Question

In: Finance

Castles in the Sand generates a rate of return of 20% on its investments and maintains...

Castles in the Sand generates a rate of return of 20% on its investments and maintains a plowback ratio of .30. Its earnings this year will be $4 per share. Investors expect a 12% rate of return on the stock.

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

b. Find the price and P/E ratio of the firm if the plowback ratio is reduced to .20. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Solutions

Expert Solution

a. The price is computed as shown below:

= Dividend / (required rate of return - growth rate)

growth rate is computed as follows:

= rate of return generates x plowback ratio

= 0.20 x 0.30

= 6% or 0.06

Dividend is computed as follows:

= Earnings per share x ( 1 - plowback ratio)

= $ 4 x (1 - 0.30)

= $ 2.80

So, the price will be as follows:

= $ 2.80 / ( 0.12 - 0.06)

= $ 46.67 Approximately

So, the PE ratio will be:

= $ 46.6666667 / EPS

= $ 46.6666667 / $ 4

= 11.67 times Approximately

b. The price is computed as shown below:

= Dividend / (required rate of return - growth rate)

growth rate is computed as follows:

= rate of return generates x plowback ratio

= 0.20 x 0.20

= 4% or 0.04

Dividend is computed as follows:

= Earnings per share x ( 1 - plowback ratio)

= $ 4 x (1 - 0.20)

= $ 3.20

So, the price will be as follows:

= $ 3.20 / ( 0.12 - 0.04)

= $ 40

So, the PE ratio will be:

= $ 40 / EPS

= $ 40 / $ 4

= 10 times

Feel free to ask in case of any query relating to this question


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