A buyer wants to know the most it should pay for a business. The business will keep producing cash after the buyer owns it. So the answer is the present value of that cash, discounted at a rate that reflects the risk. This is the same method used to appraise a project, applied to a whole company.
The extra problem is that a business has no fixed end date, so someone has to put a value on all the cash that arrives after the forecast stops.
This topic covers the discounted cash flow basis of valuation, the NPV method, the terminal value (with and without growth), shareholder value analysis (SVA), free cash flow to the firm and to equity, the different views of capital expenditure, and the single-stage residual income model. The previous topic covered value-based management. The next covers mergers and acquisitions.
The November 2014 Pathfinder paper had a 20-mark question that asked for an appraisal of an acquisition from forecast cash flows.
In 30 seconds
Value a business as the present value of its expected free cash flows, discounted at a cost of capital that matches their risk. Cash is better than profit because it is what shareholders actually receive and what pays for the financing. Split the future into an explicit forecast period (about five years) and a terminal value.
Terminal value at time T = next year’s cash flow ÷ (r − g) (with no growth, cash flow ÷ r), then discount it back from time T. Free cash flow to the firm (FCFF) = EBIT − tax on EBIT + depreciation − working capital increase − capital expenditure; it is before interest. Value of equity = value of the firm − value of debt (SVA).
The maximum price is the PV of the cash flows after any extra investment the buyer must make. Single-stage residual income: P0 = B0 + (ROE − r) × B0 ÷ (r − g).
Key terms in plain English
| Term | What it means |
|---|---|
| Free cash flow | Cash left for management to use freely after essential payments |
| FCFF | Free cash flow to the firm: before interest, belonging to all capital providers |
| FCFE | Free cash flow to equity: after interest, belonging to shareholders |
| Explicit forecast period | The years for which cash flows are forecast in detail |
| Terminal value | The value, at the end of that period, of all later cash flows |
| Shareholder value analysis (SVA) | Value of equity = PV of free cash flows less debt |
Syllabus check
This topic is in syllabus area B (business analysis). It covers:
- discounted cash flow based valuation and free cash flow models;
- short- and long-term growth rates and terminal values;
- economic profit methods.
CAMA 2020 and acquisitions
The Companies and Allied Matters Act 2020 (CAMA 2020) is the company law of Nigeria.
| Section | What it says | Link to this topic |
|---|---|---|
| s. 305 | A director must act in good faith in the best interests of the company | A price paid for a business should be justified by its cash flows, for the benefit of the company |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should test the cash flow forecasts behind an acquisition price |
| s. 377(1) and s. 378 | Directors prepare statements that follow IFRS and give a true and fair view | Decisions later affect reported assets, profit and cash |
| s. 385 | The directors’ report covers performance and risk | Major plans and risks are reported to shareholders |
The DCF basis
A DCF valuation fits a takeover. The acquisition is a capital investment, so it can be evaluated by NPV. After the acquisition, the target’s cash flows come under the buyer’s control. The maximum price is the PV of the cash flows the buyer expects, discounted at a suitable cost of capital (perhaps the buyer’s WACC).
It can value the whole company (equity and debt) or the equity alone.
Why cash, not profit: cash flows are more closely correlated with value and shareholder wealth than accounting profit; and returns must cover the cost of all the finance used, equity as well as debt. If the price exceeds the PV of the returns at the buyer’s cost of capital, the acquisition destroys value.
The cash flows should be incremental, including any extra investment the buyer plans after the purchase and any synergies.
The terminal value
A business lasts indefinitely, but forecasts become unreliable further out, so use an explicit forecast period and a terminal value. The terminal value is a present value calculated in the future: the cash equivalent, at the end of the forecast, of every later cash flow. It must then be discounted back to today.
ICAN’s example (no growth). Cash flows are ₦10,000, ₦15,000 and ₦20,000 in years 1 to 3, then ₦21,000 a year for ever from year 4. The cost of capital is 8%.
- Terminal value at year 3 = 21,000 ÷ 0.08 = ₦262,500.
- Year 3 total = 20,000 + 262,500 = 282,500.
- PV = 10,000 × 0.926 + 15,000 × 0.857 + 282,500 × 0.794 = 9,260 + 12,855 + 224,305 = ₦246,420.
With growth: if the year 3 cash flow of ₦20,000 grows 5% for ever, the year 4 flow is ₦21,000 and the terminal value at year 3 is 21,000 ÷ (0.08 − 0.05) = ₦700,000. PV = 9,260 + 12,855 + 720,000 × 0.794 = ₦593,795.
