Question

Castle-in-Sand generates a rate of return of \(20 \%\) on its investments and maintains a plowback ratio of \(0.30 .\) Its earnings this year will be \(\$ 4\) per share. Investors expect a \(12 \%\) rate of return on the stock.

Required:

(a.) Find the price and \(\mathrm{P} / \mathrm{E}\) ratio of the firm.

(b.) What happens to the P/E ratio if the plowback ratio is reduced to 0.20? Why?

(c.) Show that if plowback equals zero, the earnings-price ratio, E/P, falls to the expected rate of return on the stock.

Answer 1

Step 1 Solution to Part a

It is given that the rate of return on investment is 20% and plowback or retention ratio is 0.30

Sustainable growth rate = 20% * 0.3 = 6%

EPS = $ 4

Dividend payout ratio = 1-plowback = 1-0.3 = 0.7

D1 = EPS * dividend payout ratio = $4 * 0.7 = $2.8

 

 

 

 

Step 2 Solution to Part a

Part a )

Using Gordon dividend model

Dividend payout ratio = 1-plowback = 1-0.3 = 0.7

D1 = EPS * dividend payout ratio = $4 * 0.7 = $2.8

Share price = D1/ ( cost of equity - g) = 2.8 / (0.12-0.06) = $46.67(rounded to 2 decimals)

P/E = Price / EPS = $46.67/4 = 11.67 (rounded to 2 decimals)

 

 

Step 3 Solution to Part b

Part b )

Dividend payout ratio = 1-plowback = 1-0.2 = 0.8

D1 = EPS * dividend payout ratio = $4 * 0.8 = $3.2

When plowback ratio is 0.2 then g = 20% * 0.2 = 4%

Share price = 3.2 / ( 0.12 - 0.04) = 3.2 / 0.08 = $40

P/E = $40 / $4 = 10

 

 

Step 4 Solution to Part c

Part c )

Dividend payout ratio = 1-plowback = 1-0 = 1

D1 = EPS * dividend payout ratio = $4 * 1 = $4

When plowback ratio is 0 then g = 20% * 0 = 0%

Share price = 4 / ( 0.12 - 0.00) = 4 / 0.12 = $33.33

P/E = $33.33 / $4 = 8.333(rounded to 3 decimals)

E/P ratio= $4/$33.33=0.1200= 12%

i.e 12% equals return on the stock.

Part a- 11.67

Part b- 10

Part c- Calculation made as per question