Question

 

 

Castle-in-Sand generates a rate of return of  on its investments and maintains a plowback ratio of  Its earnings this year will be  per share. Investors expect a  rate of return on the stock.

Required:

(a.) Find the price and  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

Explanation:

a.Calculating the Price and P/E Ratio of the firm when the flow back ratio is 0.30 :

Calculate the growth rate;

As per the information given in the question we have

Rate of return = ROE = 20 %    ; Plow back ratio = 0.30   ;   Earnings per share = $ 4 per share ;

Investor’s expected rate of return = 12 % = 0.12

The formula for calculating the growth rate is :

Growth rate = ROE * Plow back Ratio

Applying the information available in the formula we have growth rate as :

= 20 % * 0.30

Hence, the growth rate = 6 %answer

Calculate the Dividend per share;

The formula for calculating the Dividend per share is

= Earnings per share * Dividend Payout ratio

= Earnings per share * ( 1 – Plow back Ratio )

As per the information given in the question we have

Plow back Ratio = 30 % = 0.30

Earnings per share = $ 4

Applying the available information in the formula for Dividend per share we have

Dividend per share = $ 4 * ( 1 – 0.30 )

= $ 4 * 0.70

= $ 2.80

hence, the Dividend per share = $ 2.80 answer

Calculate the price per share ;

The formula for calculating the price is = D / ( Ke – g)

Where

D = Dividend per share   ;   Ke = Investor’s expected rate of return ; g = growth rate ;

As per the information given in the question we have

D = $ 2.80   ; Ke = 12 % = 0.12 ; g = 6 % = 0.06

Applying the above information in the formula we have price as follows:

= $ 2.80 / ( 0.12 – 0.06 )

= $ 2.80 / 0.06

= $ 46.6667

= $ 46.67 ( when rounded off to two decimal places )

Hence the price is = $ 46.67 answer

Calculate the P/E Ratio ;

The formula for calculating the P/E Ratio = Price per share / Earnings price per share

As per the information available we have

Price per share = $ 46.6667   ;    Earnings price per share = $ 4

Applying the available information in the formula we have P/E Ratio as

= $ 46.6667 / $ 4

= 11.6667

= 11.67 ( when rounded off to two decimal places )

Hence the P/ E Ratio is = 11.67 answer

b.Calculate the Price and P/E Ratio of the firm when the plow back ratio is reduced to 0.20 :

Calcululate the  growth rate;

As per the information given in the question we have

Rate of return = ROE = 20 %    ; Plow back ratio = 0.20   ;   Earnings per share = $ 4 per share ;

Investor’s expected rate of return = 12 % = 0.12

The formula for calculating the growth rate is :

Growth rate = ROE * Plow back Ratio

Applying the information available in the formula we have growth rate as :

= 20 % * 0.20

Hence the growth rate = 4 % answer

Calculate the Dividend per share;

The formula for calculating the Dividend per share is

= Earnings per share * Dividend Payout ratio

= Earnings per share * ( 1 – Plow back Ratio )

As per the information given in the question we have

Plow back Ratio = 0.20

Earnings per share = $ 4

Applying the available information in the formula for Dividend per share we have

Dividend per share = $ 4 * ( 1 – 0.20 )

= $ 4 * 0.80

= $ 3.20

Hence the Dividend per share = $ 3.20 answer

Calculate the price per share ;

The formula for calculating the price is = D / ( Ke – g)

Where

D = Dividend per share   ;   Ke = Investor’s expected rate of return ; g = growth rate ;

As per the information given in the question we have

D = $ 3.20   ; Ke = 12 % = 0.12 ; g = 4 % = 0.04

Applying the above information in the formula we have price as follows:

= $ 3.20 / ( 0.12 – 0.04 )

= $ 3.20 / 0.08

= $ 40

= $ 40.00 ( when rounded off to two decimal places )

Hence the price is = $ 40.00 answer

Calculate the P/E Ratio ;

The formula for calculating the P/E Ratio = Price per share / Earnings price per share

As per the information available we have

Price per share = $ 40   ;    Earnings price per share = $ 4

Applying the available information in the formula we have P/E Ratio as

= $ 40 / $ 4

= 10

= 10.00 ( when rounded off to two decimal places )

hence the P/ E Ratio is = 10.00 answer

a.Calculating the Price and P/E Ratio of the firm when the flow back ratio is 0.30 ;

answer,Price = $46.67

Answer P/E=11.67

b. Calculating the Price and P/E Ratio of the firm when the plow back ratio is reduced to 0.20 

Answer= $40

Answer=10