Valuation
DCF valuation. Hieu Van Nguyen
A discounted cash flow values a company at the cash it is expected to produce. This build uses an invented company. Change growth, margin, tax, reinvestment and the discount rate and watch enterprise value, equity value and value per share move. The sensitivity grid and the football field show how wide the honest range really is.
What this shows
Free cash flow built from revenue, margin, tax, capital spending and working capital
Weighted average cost of capital built from its parts
Terminal value by growth rate and by exit multiple, side by side
A sensitivity grid and a football field of valuation methods
Sample build: DCF of an invented company
Alderfield Industrial is an invented mid-size manufacturer. The build projects five years of free cash flow, discounts them at a rate built from its parts, adds a terminal value two ways and bridges to value per share against an invented share price.
Synthetic inputs for illustration. Not data from any employer.
What to try
- Raise beta on the Discount rate tab, then read the terminal value share at the top of the page. A higher rate hits the distant cash flows hardest.
- On the Valuation tab, switch the terminal value method and compare the cross-check rows. A sound pair of assumptions implies similar numbers both ways.
- Turn on mid-year timing and watch value per share rise, because every cash flow now arrives half a year sooner.
- Press Higher rates, then open the football field to see how far the DCF bars move against comparables and deals.
The starting inputs.
Value per share
$15.45
Perpetual growth method
Against current price
+6.6%
Price $14.50
Enterprise value
$1,915M
Equity value $1,545M
Terminal value share
77%
Discount rate 8.72%
From revenue to free cash flow
The company earned revenue of 1,000 and EBITDA of 165.0 over the last twelve months. All figures are millions of dollars. Click a line to see its working for any year.
| Line | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 |
|---|---|---|---|---|---|
| Last year's revenue grown by this year's growth rate. | 1,060.0 | 1,117.0 | 1,170.0 | 1,218.3 | 1,260.9 |
| Fades in a straight line from the year one rate to the year five rate. | 6.0% | 5.4% | 4.8% | 4.1% | 3.5% |
| Earnings before interest, tax, depreciation and amortization: revenue times the margin, a rough measure of operating cash profit. | 180.2 | 196.9 | 213.5 | 230.0 | 245.9 |
| The yearly write-down of equipment and acquired assets. A real cost on paper, but no cash leaves. | -42.4 | -44.7 | -46.8 | -48.7 | -50.4 |
| EBITDA less depreciation and amortization: profit from operations. | 137.8 | 152.2 | 166.7 | 181.2 | 195.4 |
| Tax as if the company had no debt. The benefit of interest is counted in the discount rate instead. | -34.5 | -38.0 | -41.7 | -45.3 | -48.9 |
| Net operating profit after tax: EBIT once the tax is taken out. | 103.4 | 114.1 | 125.0 | 135.9 | 146.6 |
| Added back, because it reduced profit but did not use any cash. | 42.4 | 44.7 | 46.8 | 48.7 | 50.4 |
| Cash spent on equipment and facilities to keep the business running and growing. | -47.7 | -50.3 | -52.7 | -54.8 | -56.7 |
| Growing sales means more customer invoices and stock to fund. The rise in that balance is cash tied up. | -6.0 | -5.7 | -5.3 | -4.8 | -4.3 |
| The cash the business produces for all of its investors, lenders and owners alike, before any debt payments. | 92.1 | 102.9 | 113.9 | 125.0 | 136.0 |
Working for the selected line
Unlevered free cash flow
- Year 1: NOPAT 103.4 plus 42.4 less 47.7 less 6.0 is 92.1.
- Year 5: NOPAT 146.6 plus 50.4 less 56.7 less 4.3 is 136.0.
Free cash flow by year
The same five numbers are in the last row of the table above.
How the discount rate is built
| Part | Value | What it means |
|---|---|---|
| Risk-free rate | 4.25% | What a government bond pays. The return for waiting with no risk. |
| Equity risk premium | 5.00% | The extra return investors want for owning shares instead of bonds. |
| Beta | 1.15 | How strongly this company's shares move with the market. Above 1.00 means they swing more than the market. |
| Cost of equity | 10.00% | Risk-free rate plus beta times the equity risk premium. This is the CAPM formula. |
| Cost of debt, before tax | 6.50% | The interest rate the company pays on its borrowing. |
| Tax shield | 1.63% | Interest is tax deductible, so a tax rate of 25% gives back this much of the interest cost. |
| Cost of debt, after tax | 4.88% | Cost of debt before tax less the tax shield. |
| Equity share of capital | 75% | The financing mix the company aims for in the long run. It is a target mix, not the balance sheet as it stands today. |
| Debt share of capital | 25% | The rest of the financing mix. |
| Equity part | 7.50% | Equity share times the cost of equity. |
| Debt part | 1.22% | Debt share times the cost of debt after tax. |
| Weighted average cost of capital | 8.72% | Equity part plus debt part. Every future cash flow is discounted at this rate. |
Where the rate comes from
Why this rate matters
Beta, the risk premium and the debt mix are judgment calls. The sensitivity tab shows the value at rates a point either side of this one.
