# price-to-earnings (P/E) ratio

Industrial Light is expected to have earnings per share (EPS) of \$5.00 per share in five years, a dividend per share of \$2.50, a cost of equity of 12%, and a long-term expected growth rate of 5%. What is the terminal trailing price-to-earnings (P/E) ratio in five years? A) 7.50. B) 3.75. C) 7.14.

A

A [0.5* (1.05)] / (0.12 - 0.05) = 7.5x

A is correct - but why did you guys use 0.5 in the numerator? I used 2.5 instead and got the answer wrong.

A. as mentioned by bpdulog and calculated by jackofalltrades. If it was asking for terminal year Leading P/E, it would have been C.

P0 = D1 / r-g P0/E0 = (D1/E0) / r-g P0/E0 = [D0/E0 (1+g)] / r-g = .5 * 1.05 / .12 - .05 = 7.5 Edit: you have take dividend payout ratio (0.5) and not the dividend itself (2.5) in calculation for P/E.

ohh okk got it thanks!

If you are looking for an actual “value”, you would use the actual dividend. If you are looking for a multiple, you would use the “dividend ratio.”

You can get the same answer by using the actual price Triailing P/E year 5 = Price in year 5/Earings in year 5 Price in Year 5 = D(1+g)/(r-g) = 2.5(1.05)/(.12-.05) = 37.5 Earnings in year 5 = 5 So trailing P/E = 37.5/5 = 7.5 The other way is obviously one mentioned above P = D1(1+g)/(r-g) P = (1-b)*E(1+g)/(r-g) P/E = (1-b)(1+g)/(r-g) 7.14 is the leading P/E which is (1-b)/(r-g) OR 37.5/(5*1.05) P.S CFAI has given derivation of each multple starting out from P = D1(1+g)/(r-g) in its foot notes