The value of any asset that produces cash is the present value of the cash it will produce. A bond is worth the discounted value of its coupons and redemption; a block of flats is worth the discounted value of its rents and eventual sale; and a business is worth the discounted value of the cash it will generate for its investors.
This is the theoretical foundation of corporate finance, and the cash-flow-based approach to valuation. It is the method a bidder with control should use, because control gives access to all the cash flows of the business, not only the dividends that a minority holder receives. It also forces the valuer to state the assumptions on growth, margins, investment and risk, instead of hiding them in a multiple.
This topic explains how to value a business by discounting free cash flows: what the free cash flow to the firm is and how to forecast it, the discount rate (the weighted average cost of capital), the terminal value, how to turn an enterprise value into an equity value, how sensitive the answer is to its assumptions, and the related economic value added approach, with worked examples. The next topic covers the valuation of bonds and preference shares.
The syllabus lists cash-flow-based valuation among the approaches to estimating the value of a business. Read dividend valuation of shares first.
In 30 seconds
Enterprise value = the present value of the free cash flows to the firm, discounted at the weighted average cost of capital (WACC). Free cash flow = net operating profit after tax (NOPAT) + depreciation − capital expenditure − increase in working capital. Forecast explicitly for a period (usually 5 to 10 years) until the business reaches a steady state, then add a terminal value: TV = FCFn × (1 + g) ÷ (WACC − g), discounted back n years.
Equity value = enterprise value − net debt (debt less cash). The result is very sensitive to the WACC and g and the terminal value is often more than half the total. Economic value added (EVA) = NOPAT − (WACC × capital employed); the present value of future EVA plus the capital employed equals the enterprise value.
Free cash flow to the firm
The free cash flow to the firm (FCFF) is the cash generated by the operations of the business that is available to all the providers of capital, after the investment needed to keep the business going and growing:
FCFF = NOPAT + depreciation and amortisation − capital expenditure − increase in working capital
where NOPAT is operating profit × (1 − tax rate). It is before interest, so it does not depend on how the business is financed; the financing is reflected in the discount rate. Example: in year 1 operating profit is ₦120m, tax 30%, so NOPAT is ₦84m; depreciation is ₦30m; capital expenditure ₦40m; working capital rises by ₦6m. FCFF = 84 + 30 − 40 − 6 = ₦68m.
Forecasts of the cash flows must be consistent: sales growth drives profit, investment and working capital, and the tax rate and capital allowances should reflect the law (the Nigeria Tax Act 2025 rate of 30% for companies other than small companies, and straight-line capital allowances).
The discount rate
FCFF is the cash flow to debt and equity holders together, so it is discounted at the WACC, based on the target’s own business risk and a sensible long-term financing mix (see the topics on the cost of capital and on project-specific rates).
If the target has a different business risk from the bidder, use a rate for the target’s risk, not the bidder’s. The cash flows and the rate must also be consistent in their treatment of inflation: nominal cash flows (including expected inflation) at a nominal rate.
In Nigeria, with high inflation and interest rates, the choice of nominal rate and a realistic growth rate matters greatly, and a foreign investor must also consider currency risk.
The terminal value
A business is assumed to continue for ever, but forecasts cannot go on for ever. After an explicit period (say five years) the cash flows are assumed to grow at a constant rate g, and the value of all later cash flows at that date is the terminal value: TV = FCFn × (1 + g) ÷ (WACC − g), discounted back n years.
(Alternatively, the terminal value is the final-year earnings before interest, tax, depreciation and amortisation (EBITDA) times a multiple from comparable companies.) The long-term growth rate g must be sustainable: no more than the long-term growth of the economy.
A worked example
A target has forecast FCFF of ₦68m, ₦74m, ₦81m, ₦88m and ₦94m in years 1 to 5. The WACC is 13% and long-term growth is 4%. Net debt is ₦150m.
| Year | FCFF ₦m | Factor at 13% | Present value ₦m |
|---|---|---|---|
| 1 | 68 | 0.885 | 60.2 |
| 2 | 74 | 0.783 | 58.0 |
| 3 | 81 | 0.693 | 56.1 |
| 4 | 88 | 0.613 | 54.0 |
| 5 | 94 | 0.543 | 51.0 |
| Present value of years 1 to 5 | 279.3 | ||
| Terminal value 94 × 1.04 ÷ (0.13 − 0.04) = 1,086.2; × 0.543 | 589.6 | ||
| Enterprise value | 868.8 | ||
| Less net debt | (150.0) | ||
| Value of equity | 718.8 | ||
The enterprise value is ₦868.8m, of which the terminal value is 589.6 ÷ 868.8 = 68%. Equity is the enterprise value less the market value of debt and any other claims, plus any surplus cash: ₦718.8m. If the target is unquoted a marketability discount may be considered for a minority holding, but a purchaser of control normally pays for the whole of the equity.
