Castles in the Sand generates a rate of return of 15% on its investments and mai

Question

Castles in the Sand generates a rate of return of 15% on its investments and maintains a plowback ratio of .20. Its earnings this year will be $6 per share. Investors expect a 10% rate of return on the stock.

Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

  P/E ratio

Find the price and P/E ratio of the firm, if the plowback ratio is reduced to .10? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Find the price and P/E ratio of the firm. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Explanation / Answer

Requirement a:

Given data,

Required Rate of Return, Ke = 15%

Plowback Ratio, b = 0.20

Dividend Payout Ratio = 1- 0.2 = 0.80

Earnings Per Share, E = $6

Dividend, D0 = E * 0.8 = 6*0.8 = $4.8

Expected Rate of Return, r = 10%

Growth Rate, g = b*r = 0.20 * 10 = 2%

Price = D0 (1+g) / (Ke - g)

= 4.8 (1+0.02) / (0.15 – 0.02)

= 4.896 / 0.13

= $37.66

P/E Ratio = Market Price/ EPS

= 37.66 / 6

= 6.2766

Requirement b:

Given data,

Required Rate of Return, Ke = 15%

Plowback Ratio, b = 0.10

Dividend Payout Ratio = 1- 0.1 = 0.90

Earnings Per Share, E = $6

Dividend, D0 = E * 0.8 = 6*0.9 = $5.4

Expected Rate of Return, r = 10%

Growth Rate, g = b*r = 0.10 * 10 = 1%

Price = D0 (1+g) / (Ke - g)

= 5.4 (1+0.01) / (0.15 – 0.01)

= 5.454 / 0.14

= $38.957

P/E Ratio = Market Price/ EPS

= 38.957 / 6

= 6.49283

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