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Instead of the wrote formula approach, this analyst shows that such problems can be decomposed into their cash flows at different points in time, which enables us to use NPV and IRR methods on a financial calculator to find the valuation as predicted by multi-stage DDM.

Although his answer was correct, I found it more intuitive to solve this way:

CF5 = 1
CF6 = 1.25
CF7 = 1.25^2 = 1.5625
CF8 = (1.25^3) + ((1.25^3 x 1.05)/0.103-0.05) = 40.64712

With those cashflows and IRR of 10.3% we still get the right answer of $20.65 after hitting the calculator's CPT button to find NPV.

So I thought, voila, this is awesome. But I encountered a different problem where I appear to be way off the mark using this approach.

An analyst feels that Brown Company’s earnings and dividends will grow at 25% for two years, after which growth fill fall to a constant rate of 6%. If the projected discount rate is 10% and Browns most recently paid dividend was $1 the value of Brown’s stock using the multistage dividend discount model would be:

A) 31.25 B) 33.54 C) 36.65

I interpreted this situation as follows:

CF0 = 1
CF1 = 1.25
CF2 = 1.25^2 = 1.5625
CF3 = 1.5625*1.06 + (1.5625*1.06)/(.1-.06) = 42.9688

With IRR at 10, the calculator gave me an NPV of 35.71. This matches none of the available choices. I fear I have blundered something.

Question

What should be the proper sequencing of cashflow inputs if to solve "Brown Company" multi-stage DDM valuation on a financial calculator?

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  • $\begingroup$ Shouldn’t your base in the third equation be 1.5625? $\endgroup$
    – Bob Jansen ♦
    Nov 9, 2021 at 6:55
  • $\begingroup$ @BobJansen Right, was a typo, good catch. My calculator inputs were 1.5625 $\endgroup$
    – Arash Howaida
    Nov 9, 2021 at 6:58

1 Answer 1

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There is a slight mistake in one of the calculations to your solution to the second question (outcome of CF3 should be 43.06) but that's not the reason you are not getting a correct result.

I reckon you are using your financial calculator alright but you are misinterpreting the timing and progress of Brown Company's cash flows a bit. The company's cash flows, as described in the question, should be

CF0 = 0
CF1 = 1.25
CF2 = 1.25^2 + (1.25^2*1.06) / (0.10-0.06) = 42.97

If one discounts these at 10% per annum, their total present value comes to 36.65 which is the answer C.

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