Question

Company Z-prime’s earnings and dividends per share are expected to grow by 4% a year. Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. Assume next year’s dividend is $9, the market capitalization rate is 9% and next year’s EPS is $14. What is Z-prime’s stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer #1

P4 = EPS_{5} / r

= [EPS1 × (1 + g1)^{3} × (1 + g2)] / r

= [$14 × (1.04)^{3} × (1.00)] / 0.09 = $15.75 / 0.09 =
$174.98

Note that $15 is the EPS for year 1. The 5 percent growth rate stops after year 4, so the exponent for the first growth rate must be 3, (Year 4 – Year 1). There is no growth in year 5.

P0 = DIV1/ (1 + r) + [DIV1× (1 + g)] / (1 + r)^{2} +
[DIV1× (1 + g)^{2}] / (1 + r)^{3} +

[DIV1× (1 + g)^{3}] / (1 + r)^{4} + P4/ (1 +
r)^{4}

P0 = $9 / 1.09 + ($9 × 1.04) / 1.09^{2} + ($9 ×
1.04^{2}) / 1.09^{3} + ($9 × 1.04^{3}) /
1.09^{4} + $174.98/ 1.09^{4}

= $8.26 + $7.88 + $7.52 + $7.17 + $123.96 = $154.78

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