Sensitivity
| WACC | g | Enterprise value ₦m |
|---|---|---|
| 12% | 4% | 980.0 |
| 13% | 4% | 868.8 |
| 14% | 4% | 779.9 |
| 13% | 3% | 804.8 |
| 13% | 5% | 948.9 |
A one-point change in the WACC moves the value by about 12%, and a one-point change in the growth rate by about 8%, so the valuer should present a range and not a single number, and be clear about the assumptions behind the terminal value.
Economic value added
Economic value added (EVA) measures the value that the business creates after charging for all the capital used: EVA = NOPAT − (WACC × capital employed). A company with NOPAT of ₦100m and capital employed of ₦800m at a WACC of 12% has a capital charge of ₦96m and an EVA of ₦4m. A positive EVA means the business earns more than its investors require.
The value of the business equals the capital employed plus the present value of all future EVA (the market value added): with an EVA of ₦11m a year for ever on capital of ₦900m and WACC of 11%, the present value of the EVA is 11 ÷ 0.11 = ₦100m and the enterprise value is 900 + 100 = ₦1,000m, the same as NOPAT ÷ WACC = 110 ÷ 0.11.
EVA is therefore a different way of arranging the same cash-flow valuation, and is also used to judge managers: a business that earns less than its WACC destroys value even when it reports a profit.
Free cash flow to equity
The alternative is to value the equity directly by discounting the free cash flow to equity (cash left after interest, tax, investment and net borrowing) at the cost of equity. It gives the same answer when the assumptions are consistent, but it requires a forecast of the amount borrowed or repaid.
The enterprise approach is more usual for takeovers because the financing of the target will be changed by the bidder.
The ideas in more depth
Why discounted cash flow suits control
A controlling shareholder can decide how much of the cash flow is paid out, reinvested or used to repay debt, so what matters is the total free cash flow. A minority holder cannot, and relies on dividends. The enterprise approach therefore measures the value of the whole business; the dividend approach measures the value of a small stake.
The two should agree if the dividends are the full distribution of the free cash flows to equity.
Why the terminal value dominates
Because a business is assumed to continue for ever, most of its value lies in the long future, especially for a growing business or when the discount rate is low. A valuer must therefore examine the terminal assumptions most carefully: whether growth of 4% is sustainable, whether the margin and the reinvestment needed to sustain it are consistent, and whether the WACC will stay constant.
A check is to compare the implied multiple (here the terminal value of ₦1,086m is 11.6 times the final-year free cash flow) with market multiples.
Sources and references
- No accounting standard prescribes the method; International Financial Reporting Standard (IFRS) 13 Fair Value Measurement describes the income approach (present value techniques) and International Accounting Standard (IAS) 36 Impairment of Assets, uses discounted cash flow for value in use. The tax rate follows the Nigeria Tax Act 2025.
These points are stated as at 5 November 2026.
Worked examples
Example 1: free cash flow. Operating profit ₦120m; tax 30%; depreciation ₦30m; capital expenditure ₦40m; working capital up ₦6m. Required: FCFF.
- NOPAT.
120 × 0.70 = ₦84m. - FCFF.
84 + 30 − 40 − 6 = ₦68m.
Example 2: terminal value. Year 5 FCFF ₦94m; WACC 13%; g 4%. Required: the terminal value and its present value.
- TV.
94 × 1.04 ÷ 0.09 = ₦1,086m. - PV.
1,086 × 0.543 = ₦590m.
Example 3: EVA. NOPAT ₦100m; capital ₦800m; WACC 12%. Required: EVA.
- Charge.
0.12 × 800 = ₦96m. - EVA.
100 − 96 = ₦4m.
How to answer in the exam
- Set out the free cash flows by year with the working, then the discount factors.
- Calculate the terminal value and discount it from the right year.
- Deduct net debt to reach the equity value.
- State the assumptions and show the sensitivity to the rate and growth.
Common mistakes in the exam
- Discounting free cash flows at the cost of equity (when they are before interest) or equity flows at the WACC.
- Forgetting to discount the terminal value or discounting it from the wrong year.
- Including interest in the free cash flow.
- Forgetting to deduct net debt.
- Using a growth rate that exceeds the discount rate or the economy.
- Forgetting the investment in working capital and capital expenditure needed for growth.
Quick revision
- FCFF = NOPAT + depreciation − capital expenditure − increase in working capital.
- Enterprise value = present value of FCFF at the WACC + present value of terminal value; equity = enterprise value − net debt.
- TV = FCFn(1 + g) ÷ (WACC − g).
