Feb 05

How to incorporate share repurchases (buybacks) into Gordon growth model

by David Harper, CFA, FRM, CIPM

This smart paper by John Stowe, Dennis McLeavey, and Jerald Pinto illustrates why share repurchases (buybacks) are not inconsistent with a Gordon growth model. The classic dividend discount model (DDM) values an asset as a growing dividend stream:

The challenge is, how to incorporate share buybacks? It is very easy to make a mistake here. The key is to correctly incorporate the repurchases by reducing the number of shares held by the owner; if you start with, say, 1.0 shares and do not reduce this number to account for buybacks, you will double count cash flows. Very nice work, guys. It took me a couple hours to really understand their math. I replicated the mechanics in the EditGrid spreadsheet below.

You need to provide the following inputs (I start with the same as the authors'):

Total growth (gT): 7%
Buyback yield (b): 2%
Dividend yield (d): 4%
Discount rate (r): 10%
Initial dividend: $0.60

Given those inputs, the following are 'solved for' (i.e., you don't need to input):

Dividend growth = 2% = gT - b (i.e., the company can either grow dividends fully at 7%, or withhold 2% for buybacks)
Initial stock price = $20 = ($0.60)/(10% - 7%). That's the Gordon growth

The point is that the dividend discount model does indeed reconcile with a total cash flow model that incorporates buybacks. The nontrivial part is the fractional share repurchase which, under a 2% buyback yield translates into a slightly smaller number. So, for example, you still get a $20 initial stock price if you grow the total cash flow (dividend plus repurchases) at a lower rate:

$1.00 / (10% - 5%) = $20.00

The above numbers are actually rounded; due to the dynamics of the fractional share repurchase, the total cash flow is a tiny bit more than $1 and the growth is a tiny bit less than 5%. But no matter, I think they have done some very nice work to show in a straighforward way how buybacks do not wreck the Gordon growth model.