Currently, the dividend-payout ratio (DIE) for the aggregate market is 60 percent, the required return (k) is 11 percent, and the expected growth rate for dividends (g) is 5 percent. a. Compute the current earnings multiplier.
b. You expect the DIE payout ratio to decline to 50 percent, but you assume there will be no other changes. What will be the P/E? c. Starting with the initial conditions, you expect the dividend-payout ratio to be constant, the rate of inflation to increase by 3 percent, and the growth rate to increase by 2 percent. Compute the expected P/E.
d. Starting with the initial conditions, you expect the dividend-payout ratio to be constant, the rate of inflation to decline by 3 percent, and the growth rate to decline by 1 percent. Compute the expected PIE.

A. 10x

B.8.33x

C.8.57x

D.15x

Explanation:

a. Computation of current earnings multiplier

Using this formula

Current earnings multiplier=Dividend-payout ratio/(Required return-Expected growth rate for dividends)

Where,

Dividend-payout ratio(D/E)= 0.60

Required return (k) = 0.11

Expected growth rate for dividend (g)= 0.05

Let plug in the formula

Current Earning multiplier =0.60/(0.11−0.05)

Current Earning multiplier=0.60/0.06

Current Earning multiplier=10x

Therefore the Current Earning multiplier will be 10x

b. Calculation for the what will be the P/E

Using this formula

P/E=Expected decline D/E payout ratio /(Required return-Expected growth rate for dividends)

Where,

Expected decline D/E payout ratio=0.50

Required return (k) = 0.11

Expected growth rate for dividend (g)= 0.05

Let plug in the formula

P/E=0.50/(0.11-0.05)

P/E=0.50/0.60

P/E=8.33x

Therefore the P/E will be 8.33x

c. Computation for increase in expected P/E

Using this formula

Increase in Expected P/E=Dividend-payout ratio(D/E)/(Increase in rate of inflation - Increase in growth rate )

Let plug in the formula

Where,

Dividend-payout ratio(D/E)=0.60

Increase in rate of inflation =(0.11+0.03=0.14)

Increase in growth rate=(0.05+0.02=0.07)

Let plug in the formula

Increase in Expected P/E=0.60/[(0.11+0.03)-(0.05+0.02)]

Increase in Expected P/E=0.60/(0.14-0.07)

Increase in Expected P/E=0.60/0.07

Increase in Expected P/E=8.57x

Therefore the increase in expected P/E will be 8.57x

d .Computation for decline in the expected P/E

Using this formula

Decline in the expected P/E=Dividend-payout ratio(D/E)/(Decline in rate of inflation - Decline in growth rate )

Let plug in the formula

Where,

Dividend-payout ratio(D/E)=0.60

Decline in rate of inflation =(0.11-0.03=0.08)

Decline in growth rate=(0.05-0.01=0.04)

Let plug in the formula

Decline in the expected P/E=0.60/[(0.11-0.03) -(0.05-0.01)

Decline in the expected P/E=0.60/(0.08-0.04)

Decline in the expected P/E=0.60/0.04

Decline in the expected P/E=15x

Therefore the Decline in the expected P/E will be 15x.