One reader values Harbor Coffee at $42.16 a share. Another gets $29.92. Both accept the same accounts for our fictional coffee business. They disagree about what happens next.
A discounted cash flow model, or DCF, brings future cash back to a value at one date. You can trace the gap to sales, spending and the return investors require.
This is the complete model in the optional valuation branch. Your job is to check what produces the answer. Harbor's $66 quote does not get to choose the inputs.
Match the cash to the rate
The cash before financing that we forecast is free cash flow to the firm (FCFF): cash for lenders and shareholders after operating taxes and reinvestment. It pairs with WACC, their weighted average cost of capital.
Value Harbor at FY3 year-end, its latest reported year. F1–F5 are the next five years, with cash arriving at each year-end. Business amounts are nominal USD millions; per-share values are dollars. Calculations keep full precision, then round for display.
Carry forward the operating forecast: start from FY3 sales of $1,100, grow them 5% annually, keep a 20% operating margin and tax operating profit at 25%. Depreciation stays at 40/1,100 of sales and capex at 60/1,100; working capital takes 20 cents per extra sales dollar.
The historical check is $220 × 75% + $40 − $60 − $10 = $135 of FCFF. Reported FCF is $120 because it deducts $20 of interest, less a $5 tax saving. Cash before interest and cash after interest need different rates.
The forecast excludes acquisitions, financing flows and non-operating income. Harbor has no cash interest income or stock compensation.
The discount-rate lesson supplies a 9% working WACC, rounded from 8.81%, and 8% and 10% alternatives. These are choices to test, just like the operating drivers.
Discount the five payments
The forecast gives F1 FCFF of $141.25 million, with operating costs and reinvestment already deducted. The new step is to account for when that cash arrives.
Using the present-value method, F1 cash is worth $141.25 ÷ 1.09 = $129.59 at FY3 year-end. F5's larger payment travels five years: $171.69 ÷ 1.09⁵ = $111.59.
More cash later can be worth less now. Each PV factor is 1 ÷ (1.09 raised to that year's number); multiplying cash by the factor gives its present value.
| Year | FCFF | Factor | PV |
|---|---|---|---|
| F1 | 141.25 | 0.91743 | 129.59 |
| F2 | 148.31 | 0.84168 | 124.83 |
| F3 | 155.73 | 0.77218 | 120.25 |
| F4 | 163.51 | 0.70843 | 115.84 |
| F5 | 171.69 | 0.64993 | 111.59 |
The five present values total $602.09 million. The 5% sales-growth input does not establish how EPS or reported FCF will grow; these cash figures come from the operating recipe.
Value the cash after year five
Harbor keeps selling coffee after F5. Terminal value puts one value on all that later cash, measured at F5 year-end. Here it represents a continuing business, with no liquidation or extra F5 operating payment.
Choose 2% annual sales growth after F5, down from 5%. This perpetual-growth approach keeps the margin, tax, depreciation and capex ratios in place forever. Growth still has an investment bill; three historical years cannot show that Harbor can sustain these ratios indefinitely.
First rebuild F6 cash. Sales rise from $1,403.91 to $1,431.99. Working-capital investment takes 20% of the $28.08 increase, or $5.62, down from $13.37 in F5. Applying the same operating recipe gives F6 FCFF of $183.15 million.
Multiplying F5 FCFF by 1.02 would give only $175.12 million. That shortcut misses the smaller working-capital bill. Slower growth leaves less new cash tied up in the business.
With those ratios fixed, FCFF grows 2% annually from F6 onward. Use r for the discount rate and g for that long-run growth rate:
At r = 9% and g = 2%, divide F6 cash by 0.07 to get $2,616.38 million at F5. Discount it back five years: $2,616.38 ÷ 1.09⁵ = $1,700.47 million.
The formula requires r > g. Both the F5 operating cash and the value of later cash sit at the same date, so both travel back five years:
Bridge from operations to one share
Add the two parts: $602.09 + $1,700.47 = $2,302.56 million of operating value. Terminal cash supplies $1,700.47 ÷ $2,302.56 × 100 = 73.85%. Most of the answer comes from years you have not forecast one by one.
The enterprise-value bridge takes you from operations to common equity. Harbor reports $105.4 million cash, $300 million debt and 50 million actual shares at FY3 year-end, with no other financing claims in the case.
Treat all cash as excess and debt book value as a proxy for its market value. Cash can be unrestricted and still needed to run the business; that part of the model needs evidence.
($2,302.56 + $105.40 − $300 − $0) ÷ 50 = $42.16 per share.
Keep the actual share count fixed, with no future issuance or buybacks. Historical weighted-average shares belong in EPS. The model keeps stock compensation expensed; adding it back while ignoring dilution would inflate the value per share.
The alternative, free cash flow to equity (FCFE), measures cash for common shareholders after debt cash flows, including net borrowing, and uses the cost of equity. That model already values common equity, so subtracting debt again counts its effect twice.
Find what changes the answer
DCF sensitivity analysis changes selected inputs to show their effect. Hold the five-year operating forecast fixed, but rebuild F6 sales and reinvestment for each g. The grid shows dollars per share:
| Discount rate | g = 1% | g = 2% | g = 3% |
|---|---|---|---|
| 8% | $44.28 | $50.03 | $58.08 |
| 9% | $38.06 | $42.16 | $47.62 |
| 10% | $33.24 | $36.26 | $40.15 |
At 2% growth, changing the rate moves value from $36.26 to $50.03. At 9%, changing growth moves it from $38.06 to $47.62. The small gap between r and g gives distant assumptions a large say in the answer.
Then change the business separately. The forecast lesson's downside uses 2% sales growth, an 18% margin, capex at 6% of sales, and 30 cents of working capital for each extra sales dollar. Carry those drivers through F6 and beyond, retaining the base tax and depreciation ratios, r = 9% and g = 2%.
That gives $477.50 million from F1–F5 and $1,213.22 million from later cash, both in present value. With the same cash, debt and shares, the result falls to $29.92. The weaker business cuts $12.24 per share; raising the discount rate alone from 9% to 10% cuts $5.90.
Look first at the cash definition, then at the assumptions behind that 73.85% terminal share. The rate/growth grid spans $33.24–$58.08; the operating downside reaches $29.92. These tested cases put no floor under the share price.
Harbor's $66 quote exceeds every result. Raising growth or lowering the rate until the model agrees would hide the disagreement. A sustained operating margin below 20% would break the base case; how much cash Harbor must retain remains unresolved.
Those are the next facts to investigate. A margin of safety can test room for error, but a discount alone cannot justify a purchase.
In short
- A DCF values the future you put into it.
- Match FCFF with WACC and FCFE with the cost of equity.
- Slower growth can reduce reinvestment: rebuild terminal cash before valuing it.
- Terminal value sits at the forecast endpoint and needs discounting too.
- Add excess cash and subtract financing claims before dividing by actual shares.
- Sensitivity shows what changes the answer; it does not prove the answer is right.