Timing Cash Flows in a Multistage Dividend Discount Model
Summary
The document explains how to value a stock with a multistage dividend discount model using a financial calculator’s net present value function. The key is to place each projected dividend at the correct time and combine the constant-growth terminal value with the dividend paid at the start of the stable-growth phase.
In the Brown Company example, dividends grow at 25% for two years and then at 6%, with a 10% discount rate and a most recent dividend of $1. The cash-flow sequence starts with zero at time zero, places the first two projected dividends in years one and two, and includes the year-three dividend plus the terminal value at year two. Discounting those cash flows gives the listed value of $36.65. The answer also notes a small arithmetic discrepancy in the questioner’s terminal cash flow; the essential correction is the timing convention. The example illustrates the method but does not discuss alternate growth assumptions or valuation risks.
Key ideas
- Start the calculator sequence with zero at time zero when valuing future dividends from the latest paid dividend.
- Project dividends through the high-growth period before calculating the stable-growth value.
- The terminal value belongs at the end of the final high-growth period and includes the subsequent dividend stream.
- Discount the correctly timed cash flows at the required return to obtain the stock value.
- The Brown Company example produces a value of $36.65 under its stated assumptions.
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# Multi-stage dividend discount model using financial calculator # Multi-stage dividend discount model using financial calculator 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? ## Answer by Alper (score 2, accepted) https://quant.stackexchange.com/a/68714 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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