# dividend discount model

Q. A stock is not expected to pay dividends of \$1.50 per share until 2 years from now. At that time, the dividend distribution is going to be 40% of net income, earnings growth is projected to be 8% and ROE is expected to be 15%. If required rate of return is 10% first 2 years and 12% thereafter, what is approximate value of stock today? If I calculate g = ROE * (1-dividend payout) = .15 * .6 = .09, should I use g = 9% or the 8% that was provided in the problem?

I read through the problem and didn’t even think about calculating g. If they give it to you, why not use it?

what was the answer? I got \$35.71 and 46.28…respectvly for 8 and 9%

Here’s what I did (G=8%) D= 1.5*1.08 Stock price= ((1.5*1.08)/(0.12-0.08) = \$40.5 PV of this at 10% for 2 years = \$33.47 Should we use an average? ((8+9)/2)=8.5%?

CF0=0 CF1=0, F1=1 at the end of the second year, an inflow of \$1.5 (the dividend). At that time, earnings were \$1.5/40%=\$3.75. One year later earnings grow at 8%, that is the earnings in year 3 are expected to be \$3.75*1.08=\$4.05. At this time, the ROE is expected to be 15%, and growth being 8%, that means the dividend payout ratio must have been 1- 8%/15%=1 - 53.33% = 46.67%. Hence, the expected dividend at the end of year 3 must have been \$4.05*46.67%=\$1.89. Now, the price of the stock at year 2 would be \$1.89/(12%-8%)=\$47.25, so the total cash flow at the end of year 2 is \$1.5+\$47.25=\$48.75 CF2=\$48.75, F2=1 Hit NPV, for I=10, get the NPV (which s how much is the stock worth today) of \$40.29

honestly, that analysis would’ve taken me 4 minutes tops to do. and we only have an average of 1 minute per question dont we?

Answer: k=RFR + B(R-RFR) = .06+.09(.11-.06)=.105 DDM Po=Do(1+g)/(k-g)= 1.4/(.105-.08)=56 I think chasingoats was right. During a timed exam I was too hung up trying to calculate something that was already given.