ICAN’s QX example. QX will invest ₦12m now to buy a division. After-tax cash flows: ₦6m, ₦8m, ₦10m and ₦8m in years 1 to 4, then ₦4m a year from year 5. Cost of capital 8%.
- Terminal value at year 4 = 4 ÷ 0.08 = ₦50m.
- PV = −12 + 6 × 0.926 + 8 × 0.857 + 10 × 0.794 + (8 + 50) × 0.735 = −12 + 5.56 + 6.86 + 7.94 + 42.63.
- NPV = ₦50.98m, the maximum QX should pay.
Shareholder value analysis and free cash flow
SVA: value of the firm (PV of free cash flows at WACC) − value of debt = value of equity. ICAN’s example: free cash flow of ₦2.5m a year for ever, WACC 8%, debt ₦7m. Firm = 2.5 ÷ 0.08 = ₦31.25m; equity = 31.25 − 7.00 = ₦24.25m.
Free cash flow is the cash available for management to use at its discretion after essential payments: tax and replacement capital expenditure. It may be measured for the firm (before interest) or for equity (after interest); the usual approach is the firm, then deduct debt.
Method: EBIT − tax on EBIT + depreciation (and other non-cash items) − increase in working capital (or + decrease) − capital expenditure = FCFF; less interest = FCFE. ICAN’s example: EBIT ₦1,500,000, tax 30% (₦450,000), depreciation ₦180,000, working capital up ₦50,000 and capital spending ₦250,000 give FCFF of ₦930,000. With a 11% cost of capital and 6% growth, value = 930,000 × 1.06 ÷ (0.11 − 0.06) = ₦19,716,000.
Which capital expenditure to deduct? There is no single answer. If expansion is a free choice, deduct only replacement spending. If expansion is needed to grow future cash flows, deduct growth spending as well (excluding acquisitions and disposal proceeds). A third view deducts all capital expenditure net of disposals.
ICAN’s two-stage case. Company BN has 4m shares. The buyer will invest ₦6m after the purchase. Equity cash flows are ₦1.0m in year 1, growing 8% for four more years and then 3% for ever. The cost of capital is 10%.
- Cash flows: 1,000; 1,080; 1,166; 1,260; 1,360 (₦000).
Year 6 flow = 1,360 × 1.03 = 1,401, so the terminal value at year 5 = 1,401 ÷ (0.10 − 0.03) = ₦20,014k. - PV = −6,000 + 909 + 892 + 876 + 861 + (1,360 + 20,014) × 0.621 = ₦10,811k.
- Per share.
10.8m ÷ 4m = about ₦2.70.
Single-stage residual income
The residual income model values equity as book value plus the PV of future residual income: P0 = B0 + (ROE − r) × B0 ÷ (r − g), where g = retention ratio × ROE. The second term is the excess value from earning more than the cost of equity, and it can be negative. It assumes constant ROE and growth, so residual income would last for ever; in practice competition drives it towards zero.
ICAN’s Leke Ltd: book value ₦23.00, ROE 14%, cost of equity 12%, payout 60%. g = 0.4 × 14% = 5.6%. P0 = 23.00 + (0.02 × 23.00) ÷ (0.12 − 0.056) = 23.00 + 7.19 = ₦30.19. The Gordon growth model gives the same: E1 = 3.22, D1 = 1.932, and 1.932 ÷ 0.064 = ₦30.19.
The rules in more depth
Why use incremental cash flows
The buyer’s question is what the acquisition adds. Cash flows that would happen anyway, or that belong to the seller’s plans, are not what the buyer is paying for.
Why the terminal value is usually most of the value
It captures all years after the forecast, so even a small change in g or r moves it a lot. Check how much of the total it makes up.
Why FCFF uses WACC and FCFE the cost of equity
FCFF belongs to all capital providers, so it needs the blended rate. FCFE belongs to shareholders alone.
Why debt is deducted
Lenders have a prior claim on the firm’s value. What is left belongs to shareholders.
Effect on analysis
State the cash flow definition, forecast period and growth, compute the value, deduct debt, and test sensitivity to the discount rate and growth.
Worked examples
Example 1: FCFF. EBIT is ₦800m, tax 30%, depreciation ₦100m, working capital up ₦40m and replacement capital spending ₦120m. WACC is 10% and growth 4%. Debt is ₦2,000m.
- FCFF = 800 × 0.7 + 100 − 40 − 120 = ₦500m.
- Firm value.
