A worked example you can check by hand

The assumptions

This example is deliberately rigged to be checkable. The growth rate is set equal to the discount rate, which makes every discounted year come out to exactly the same number. If you work through it by hand and your figures match, the tool is doing what it claims.

Money figures are in millions and the share count is in millions. Because both use the same scale, the scale cancels when we divide, and the value per share lands in ordinary pounds or dollars.

1. Free cash flow over the last twelve months: 100
2. Forecast years: 10
3. Growth rate: 10% every year
4. Discount rate: 10%
5. Terminal growth rate: 2.5%
6. Total debt: 500
7. Cash and equivalents: 200
8. Diluted shares outstanding: 50

Projecting and discounting

Year one is 100 grown by 10%, which is 110. Discount it by one year at 10%: 110 divided by 1.1 is exactly 100.

Year two is 110 grown by 10%, which is 121. Discount it by two years: 121 divided by 1.1 squared, which is 1.21, is again exactly 100.

This is the trick that makes the example checkable. Because the cash flow grows at precisely the rate we discount at, the two effects cancel and every single year has a present value of exactly 100. Ten years therefore contribute exactly 1,000.

The final forecast year, year ten, has a projected cash flow of 100 times 1.1 to the tenth power, which is 259.374246.

The terminal value

The perpetuity starts the year after the forecast ends, so first step year ten up by one more year of terminal growth: 259.374246 times 1.025 gives 265.858602.

Now divide by the discount rate minus the terminal growth rate. That is 10% minus 2.5%, which is 0.075. So 265.858602 divided by 0.075 gives a terminal value of 3,544.781362.

That figure is expressed in end-of-year-ten money, so it is discounted by ten years, the same as the final forecast year. Dividing 3,544.781362 by 1.1 to the tenth power gives 1,366.666667.

A useful cross-check: because the growth and discount rates cancel again, this reduces exactly to 100 times 1.025 divided by 0.075, which is 4,100 divided by 3. The result is exactly one thousand three hundred and sixty-six and two thirds.

Enterprise value, then equity value

Add the discounted forecast to the discounted terminal value: 1,000 plus 1,366.666667 gives an enterprise value of 2,366.666667. Note that the terminal value is 58% of the total, which is typical.

Now the step the arithmetic is easy to skip. Net debt is total debt minus cash: 500 minus 200 is 300. Subtract that from the enterprise value: 2,366.666667 minus 300 gives an equity value of 2,066.666667.

Divide by the 50 million shares: the value per share is 41.333333.

The mistake this example is designed to catch

If you divide the ENTERPRISE value by the share count instead — 2,366.666667 divided by 50 — you get 47.333333 per share. That is fourteen and a half percent too high, and it is wrong because it quietly hands the lenders’ 300 million to the shareholders.

The gap is exactly net debt divided by shares: 300 divided by 50 is 6, and 47.333333 minus 41.333333 is 6. This is not a rounding artefact; it is a whole missing step.

This is not a hypothetical error. It is the defect our audit found in the source project this tool was rebuilt from, and it is why the tool displays the bridge from enterprise value to value per share as four explicit lines. Our test suite asserts both numbers so the bug cannot come back unnoticed.

Changing one thing at a time

Switch the terminal method to a 12 times exit multiple and the terminal value becomes 259.374246 times 12, which is 3,112.490952. Discounted, that is exactly 1,200, the enterprise value becomes 2,200, and the value per share falls to 38.00. A different terminal assumption moved the answer by over eight percent.

Switch the convention to mid-year and every exponent drops by half a year. The enterprise value rises to 2,482.180941 and the value per share to 43.64, because the same cash is assumed to arrive sooner.

Give the company a net cash position instead — 100 of debt and 400 of cash — and net debt becomes negative 300. Subtracting a negative adds, so the equity value rises to 2,666.666667 and the value per share to 53.33, above the enterprise value per share rather than below it.

Three assumption changes, three materially different answers, from identical cash flow projections. That is the honest lesson of this example.

Questions

Limitations

• This example is constructed for checkability, not realism. Growth exactly equal to the discount rate for ten straight years is not a typical business.
• The figures demonstrate the arithmetic only. They are not a valuation of any real company and carry no view on any security.
• Reproducing the example by hand verifies the tool’s arithmetic. It does not validate the assumptions, which remain your responsibility in any real model.