Question

Nana Milk, a dairy product company, reported EPS of $2.40 in 2019 and paid dividends per share of $1.06. The earnings and dividends had grown 7.5% a year over the prior five years and were expected to grow 6% a year in the long term (starting in 2020). The stocks required return is 12.775%, and the actual P/E ratio is currently 10.

a) Estimate the fair P/E ratio for Nana Milk.

b) What long-term growth rate is implied in the firm's current P/E ratio?

Answer 1

Given, EPS₀ = $2.4

• DPS₀ = $1.06
• Past Growth = 7.5%
• Future Growth (G) = 6%
• Required Return (Ke) = 12.775%
• Actual PE = 10

Now, Calculating the price of share at t=0 based on Earnings growth model,

Price (P₀) = EPS₁ / ( Ke - G​​​​​​​​​​​​​​ ) = EPS₀ x (1 + G) / ( Ke - G) = $2.4 x (1.06) / (12.775% - 6%) = $37.55 (Approx)

A.) Fair PE = P₀ / EPS₀ = $37.55 / $2.4 = 15.65

B.) Long term Growth in Current PE of 10

Price (P₀) as per current PE = EPS₀ x PE = $2.4 x 10 = $24

Now Calculating the growth rate as per arrived price,

P₀ = EPS₁ / (Ke - G)

24 = 2.4 (1+G) / (12.775% - G)

10 = (1+G) / (12.775% - G)

1.2775 - 10 G = 1 + G

0.2775 = 11G

G = 2.5227 %