Advanced Financial Management · Valuation for acquisitions and mergers

Cash Flow Based Valuation: DCF and Free Cash Flow for ACCA AFM

Updated 11 October 2026 · Fact-checked

Cash flow based valuation finds what a target is worth by discounting its future free cash flows. Forecast free cash flow to the firm, discount it at WACC, add a terminal value, then deduct debt to reach equity value. Add the value of synergies separately and test the financing effects, for example with APV.

Understand Cash Flow Based Valuation: DCF and Free Cash Flow

A business is worth the cash it will generate for its investors, discounted for time and risk. That is the idea behind discounted cash flow (DCF) valuation. You forecast cash, choose a discount rate that matches the risk, and add it up in present value terms.

Free cash flow to the firm (FCFF) is the cash available to all providers of finance, both lenders and shareholders, after tax and after the investment needed to keep the business running and growing. It is measured before interest. You discount it at the WACC to get enterprise value. Then you deduct the market value of debt (and add surplus cash) to get equity value.

Free cash flow to equity (FCFE) is the cash left for shareholders after interest and after borrowing or repaying debt. You discount it at the cost of equity and the result is equity value directly. Use FCFF when the target's gearing may change after the deal, because WACC is then hard to keep constant. FCFE needs a stable financing pattern.

Forecasts only run for a few years, so most of the value sits in the terminal value. This is the value at the end of the forecast of all later cash flows. The usual method is a growing perpetuity. Growth must be realistic and below the long-run growth of the economy. A small change in growth or WACC moves the answer a lot, so say so in your report.

Synergies are extra cash flows that exist only because of the combination, such as cost savings or higher revenue. Value them separately, discount them at a rate that reflects their risk, and compare the total with the price. If the acquirer changes the target's financing, value the operations first and then add the financing effects. This is adjusted present value (APV): base case NPV at the ungeared cost of equity plus the PV of the tax shield and issue costs.

Key rules to remember

Free cash flow to the firm: FCFF = EBIT × (1 − t) + depreciation − capital investment − increase in working capital; Capital investment must cover both replacement and expansion. Use the tax rate on operating profit, not on profit after interest.
Free cash flow to equity: FCFE = FCFF − interest × (1 − t) + net new borrowing; Equivalent to profit after tax + depreciation − capital investment − increase in working capital + net new debt. Discount at the cost of equity.
Terminal value (growing perpetuity): TV at year n = FCF(n+1) ÷ (r − g) = FCF(n) × (1 + g) ÷ (r − g); Valid only if r > g. TV is a value at year n, so discount it using the year n factor. For a no-growth perpetuity set g = 0.
Enterprise value and equity value: EV = Σ FCFF(t) ÷ (1 + WACC)^t + TV ÷ (1 + WACC)^n ; Equity value = EV − market value of debt + surplus cash; Use market value of debt where given, not book value.
WACC: WACC = [E ÷ (E + D)] × ke + [D ÷ (E + D)] × kd × (1 − t); Use market values for E and D, and the gearing the target will have after the deal if it changes.
Sustainable growth: g = retention (reinvestment) rate × return on new investment; Use it to check that your terminal growth rate is supported by the reinvestment in the forecast.
Ungeared cost of equity (Modigliani and Miller with tax): ke(g) = ke(u) + (ke(u) − kd) × (1 − t) × D ÷ E; Rearrange to find ke(u). Alternatively, asset beta = equity beta × E ÷ [E + D(1 − t)] when debt beta is taken as zero.
Adjusted present value: APV = base case NPV at ke(u) + PV of tax shield on debt − issue costs; Tax shield per year = debt × interest rate × tax rate. Discount it at the pre-tax cost of debt unless told otherwise.

How to solve Cash Flow Based Valuation: DCF and Free Cash Flow questions

Use this order for any free cash flow valuation question. It keeps the working tidy, so marks follow even if one number is wrong.

1Read the requirement. Decide whether you need enterprise value, equity value, a price range, or the value of synergies, and which currency and units to use.
2Build the free cash flow for each year. Start from EBIT, deduct tax on EBIT, add back depreciation, deduct capital investment and working capital increases. Ignore interest and financing flows in FCFF.
3Choose the discount rate. Use WACC for FCFF and cost of equity for FCFE. If the target's risk or gearing differs from the acquirer's, build a rate for the target using its own data.
4Calculate the terminal value with the growing perpetuity formula at the end of the forecast. Then discount it with the same factor as the last year's cash flow.
5Add the present values to get enterprise value. Deduct debt (and add surplus cash) to get equity value. Divide by the number of shares if a price per share is asked for.
6Add synergies and financing effects separately. Discount synergies at a rate that matches their risk. If financing changes, use APV and show the tax shield and issue costs clearly.
7Compare with the offer price and conclude. State the maximum price the acquirer can pay, the gain or loss, and the key assumptions and sensitivities (growth, WACC, synergy delivery).
8Write for the reader. Give a short recommendation with reasons, and note limits such as forecast uncertainty and the large share of value in the terminal value.

Quickest way: Perpetuity shortcut with a table for the explicit years

When to use it: Use when the exam gives a few years of forecasts and then steady growth. It also helps when time is tight in Section A.

Write a small table with years across the top and rows for FCFF, discount factor and present value. Do not rebuild FCFF if the question already gives it.
Calculate the terminal value in one line: last FCFF × (1 + g) ÷ (WACC − g).
Multiply the terminal value by the last year's discount factor. Do not discount it separately again.
Sum the present values, deduct debt, and put a box round the equity value.
Give a one-line comment on the biggest risk, usually the terminal value share, and move on.

