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

Answer (a):

Formula for Growth Rate = Retention Ratio * Return on Investment

Retention Ration for year 1 to 4 = 60 % = 0.60

Return on investment for year 1 to 4 = 10 % or 0.10

Therefore growth rate is as follows:

Year 1 to 2 = 0.60 * 0.10 = 0.06 or 6 %

Year 2 to 3 = 0.60 * 0.10 = 0.06 or 6 %

Year 3 to 4 = 0.60 * 0.10 = 0.06 or 6 %

Answer (b):

Formula for Growth Rate = Retention Ratio * Return on Investment

Retention Ration after year 4 = (1-0.60) = 0.40 or 40%

Return on investment for after year 4 = 5 % or 0.05

Therefore long term growth rate after year 4 = (0.40*0.05) = 0.02 or 2 %

Answer (c) :

Calculation of Earnings per share :

Earnings per share of Year 1 = $4

Earnings per share of Year 2 = EPS₁(1+g) = $4 (1+0.06) = $4.24

Earnings per share of Year 3 = EPS₂(1+g) = $4.24 (1+0.06) = $4.49

Earnings per share of Year 4 = EPS₃(1+g) = $4.49 (1+0.06) = $4.76

Earnings per share of Year 5 = EPS₄(1+g) = $4.76 (1+0.02) = $4.86

Answer (d) :

Calculation of Dividend per share :

Dividend per share = Earnings per share * Dividend Payout Ratio

Dividend per share of Year 1 = ($4*0.40) = $1.6

Dividend per share of Year 2 = ($4.24*0.40) = $1.696

Dividend per share of Year 3 = ($4.49*0.40) = $1.796

Dividend per share of Year 4 = ($4.76*0.40) = $1.90

Dividend per share of Year 5 = ($4.86*0.60) = $2.92

Answer (e):

Calculation of Current Share Price Using Dividend Discount Model:

Present value of the stock = [D₁ / (1 + r)¹] + [D₂ / (1 + r)²] + [D₃ / (1 + r)³] + [D₄ / (1 + r)⁴] + [Perpetuity Value / (1 + r)⁴]

D₁ = $1.6

D₂ = $1.696

D₃ = $1.796

D₄ = $1.90

D₅ = $ 2.92

After Year 4 dividends are expected to grow @ 2% per year forever, therefore for that we need to find out the perpetuity value at the end of year 4.

Perpetuity Value = (D₅ / (cost of capital - growth rate)

= $2.92 / (0.04-0.02)

= $146

Present value of the stock = [$1.6 / (1 + 0.04)¹] + [$1.696 / (1 + 0.04)²] + [$1.796 / (1 + 0.04)³] + [$1.90 / (1 + 0.04)⁴]+ [$146 / (1 + 0.04)⁴]

= $1.54 + $1.57 + $1.60 + $1.62 + $124.80

=$131.13

Present Value of stock today = $131.13

Calculation of Current Share Price Using P/E Model:

Price/Earnings = 30

Earnings Per share = $4

Price / $4 = 30

Therefore Price of share = 30 * $4

= $130

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