### CFA Practice Question

The forward P/E ratio of a stock equals 7.1. The company has just released its earnings figures at \$12.20 per share. The firm's dividend payout ratio is 28%. If the current stock price is \$100, what is its 1-year expected return under the dividend discount model?
A. 19.40%
B. 14.83%
Explanation: It is important to remember that the forward P/E ratio is the ratio of the current stock price and next year's expected earnings. The firm's expected earnings next year equal 100/7.1 = \$14.09 per share. Since the current earnings equal \$12.2, the dividend growth rate equals (14.09/12.2 - 1) = 15.45%. To get the 1-year expected return, first calculate the expected price next year. Under the dividend discount model, the P/E ratio remains constant if the firm makes no policy changes and there are no market disruptions. Therefore, the price next year is expected to be \$100*(1 + 15.45%) = \$115.45. The dividend next year equals \$14.09 * 0.28 = \$3.95 per share. Thus, the 1-year expected return (capital gains + dividends) = (P1+D1)/P0 = (115.45 + 3.95)/100 - 1 = 19.4%.

User Comment
shasha growth rate "g" is for both dividend growth and price growth. so P1 = P0*(1+g) = 100*1.1545
derekt If the P/E ratio is the historical P/E one the growth could be estimated from the information given and used to find next years EPS.
danlan E=100/7.1, g=E/12.2-1,

The result is
(100*(1+g)+E*0.28)/100-1
=g+E*0.28/100=g+0.28/7.1
jerepast where does this come from? [dividend growth rate = (NI(n+1)/NI(n) - 1)]
ontrack Try this method: Po/E1=(D1/E1)/k-g
Po/E1 is 7.1, g=15.45% as per the soultion given, D1/E1 is .28(also given in Qs). Put in values to get k=19.33%=expected discount rate or returns expected .
steved333 7.1x12.20=86.62
.28x12.20=3.416
100-86.62=13.38
(13.38+3.416)/86.62= .1939

Not hard if you use the STO and RCL buttons on the BAII.
steved333 Just figure out the original price then use the HPY formula of (FV-PV+Div)/PV.
surob looks like it is not that difficult question
Hervz You always have to keep in mind that the dividends are growing at the same pace as the earnings (RR stays th same). - for the purpose of the test, anyway
serboc HERVZ: So your telling me that you can take g (if given) X Eo = E1?
mekc thx ontrack... like that method
SaeedAlam Thanks Steve that really helped it matches with the notes on price multiples!
dipu617 @steved333
Could you please tell us how to use STO and RCL buttons on BA II Plus for this problem? Thank you.
santibanez PER=PayOut/(r-g)
Obtain g by estimating E1 first
r=(PayOut/PER)+g
r=(.28/7.1)+.15447
r=.1938