Question

. PPG is expected to earn $4 per share in one year. The market demand for the new product is expected to be high so PPG decides to retain 60% of its earnings in year 1, 2, and 3. The reinvestments are expected to generate 10% return. Starting from year 4, PPG will maintain an 60% dividend payout rate because the investment return is expected to decline to 5% due to increased competition from similar products. (round to two decimal places for all the answers)

a. What is the earnings growth rate for year 1 to 2, year 2 to 3, and year 3 to 4?

b. What is the long term growth rate after year 4?

c. Calculate the earnings per share for year 1, 2, 3, 4, and 5.

d. Calculate the dividend per share for year 1, 2, 3, 4, and 5.

e. If the cost of equity capital is 4%, find the current share price.

f. PPG manager decides to try alternative valuation method based on multiples from the industry peers. The average forward P/E ratio (i.e., price divided by earnings in the coming year) of the same industry is 30. What is should be the per share price of PPG based on the P/E ratio?

Answer 1

a.

Growth rate = retention ratio*return on reinvestment

Year 1 to 2 = 0.6*10% = 6%

Year 2 to 3 = 0.6*10% = 6%

Year 3 to 4 = 0.6*10% = 6%

b.

longterm growth rate after year 4 = retention ratio*return on reinvestment = (1 - dividend payout)*10% = (1 - 0.6)*10 = 4%

c.

Earnings per share = Previous Earning per share*growth rate

till year 3 growth rate is 6%

Year 1 = 4*1.06 = 4.24

Year 2 = 4*(1.06^2) = 4.495

Yer 3 = 4*(1.06^3) = 4.764

After year 3 the growth rate becomes 4%

Year 4 = 4*(1.06^3)*(1.04) = 4.955

Year 5 = 4*(1.06^3)*(1.04^2) = 5.153

d.

Dividend per share = earning per share*(1 - retention ratio) or earning per share*dividend payout ratio

Year 1 (D1) = 4*1.06*(1- 0.6) = 1.696

Year 2 (D2) = 4*(1.06^2)*(1-0.6) = 1.798

Year 3 (D3) = 4*(1.06^3)*(1-0.6) = 1.906

Dividend per share = earning per share*dividend payout ratio

Year 4 (D4) = 4*(1.06^3)*1.04*0.6 = 2.973

Year 5 (D5) = 4*(1.06^3)*(1.04^2)*0.6 = 3.092

e.

cost of equity capital is 4%

The current share price is the PV of all the future cash flows = D1/1.04 + D2/1.04^2 + D3/1.04^3 + P3/1.04^3

where P3 is the price at year 3 which can be calculated using constant growth of the dividend model i.e.

P3 = D4/(cost of equity - growth rate)

=> P3 = 2.973/(4% - 4%) = infinite

So this is the limitation of dividend gordon model where the growth rate = cost of capital.

So we have to use the relative valuation technique which is the next question

f.

forward P/E ratio = 30

Forward earnings will be = Earning of year 1 = 4.24

Price = P/E * Earnings = 10*4.24 = 42.4