Terminal value, two ways
The terminal value stands for everything the company earns after year 5. One method grows the year 5 cash flow forever. The other sells the company at a multiple of year 5 EBITDA. Each is worked out in full here, and the one chosen above feeds the headline.
| Line | Perpetual growth (in use) | Exit multiple |
|---|---|---|
| Assumption | 2.50% a year | 9.0x EBITDA |
| Terminal value at the end of year 5 | 2,241.9 | 2,212.9 |
| Present value of the terminal value | 1,476.0 | 1,457.0 |
| Enterprise value | 1,915.3 | 1,896.3 |
| Value per share | $15.45 | $15.26 |
| Terminal value share of enterprise value | 77.1% | 76.8% |
| Cross-check: exit multiple each method implies | 9.1x | 9.0x |
| Cross-check: perpetual growth each method implies | 2.50% | 2.42% |
A perpetual growth rate of 2.50% implies an exit multiple of 9.1x. An exit multiple of 9.0x implies growth of 2.42% a year. If the two sit far apart, one assumption is out of line with the other.
Discounting each year
A dollar later is worth less than a dollar now. Each year's free cash flow is multiplied by a discount factor. With year-end timing the cash is assumed to arrive on the last day of each year.
| Line | Year 1 | Year 2 | Year 3 | Year 4 | Year 5 | Total |
|---|---|---|---|---|---|---|
| Free cash flow | 92.1 | 102.9 | 113.9 | 125.0 | 136.0 | 569.8 |
| Years from today | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | |
| Discount factor | 0.9198 | 0.8460 | 0.7782 | 0.7158 | 0.6584 | |
| Present value | 84.7 | 87.0 | 88.6 | 89.5 | 89.5 | 439.3 |
From enterprise value to value per share
| Step | Amount |
|---|---|
| Present value of free cash flow, years 1 to 5 | $439.3M |
| Present value of terminal value (perpetual growth) | $1,476.0M |
| Enterprise value | $1,915.3M |
| Less: debt | -$450.0M |
| Plus: cash | $80.0M |
| Equity value | $1,545.3M |
| Diluted shares | 100.0 million |
| Value per share | $15.45 |
| Current share price | $14.50 |
| Upside or downside against the price | +6.6% |
Equity value in three steps
Reading the terminal value share
Sensitivity: value per share
Each cell reruns the whole valuation with a different pair of assumptions and every other input held where you set it. The outlined cell is the current case, so it matches the headline when the same terminal value method is chosen. Change inputs on the other tabs and these grids move with them.
| Discount rate | 1.50% | 2.00% | 2.50% | 3.00% | 3.50% |
|---|---|---|---|---|---|
| 7.72% | $16.13 | $17.55 | $19.24 | $21.29 | $23.83 |
| 8.22% | $14.60 | $15.79 | $17.18 | $18.84 | $20.85 |
| 8.72% | $13.28 | $14.29 | $15.45 | $16.82 | $18.45 |
| 9.22% | $12.14 | $13.00 | $13.98 | $15.13 | $16.47 |
| 9.72% | $11.14 | $11.88 | $12.72 | $13.69 | $14.81 |
| Discount rate | 7.0x | 8.0x | 9.0x | 10.0x | 11.0x |
|---|---|---|---|---|---|
| 7.72% | $12.69 | $14.38 | $16.08 | $17.77 | $19.47 |
| 8.22% | $12.35 | $14.01 | $15.66 | $17.32 | $18.98 |
| 8.72% | $12.03 | $13.64 | $15.26 | $16.88 | $18.50 |
| 9.22% | $11.71 | $13.29 | $14.87 | $16.45 | $18.04 |
| 9.72% | $11.40 | $12.94 | $14.49 | $16.04 | $17.58 |
Which assumption moves the answer more
Down the middle column of the first grid, the discount rate runs from 7.72% to 9.72% and value per share runs from $19.24 to $12.72.
Across the middle row, perpetual growth runs from 1.50% to 3.50% and value per share runs from $13.28 to $18.45. Compare the two spreads to see which assumption deserves the argument.
Football field: four ways to value the same company
No single method decides. The bars show the range each method supports, in value per share. The DCF bars come from the middle of the grids above. The comparable and deal ranges use invented multiples listed below. The 52-week bar is trading history, not a valuation.
The four valuation methods agree between $14.12 and $14.45. The current price of $14.50 is inside the DCF range of $13.00 to $18.84.
| Method and basis | Low | High |
|---|---|---|
| 52-week trading rangeLowest and highest share price over the last 52 weeks | $12.40 | $17.20 |
| Trading comparables9.6x to 11.0x EV/EBITDA, the middle half of five invented peers, times last twelve months EBITDA of $165.0M | $12.14 | $14.45 |
| Precedent transactions10.8x to 12.3x EV/EBITDA, the middle half of five invented deals, times last twelve months EBITDA of $165.0M | $14.12 | $16.60 |
| DCF, exit multipleMiddle nine cells of the exit multiple grid: discount rate half a point either side, multiple one turn either side | $13.29 | $17.32 |
| DCF, perpetual growthMiddle nine cells of the perpetual growth grid: discount rate half a point either side, growth half a point either side | $13.00 | $18.84 |
| Set | Multiples | Middle half |
|---|---|---|
| Trading peers A to E | 8.8x, 9.6x, 10.3x, 11.0x, 12.1x | 9.6x to 11.0x |
| Precedent deals A to E | 10.2x, 10.8x, 11.5x, 12.3x, 13.4x | 10.8x to 12.3x |
Precedent deals usually sit above trading peers because a buyer pays a premium for control. These ranges are invented for illustration and do not describe any real company or transaction.
With a discount rate of 8.72% and perpetual growth of 2.50%, enterprise value is $1,915M, which is $15.45 a share. That is 6.6% above the $14.50 price, and the terminal value is 77% of enterprise value.
How I use it
Sanity-checking a deal price against what the cash flows can support
Showing leadership which assumption drives the answer
Pairing a DCF with comparable companies so no single method decides