Question

A stock is currently selling on the NYSE for $40 per share. Based on the last twelve months, this represents a P/E ratio of 12.5 and a dividend yield of 4.8%. After an analysis of all the relevant variables, you estimate that the dividends per share will grow at an annual compouind rate of 8% and that GMA will maintain the same payout ratio each year as the previous year. GMA stock is expected to sell at a 15 P/E ratio at he end of the third year. Your required rate of return is 12% per year. Based on a three-year investment horizon and assuming that all your estimates are correct, how much is the stock currently over or under priced?

Answer 1

First year P / E = 12.5

Current share price = $40

P / E = Current share price / Earnings per share

=> Earnings per share = Current share price / (P / E)

= $40 / 12.5

= $3.20

Dividend yield = 4.8%

Dividend yield = Dividend per share / Share price

=> Dividend per share = Share price * Dividend yield

Current dividend per share = $40 * 4.8%

= $1.92

Dividend payout = Dividend per share / Earnings per share

= $1.92 / $3.20

= 60%

Payout ratio = Dividend per share / Earnings per share

= $1.92 / $3.20

= 60%

Dividend after first year = $1.92 * (1 + 8%)

= $1.92 * 1.08

= $2.07

Dividend after second year = $2.07 * (1 + 8%)

= $2.07 * 1.08

= $2.24

Dividend after third year = $2.24 * (1 +8%)

= $2.24 * 1.08

= $2.42

Third year P / E ratio = 15

Payout ratio = Dividend per share / Earnings per share

This implies, Earnings per share = Dividend per share / Payout ratio

Third year earnings per share = $2.42 / 60%

= $4.03

Third year share price = P / E * Earnings per share

= 15 * $4.03

= $60.47

Total equity value per share in the third year = Third year share price + third year dividend + second year dividend + first year dividend

= $60.47 + $2.42 + $2.24 + $2.07

= $67.20

Three-year CAGR = ($67.20 / $40) ^ (1 / 3) - 1

= ($1.68) ^ (1 / 3) – 1

= 18.88%

The CAGR is 18.88%, which means the share price is under-priced. If the share price were higher and the dividends per share remain the same, the return would be lower than 18.88%.

Current share price at 12% annual return = $67.20 / ((1 + 12%) ^ 3)

= $67.20 / ((1.12) ^ 3)

= $67.20 / 1.40

= $47.83

Current share price under-valuation = ($40 / $47.83) – 1

= 0.84 – 1

= -16.37%