Question on Dividend Discount Model.

CFA Level I Corporate Finance
#1

Hullo!

sorry for the long winded questions below. Both are related to the number of periods which i am confused about.

Question 1 which got me stumped on the use of the power (squared or cube) used on this question:

Say ABC Corp is expected to pay a dividend of $2.25 per share this year. Sales & profit for ABC are forecasted to grow at a rate of 20% for 2 yrs and thereafter, grow at 5% per yr forever. Dividend and sales growth are expected to be equal. If ABC’s shareholders require a 15% return, the per share value of ABC’s common stock based on the dividend discount model is closest to:

a. $22.75

b. $26

c. $28.50

The answer is C - $28.50.

P2 = D3/k-g = 2.25(1.2)squared/0.15-0.05 = 32.40

P0 = 2.25/1.15 + 2.70/(1.15)squared + 32.40/(1.15)squared = $28.50

My question is with regards to P2 = D3/k-g = 2.25(1.2) squared /0.15-0.05

Shouldn’t it be 2.25 (1.2) cube /0.15-0.05 instead?

Reason being the formula for Pn = D n+1 / (k-g). Hence, as n=2, shouldn’t cube be used instead of squared?

Question 2 concerning the number of periods to use:

A stock with dividends is expected to grow at 20% per year for 4 yrs, thereafter they are expected to grow at 5% per year forever. The last dividend paid was $1 and ke = 10%. Calculate the value of this stock using the multistage growth model.

The answer is as follows:

1.20/1.1 + 1.44/(1.1)squared + 1.73/(1.1)cube + 41.60/(1.1)cube = $34.84

I am very confused over the number of periods to use.

Both questions seem so similar but they each use different periods: 2 for the first one and 3 for the second. To me, i would use 4 periods for the second question because the stock is expected to grow for the first 4 years.

Am i missing something here? Your help is greatly appreciated.

Thanks!

#2

For these types of problems, it’s best not to get worked up over the numerator by squaring and such. They cover such a small period that it works better to deal with this visually.

Draw a line:

|------|-------|-------|-------| 0 D1 D2 D3

Mark above the line the undiscounted dividends so that it looks like this:

2.25 2.7 3.24

|--------|---------|---------|-------| 0 D1 D2 D3

D3 grows forever so we have can used the dividend discount model to find P2.

P2=3.24/(.1-.05)=32.4

Now this P2 is the price 2 years from now (I believe this is where you’re getting confused), so we have to discount it 2 periods. D2 has to be discounted two periods, D1 discounted one period. Also, I am seeing that you are discounting by the wrong rate, you only need to use g for the dividend discount model. Once you find that P2, you don’t use g anymore because you only needed it for the DDM.

All you have to do is discount as such:

32.4/1.15^2=24.5

2.7/1.15^2=2.09

2.25/1.15=1.95

Add the values: 24.5+2.09+1.95 = ~28.50

#3

|——|——-|——-|——-|——-|

0 D1 D2 D3 D4

Mark above the line the undiscounted dividends so that it looks like this:

1.2 1.44 1.73 2.08

|——–|———|———|——-| 0 D1 D2 D3 D4

Similarly from this timeline, we use D4 to calculate P3?

Hi FratBoyDeluxe, i think i’m on my way to understanding this…between both questions above, i probably got confused. The first undiscounted payment ($2.25) should be depicted in the first year (D1) whereas in the second question, the first undiscounted payment ($1.20) should already incorporate its growth of 20%.

Can i say that when drawing the timeline, the final undiscounted payment should be the last year of the existing growth rate?

#4

Yes.

Hi

Yes, that’s very important. And with this last undiscounted dividend you will see perpetual smaller growth to calculate P3 using D4. I had trouble with this at first, but it helps to say “OK this is the last of the high growth and it is from this dividend onwards that it will grow @ 5%”

Don’t make it complicated on yourself, always, always, draw the timeline.

Hope this helps.

#5

Yes it certainly helped. Appreciate your efforts here.

Thanks FratBoyDeluxe.