500 × 1.04 ÷ (0.10 − 0.04) = ₦8,667m. - Equity = 8,667 − 2,000 = ₦6,667m.
Example 2: terminal value with growth. Flows are ₦30m, ₦35m and ₦40m, then growth of 3% for ever. The cost of capital is 9% (factors 0.917, 0.842, 0.772).
- Year 4 flow = 40 × 1.03 = ₦41.2m.
Terminal value at year 3 = 41.2 ÷ 0.06 = ₦686.7m. - PV = 30 × 0.917 + 35 × 0.842 + (40 + 686.7) × 0.772.
- PV = 27.5 + 29.5 + 561.0 = ₦618.0m.
Example 3: SVA. Free cash flow is ₦5m a year for ever. WACC is 10% and debt is ₦12m.
- Firm = 5 ÷ 0.10 = ₦50m.
- Equity = 50 − 12.
- Equity = ₦38m.
Example 4: residual income. Book value is ₦20, ROE 15%, cost of equity 11% and payout 50%.
- g = 0.5 × 15% = 7.5%.
- P0 = 20 + (0.04 × 20) ÷ (0.11 − 0.075) = 20 + 0.8 ÷ 0.035.
- P0 = ₦42.86 (the Gordon model also gives ₦42.86).
How to score full marks
- List the incremental cash flows, including extra investment and synergies.
- Tax the operating profit and keep interest out of FCFF.
- Compute the terminal value at the right date and discount it.
- Deduct debt to get equity.
- State the cost of capital and why.
- Comment on sensitivity and the share of value in the terminal value.
Common mistakes in the exam
- Using accounting profit instead of cash flow.
- Deducting interest in FCFF.
- Discounting the terminal value from the wrong year.
- Using the dividend growth formula without growing the first flow.
- Forgetting the investment the buyer must make.
- Forgetting to deduct debt.
Quick revision
- Value = PV of free cash flows; maximum price for an acquisition.
- Terminal value at T = CFT+1 ÷ (r − g); discount it from T.
- FCFF = EBIT(1 − t) + depreciation − Δ working capital − capital expenditure.
- Equity = firm value − debt.
- Residual income.
P0 = B0 + (ROE − r)B0 ÷ (r − g). - CAMA 2020: ss. 305, 308, 377(1), 378, 385.
Practice questions
These are original questions written in the style of the Institute of Chartered Accountants of Nigeria (ICAN) exam. Try each one before you open the answer. Full model answers follow the written questions.
Recall check: multiple choice
Recent ICAN papers are written, although older papers such as May 2014 included multiple-choice questions. These questions are for quick recall. The written questions that follow are closer to the exam.
Question 1. In a DCF valuation the maximum price for a target is the:
- PV of expected cash flows
- Book value
- Dividend
- Interest
Show the answer
A. At a suitable cost of capital.
Question 2. Terminal value at the end of the forecast with growth is:
- Next cash flow ÷ (r − g)
- Cash flow × r
- Cash flow ÷ g
- Cash flow × (1 + r)
Show the answer
A. Then discounted back.
Question 3. A constant ₦21,000 from year 4 at 8% has a terminal value at year 3 of:
- ₦262,500
- ₦168,000
- ₦21,000
- ₦284,000
Show the answer
A. 21,000 ÷ 0.08.
Question 4. FCFF is calculated:
- Before interest
- After interest
- After dividends
- Before tax and depreciation
Show the answer
A. It belongs to all capital providers.
Question 5. Equity value in SVA equals:
- Firm value minus debt
- Firm value plus debt
- Debt only
- EBIT
Show the answer
A. Lenders have a prior claim.
Question 6. Cash flow is preferred to profit because it:
- Is closer to shareholder wealth
- Is easier to manipulate
- Ignores tax
- Includes depreciation
Show the answer
A. And covers the cost of finance.
Question 7. The extra investment a buyer plans after the purchase should:
- Be deducted from the cash flows
- Be ignored
- Be added to the value
- Be taxed
Show the answer
A. It is part of the acquisition cost.
Question 8. The single-stage residual income model assumes:
- Constant ROE and growth
- Zero growth
- Zero ROE
- No book value
Show the answer
A. So residual income lasts for ever.
Question 9. FCFE is:
- FCFF less interest
- FCFF plus interest
- EBIT
- Dividends
Show the answer
A. The cash to shareholders.
Question 10. Which section of CAMA 2020 sets the director’s duty of care and skill?
