# Margin or growth *Price growth on what the new capital earns, not on the growth rate* --- Two papers in the same board pack. The chief operating officer wants a cost programme that takes about £1.3m a year out of the base and drops it straight to profit, banked in the run rate and the kind of thing this team has done before. The commercial director wants an expansion that lifts growth from 5% to 8%, in a market the business has not sold into, with a return nobody can yet evidence. Most boards take the first one, and I understand why: it is bankable, it is theirs, and the second one is a story about a market that does not exist yet. I've bought a few businesses, so I've run this comparison with some interest, and the arithmetic surprises people who haven't. <iframe src="https://anishshailpatel.github.io/instruments/margin-or-growth.html" title="What a cost programme and an expansion are each worth" width="100%" height="1420" style="width:100%;border:0;display:block;margin:1.2em 0;" loading="lazy" sandbox="allow-scripts allow-same-origin"></iframe> The business earns 16% on its capital against investors who would settle for 10%, and makes £10m. As it stands it is worth about £138m. The cost programme lifts profit to £11.3m and the return on that same capital to 18%, taking the business to £162m, so it creates £25m. The expansion takes it to £250m, which is £112m created. Same £10m of profit, no cost saving at all, and about four and a half times as much value. It is not free. Growing at 8% rather than 5% means reinvesting half the profit rather than a third, so the cash you can take out drops by roughly £2m a year. The £112m is what you are being paid for giving that up. ## Why growth wins A point of margin is worth the same at any level of return. It arrives once, it lands in the run rate, and that is the end of it. Growth wins because every pound reinvested earns six points more than investors require, and growth multiplies that spread across a larger and larger base each year. The spread is doing all the work. Set the second slider so the new market earns exactly 10%, the hurdle, and the curve goes flat. Growing faster adds nothing at all, because every extra pound reinvested is earning precisely what it costs. Below the hurdle the same arithmetic runs in reverse and growth destroys value while looking, in the management accounts, like success. ## Where the case breaks The denominator in a growth valuation is the gap between your hurdle and your growth rate, and near the hurdle that gap is only a couple of points wide, so small misses move the answer a long way. Deliver 7% instead of 8% and the £112m created becomes £50m. At 6% the cost programme is the better call. Drag the growth slider slowly and watch how much of the case rests on the last half a point. The second one actually kills deals. The number that decides the case is the return on the *new* capital, and it is easy to assume the new market pays what the old one does. It usually doesn't, at least at first. Set the return on the new market to 12% where the core earns 16% and the expansion is worth £167m against the cost programme's £162m, which is not an argument any more. Below about 12% the cost programme wins outright. Both cautions land on the growth case, and the model is being kind to the other one: it lets the whole £1.3m of savings arrive and stay out for five years, where in practice a good part of most cost programmes leaks back within two. > [!note]- The working > $\text{value} \approx \frac{\text{free cash flow}}{\text{required return} - \text{growth}}$ > Free cash flow is operating profit less the reinvestment growth demands, and the reinvestment rate is growth ÷ return on capital. The instrument runs the same equation and shows the three cases side by side before it draws the curve. So the honest version of the commercial director's paper is not "growth is worth more than margin". It is "growth is worth more than margin if this market returns at least 12%, and here is why I think it will". That is harder to write, which is most of why it is worth reading, and it is the paper [[Buying growth|you should be asking for]]. ---