 = D4 / (r - g)
P3 = $1.8217 / (0.12 - 0.06)
P3 = $30.3617

PV = P3 / (1+1.12)^3 = $21.61(approx)

b) Hence the PV of firm at the end of year 3 is $21.61(approx)

P2 = D3/(1+r) + P3/(1+r)
P2 = $1.7186/1.12 + $30.3617/1.12
P2 = $28.6431

P1 = D2/(1+r) + P2/(1+r)
P1 = $1.5209/1.12 + $28.6431/1.12
P1 = $26.9321

P0 = D1/(1+r) + P1/(1+r)
P0 = $1.3225/1.12 + $26.9321/1.12
P0 = $25.2273

Year 1:

Dividend Yield = D1 / P0
Dividend Yield = 1.3225 / 25.2273 = 5.24%

Capital Gain Yield = Required Return - Dividend Yield
Capital Gain Yield = 12% - 5.24% = 6.76%

Year 2:

Dividend Yield = D2 / P1
Dividend Yield = $1.5209 / $26.9321 = 5.65%

Capital Gain Yield = Required Return - Dividend Yield
Capital Gain Yield = 12.00% - 5.65% = 6.35%

Year 3:

Dividend Yield = D3 / P2
Dividend Yield = $1.7186 / $28.6431 = 6.00%

Capital Gain Yield = Required Return - Dividend Yield
Capital Gain Yield = 12.00% - 6.00% = 6.00%

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