- Section 308
- Section 400
- Section 405
- Section 409
Show the answer
A. Directors should test the assumptions behind a decision.
Written questions
Question 11 (10 marks). (a) Explain why a DCF basis is preferred for valuing a target. (4 marks) (b) Explain the role of the terminal value. (3 marks) (c) State two weaknesses of a DCF valuation. (3 marks)
Question 12 (20 marks). EBIT of a target is ₦200m, tax 30%, depreciation ₦40m, working capital rises by ₦10m and replacement capital expenditure is ₦50m. Forecast free cash flows (before the extra investment) are ₦12m, ₦15m and ₦18m in years 1 to 3, then grow 4% a year for ever. The buyer must invest ₦20m now. WACC is 11% (factors 0.901, 0.812, 0.731). Debt is ₦60m. (a) Calculate the current-year FCFF.
(4 marks) (b) Calculate the terminal value and the maximum price for the whole business. (10 marks) (c) Calculate the maximum price for the equity. (3 marks) (d) State the three views on capital expenditure in free cash flow. (3 marks)
Question 13 (10 marks). (a) A company has book value per share of ₦20, ROE 15%, cost of equity 11% and payout 50%. Calculate its value by the single-stage residual income model. (5 marks) (b) Distinguish FCFF and FCFE. (3 marks) (c) Explain why debt is deducted in SVA. (2 marks)
Model answers
Show the model answer to Question 11
(a) DCF (4 marks). Cash flows are more closely related to value and shareholder wealth than accounting profit. (2) Returns must cover the cost of all finance, which a DCF at the cost of capital tests directly, so an over-priced acquisition shows as negative NPV. (2)
(b) Terminal value (3 marks). It represents all cash flows after the explicit forecast period, because a business goes on and later forecasts are unreliable. (2) It is a present value at the end of the forecast and must be discounted back. (1)
(c) Weaknesses (3 marks). The forecasts are uncertain. (1) The value is very sensitive to the growth rate and the discount rate, and the terminal value is a large share of the total. (2)
Show the model answer to Question 12
(a) FCFF (4 marks).
- 200 × 0.7 = 140
- + 40 − 10 − 50 = ₦120m. (4)
(b) Maximum price (10 marks).
- Year 4 flow = 18 × 1.04 = ₦18.72m. (1.5)
- Terminal value at year 3 = 18.72 ÷ (0.11 − 0.04) = ₦267.4m. (3)
- PV = 12 × 0.901 + 15 × 0.812 + (18 + 267.4) × 0.731 = 10.81 + 12.18 + 208.6 = ₦231.6m. (4)
- Less the extra investment of ₦20m gives ₦211.6m. (1.5)
(c) Equity (3 marks). 211.6 − 60 = ₦151.6m. (3)
(d) Views (3 marks). Deduct only replacement capital expenditure; deduct replacement and growth capital expenditure but not acquisitions or disposals; deduct all capital expenditure net of disposals. (1 each)
Show the model answer to Question 13
(a) Residual income (5 marks).
- g = 0.5 × 15% = 7.5%. (1.5)
- P0 = 20 + (0.15 − 0.11) × 20 ÷ (0.11 − 0.075) = 20 + 0.8 ÷ 0.035 = 20 + 22.86 = ₦42.86. (3.5)
(b) FCFF and FCFE (3 marks). FCFF is before interest and belongs to all providers of capital, discounted at WACC. (1.5) FCFE is after interest and belongs to shareholders, discounted at the cost of equity. (1.5)
(c) Debt (2 marks). The PV of free cash flows is the value of the whole firm. Lenders have a prior claim on it, so debt is deducted to leave the shareholders’ value. (2)
Pathfinder on DCF valuation, terminal value, free cash flow and SVA
These are the ICAN Pathfinder questions that test this topic. ICAN owns the questions and the suggested solutions, so we point you to them and do not copy them. Open your Pathfinder, attempt each question under exam conditions, then check your answer against the notes above.
The 20-mark question gave Syntax Plc a target, Synapse Chemical, with five years of forecast revenue, costs and profit, a sale of assets with a tax written down value, capital expenditure, a one-year tax delay, a 22% after-tax WACC and an agreed price of ₦20m. It asked for an appraisal of the acquisition and advice to the board in the form of a report. The cash flow method in this topic is the approach to take: build free cash flows from profit, tax, capital spending and the disposal, then discount. Read the sections on the DCF basis and free cash flow.
Revise first: Shareholder value analysis and free cash flow
Questions ask for the value after a forecast period. See the section on the terminal value.
Revise first: The terminal value
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: November 2014 question 3.
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