- EVA = NOPAT − WACC × capital employed.
Practice questions
These are original questions written in the style of the Institute’s exams. Try each one before you open the answer. Section A is a recall check, because the paper itself is written.
Recall check: multiple choice
Question 1. A business’s value by discounted cash flow is:
- Its net assets
- Its earnings
- The present value of its future free cash flows
- Its share price
Show the answer
C. The cash it will generate for investors.
Question 2. Free cash flows to the firm are discounted at:
- The cost of equity
- The WACC
- The risk-free rate
- The inflation rate
Show the answer
B. They belong to all providers of capital.
Question 3. The terminal value is:
- FCFn(1 + g) ÷ (WACC − g)
- FCFn × g
- FCFn ÷ WACC × g
- Zero
Show the answer
A. A growing perpetuity at the end of the forecast.
Question 4. Equity value equals the enterprise value:
- Plus net debt
- Times net debt
- Divided by net debt
- Less net debt
Show the answer
D. Debt holders have first claim.
Question 5. Free cash flow equals:
- Profit before tax
- NOPAT + depreciation − capital expenditure − increase in working capital
- Revenue − cost
- Dividends
Show the answer
B. Cash available to all providers of capital.
Question 6. The value is very sensitive to:
- The WACC and the long-term growth rate
- The company name
- The auditor
- The year end
Show the answer
A. Particularly through the terminal value.
Question 7. The terminal value usually represents:
- A small part of the value
- No value
- A large part of the value
- The tax
Show the answer
C. Because the business is assumed to continue for ever.
Question 8. Economic value added is:
- Revenue less cost
- Net assets
- Dividends
- NOPAT less a charge for the capital employed
Show the answer
D. Profit after charging for the capital used.
Question 9. The enterprise cash-flow method suits a bidder because it:
- Ignores risk
- Uses only dividends
- Values the whole business, including control of all the cash flows
- Is exact
Show the answer
C. A controlling owner has access to all of them.
Question 10. The growth rate in the terminal value should be:
- Sustainable in the long term
- Above the WACC
- Above the discount rate
- Negative
Show the answer
A. No more than the long-term growth of the economy.
Section B style: written questions
Question 11 (10 marks). (a) State how free cash flow to the firm is calculated. (3 marks) (b) State why it is discounted at the WACC. (3 marks) (c) State why the terminal value needs careful assessment. (4 marks)
Question 12 (15 marks). A business has NOPAT of ₦110m a year for ever, capital employed of ₦900m and a WACC of 11%. (a) Calculate the capital charge and EVA. (5 marks) (b) Calculate the present value of the EVA. (4 marks) (c) Calculate the enterprise value and check it against NOPAT ÷ WACC. (6 marks)
A further written question
Question 13 (20 marks). Forecast free cash flows to the firm are ₦40m, ₦46m, ₦52m and ₦57m in years 1 to 4. The WACC is 12% and long-term growth 3%. Net debt is ₦90m and there are 50m shares.
(a) Calculate the present value of years 1 to 4. (6 marks) (b) Calculate the terminal value and its present value. (6 marks) (c) Calculate the enterprise value, equity value and value per share. (6 marks) (d) State the percentage of the enterprise value from the terminal value. (2 marks)
Model answers
Show the model answer to Question 11
(a) NOPAT + depreciation − capital expenditure − increase in working capital (3).
(b) The cash flow is before interest, so it is available to both lenders and shareholders, and the discount rate must be their average required return after tax (3).
(c) It is a large part of the value; it depends on the growth rate and discount rate, which are estimates; and the growth must be sustainable (4).
Show the model answer to Question 12
(a)
- Capital charge 11% × 900 = ₦99m (3)
- EVA 110 − 99 = ₦11m (2).
(b) 11 ÷ 0.11 = ₦100m (4).
(c)
- 900 + 100 = ₦1,000m (3)
- NOPAT ÷ WACC.
110 ÷ 0.11 = ₦1,000m, the same (3).
Show the model answer to Question 13
(a) 40 ÷ 1.12 = 35.7; 46 ÷ 1.2544 = 36.7; 52 ÷ 1.4049 = 37.0; 57 ÷ 1.5735 = 36.2; total ₦145.6m (6).
(b)
- TV = 57 × 1.03 ÷ (0.12 − 0.03) = ₦652.3m (3)
- present value 652.3 ÷ 1.5735 = ₦414.6m (3).
(c)
- Enterprise value 145.6 + 414.6 = ₦560.2m (2)
- equity 560.2 − 90 = ₦470.2m (2)
- per share 470.2 ÷ 50 = ₦9.40 (2).
(d) 414.6 ÷ 560.2 = 74% (2).
Spotted a mistake? Tell us and we will check it.
