Dividend Discount Model

If you can do this problem you’re golden for any DDM. A stock that currently does not pay a dividend is expected to pay its first dividend of $1.00 five years from today. Thereafter, the dividend is expected to grow at an annual rate of 25% for the next three years and then grow at a constant rate of 5% per year thereafter. The required rate of return is 10.3%. What is the value of the stock today? A. $20.65 B. $20.95 C. $22.72 D. $23.87

This ain’t easy bro. 2 period DDM. d1 = 1 d2 = 1.25 d3 = 1.25 * 1.25 d4 = 1.953125 p3 = 1.953125/.103 - .05 p3 = 36.85 thats how i far can go. lol

That would be A. The easiest way for me is to use CF and the NPV function. CF0=0 CF1=0, F1=4 CF2=1, F2=1 CF3=1.25. F3=1 CF4=1.25^2, F4=1 CF5=1.25^3 + stock price at CF5, which is 1.25^3*1.05/(10.3%-5%)=1.953+38.694=40.647 Hit NPV, insert I=10.3, got A.

correct map1 i am definitely going to master the technique you just posted, using the calculator to solve DDM looks like a huge time saver my problem usually stems from identifying whether the payment is received at the end or beginning of a period (“will pay a dividend for the first time 5 years from today”) and how to properly discount the values from that

well, 5 years from today is the end of he 5th year, beginning of the 6th. At the end of the first 4 years pays nothing, it pays $1 at the end of the 5th. A time line might help.

The sweet thing with CF is that you can make whatever calculus before hitting enter to set the value for CF.

Got A too.

Thanks map, I finally got it. Need another question like this!

  1. Discount the dividends to today, using 5, 6, 7, and 8 years for each, making sure you incresae the dividend by 25% each year. 2) At end of year 8, you need to calculate the value of the stock, which is : P=($1.95*1.05)/(0.103-0.05)= $38.63 3) Disount $38.63 for 8 years, and add to sum of (1) above. That will work too.

Pepp - You just need to add the extra step of discounting those values and adding them up. 1/1.103^5 + 1.25/1.103^6 + (1.5625+36.85)/1.103^7 = 20.65 Just need to remember that the $36.85 is at t = 7 because its based on the t=8 dividend of $1.953 growing at 5%.

thanks, needed to draw a time line. very helpful.

Dreary - You have to discount the $36.85 for 7 years not 8.

A. D5 = 1 D6 = 1.25 D7 = 1.5625 D8 = 1.953 P8 = D9/(.103-.05) = 2.051/(.103-.05) = 38.69 Price of the stock today = 1/(1.103)^5 + 1.25/(1.103)^6 + 1.5625/(1.103)^7 + 1.9523/(1.103)^8 + 38.69/(1.103)^8 = 20.65.

No, it is 8 years, because the value of the stock at the end of year 8 is $38.63. Next Dividend at End of year 9 is $1.95 * 1.05.

… see jdosh’s number too.

Well we’re all right, you guys are just adding an extra step that you don’t need to. Its easier to discount the first three dividends and then use the constant growth model on the 8th dividend NOT the 9th. The 8th dividend of $1.953 is the first dividend to start growing constantly at 5% so you can get the price at t = 7. They both get to the right answer but you guys have one extra dividend that you’re discounting.

SirViper, I don’t think so. Your answer comes to $20.90, which is not = to $20.65! Mine, comes to $20.61, so check to make sure you don’t miss.

what jdoshi has done is absolutely correct and easy to follow. that’s how i should be thinking too. what map has done is absolutely correct but he does it so fast, that i can’t follow him a lot of times. its like hes on a different wavelength.

No it works 1/1.103^5 + 1.25/1.103^6 + (1.5625+36.85)/1.103^7 = 20.65

SirViper Wrote: ------------------------------------------------------- > No it works > > 1/1.103^5 + 1.25/1.103^6 + (1.5625+36.85)/1.103^7 > = 20.65 That is correct too. you’ve discounted one period less and found the price at the end of T7. which includes the dividend for the fourth year.