DDM Question

CFA Level I Equities
#1

This is a Schweser question.

Assume the Wansch Corporate is expected to pay a dividend of $2.25 per share this year. Sales and profit for Wansch are forecasted to grow at a rate of 20% for two years after that, and then grow at 5% per year forever. Dividend and sales growth are expected to be equal. If Wansch’s shareholders require a 15% return, the per-share return value of Wansch’s common stock based on the DDM is closest to.

My thought of reasoning:

CF0 = $2.25

CF1 = $2.7 (grow at 20%)

CF2 = $3.24 (grow at 20%) + $34 (calculated below stock price)

Stock Price: $3.40 (next year’s dividend - grown at 5%) divided by .1 (15% return - 5% growth) = $34

Discounted at 15% = $32.76

The book gives the following CF:

CF1= $2.25

CF2 = $2.7 + $32.40

(2.25(1.2)^2) / (.1) = $32.40

If we receive the $2.25 dividend this year, why would we discount it?

I looked at the multi-stage DDM formula again and it seems that we don’t have to take the “growth” dividend because it is already factored into the price when we do the required rate of return minus the growth rate. That’s one area where I messed up. I could have sworn we took the first dividend with the stable growth rate, so if any one can officially clarify that would be very helpful.

#2

Presumably, “a dividend of $2.25 per share this year” means at the end of this year, not today.

It’s a poorly written question.

Don’t give it another thought. The questions on the real exam will be well-written.

#3

Thanks!

Regarding the terminal value, do we use the first dividend with the stable growth rate, or the last dividend with the high growth rate?

#4

Either; you’ll get the same answer. (Try it.)

#5

Thanks again! This is very helpful.

#6

My pleasure.

#7

You can use the constant growth formula to get a terminal value as long as dividends AFTER the given one grow at a constant rate. Since the $2.25 is “expected” I would assume that’s D1 (i.e. CF1), D2 is 2.70 and D3 is 3.24.

Since all dividends AFTER D3 grow at a constant rate, we can use the 3.24 to get P2 (Price at time 2) of 32.40 Discounting the 2.25 (CF1) and (32.40+2.70) (CF2) at 15% gives a price of 28.50.

If you used D4 (3.420) to get P3, the answer is the same.

The reason you can use either D3 or D4 is that since everything is growing at a constant rate after D3, it’s also growing at a constant rate at any point after D3.

Whether you’re using a constant or multi-stage model, you’re calculating the PV of an infinite stream of dividends. Think of those dividends as an infinitely long carpet. Calculating a terminal value allows you to “roll up” the value of ALL dividends following that point. So, you’ve effectively “rolled up” the carpet to that point. Then, you discount all cash flows up to that point back to the present. In other words, in the second step, you “roll the carpet” the rest of the way to time zero.

-s

diviTo know which dividend you can use to get the terminal value