Common mistakes in Cash Flow Based Valuation: DCF and Free Cash Flow

Discounting FCFF at the cost of equity, or FCFE at WACC.
Students remember the formula but not which cash flow belongs to which investor group.
Fix: Match the rate to the cash flow. Cash to all providers of finance uses WACC. Cash to shareholders only uses the cost of equity.
Deducting interest in FCFF or ignoring tax on EBIT.
Students start from profit after tax out of habit.
Fix: Start from EBIT and tax it at the full rate. The tax benefit of debt is already in the WACC, so deducting interest would count it twice.
Using the wrong timing for terminal value, for example discounting by year n+1.
The formula uses the year n+1 cash flow, which looks like it belongs to year n+1.
Fix: The formula gives a value at year n. Discount it with the year n factor.
Forgetting to deduct debt, or deducting book value instead of market value.
The enterprise value looks like the answer, and the debt figure is hidden in the scenario.
Fix: Read the data for debt, leases and cash. Always move from enterprise value to equity value before comparing with the offer for shares.
Using terminal growth at or above the discount rate, or higher than long-run economic growth.
Students copy a high short-term growth rate into the perpetuity.
Fix: Check g is below r, and justify it against inflation and long-run growth. Use a lower terminal rate than the forecast period growth when the business matures.
Counting synergies at the full target discount rate without comment, or double counting them in cash flows and in the price.
The numbers are mixed into one forecast and the risk difference is ignored.
Fix: Show standalone value and the PV of synergies separately. Discount cost savings and revenue synergies at rates that reflect their risk and say how much of the gain you would let the target's shareholders keep.

Worked examples

Example 1

Zeta plc is a target. Forecast free cash flow to the firm is $12m in year 1, $14m in year 2 and $15m in year 3. After year 3 it grows at 3% a year forever. Zeta's WACC is 10%. Its debt has a market value of $40m. Estimate Zeta's equity value. Discount factors at 10%: year 1 0.9091, year 2 0.8264, year 3 0.7513.

Show the solution

PV of year 1 = 12 × 0.9091 = $10.91m.
PV of year 2 = 14 × 0.8264 = $11.57m.
PV of year 3 = 15 × 0.7513 = $11.27m. Total PV of explicit flows = $33.75m.
Terminal value at year 3 = 15 × 1.03 ÷ (0.10 − 0.03) = 15.45 ÷ 0.07 = $220.71m.
PV of terminal value = 220.71 × 0.7513 = $165.82m.
Enterprise value = 33.75 + 165.82 = $199.57m.
Equity value = 199.57 − 40 = $159.57m.

Answer: Enterprise value is about $199.6m and equity value is about $159.6m. The terminal value is about 83% of enterprise value, so the result is very sensitive to the growth and WACC assumptions.

Example 2

Alpha is considering buying Beta's business, with an enterprise price of $135m (the debt is taken over within this price). Beta's operating free cash flow next year is $9m, growing at 2% a year forever. The ungeared cost of equity for this business is 9%. Alpha will fund the purchase partly with permanent debt of $50m at 5% pre-tax. The tax rate is 25%. Issue costs, net of tax, are $1m. Discount the tax shield at the pre-tax cost of debt. Calculate the APV of the acquisition and say whether the price is justified.

Show the solution

Base case value = 9 ÷ (0.09 − 0.02) = 9 ÷ 0.07 = $128.57m.
Annual tax shield = 50 × 5% × 25% = $0.625m.
PV of tax shield as a perpetuity at 5% = 0.625 ÷ 0.05 = $12.5m. This equals 50 × 25%.
Issue costs = $1m, deducted.
APV = 128.57 + 12.5 − 1 = $140.07m.
Compare with the price: 140.07 − 135 = $5.07m.

Answer: APV is about $140.1m, which is $5.1m above the $135m price, so the purchase adds value on these assumptions. Note that the tax shield is only valid if the debt is truly permanent and the firm has enough taxable profit to use it, and that $128.6m is the value without any financing benefit.

Exam tips

Show a clear layout: years, FCFF, discount factor, PV. Marks are given for method, so a neat table protects you from one arithmetic slip.
State your assumptions in a sentence each, such as the discount rate for synergies, the growth rate, and whether debt is at market value. Section A also rewards professional skills, so end with a clear recommendation for the board.
Read whether the question asks for enterprise value, equity value or price per share. Many students lose marks by stopping one step early.
Comment on the limits of the valuation, such as the weight of the terminal value, forecast uncertainty and the effect of a change in gearing on WACC. Keep comments linked to the scenario.
When financing changes after the deal, think APV. Say why WACC is unreliable in that case, then calculate the base case and financing effects separately.

Practice questions from Valuation for acquisitions and mergers

Cash Flow Based Valuation: DCF and Free Cash Flow in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Cash Flow Based Valuation: DCF and Free Cash Flow: frequently asked questions

What is the difference between FCFF and FCFE?

FCFF is the cash available to both lenders and shareholders before interest, and you discount it at WACC to get enterprise value. FCFE is the cash left for shareholders after interest and net borrowing, and you discount it at the cost of equity to get equity value directly. FCFF is safer when the target's gearing will change.

How do I calculate terminal value in a DCF question?

Take the final forecast year's free cash flow, grow it by one year, and divide by the discount rate minus the growth rate. This gives the value at the end of the forecast. Discount it back using the same factor as the final year's cash flow.

Do I deduct debt from the DCF value of a target?

Yes, if you discounted FCFF at WACC. That gives enterprise value, so you deduct the market value of debt and add any surplus cash to get equity value. If you discounted FCFE at the cost of equity, the answer is already equity value and you do not deduct debt again.

When should I use APV instead of WACC to value an acquisition?

Use APV when the acquirer will change the target's financing, for example by adding a lot of debt, or when there are special financing effects such as subsidised loans or issue costs. APV values the operations at the ungeared cost of equity and then adds the financing effects. WACC is simpler when gearing stays constant.