A project promises ₦50m a year. Over four years prices will rise. The ₦50m of year 4 will buy much less than the ₦50m of year 1, but the company’s investors want a return that already allows for that loss of buying power. Mix the two bases up and the answer is wrong.
Use real cash flows with a money discount rate, or money cash flows with a real rate, and the NPV is distorted. This topic gives the rules that keep them consistent.
This topic covers real and money cash flows, the money and real cost of capital, the Fisher equation, discounting money cash flows at the money rate, discounting real cash flows at the real rate, specific and general inflation, and the usual assumptions about year 1. The previous topic covered tax and capital allowances. The next covers risk, sensitivity analysis and expected values.
The November 2014 Pathfinder paper expects inflation to be handled with tax in project appraisal.
In 30 seconds
Real cash flows are in today’s prices. Money cash flows are the amounts actually paid or received, after inflation: money flow = real flow × (1 + i)n. The money cost of capital includes inflation and the real cost does not. The Fisher equation links them: (1 + m) = (1 + r) × (1 + i). Method 1 (the usual one): inflate each cash flow and discount at the money rate.
Method 2: discount real flows at the real rate. Both give the same NPV when one general rate of inflation applies to everything. When items inflate at different specific rates, use Method 1. Unless told otherwise, assume figures are at current prices, so year 1 flows are inflated by a full year.
Key terms in plain English
| Term | What it means |
|---|---|
| Real cash flow | A cash flow at today’s price level, before inflation |
| Money (nominal) cash flow | The amount actually paid or received in the future |
| Money cost of capital | The required return including compensation for inflation |
| Real cost of capital | The required return excluding inflation |
| Fisher equation | The link between money rate, real rate and inflation |
| General inflation | One average rate across all prices |
| Specific inflation | Different rates for different items, such as sales and costs |
Syllabus check
This topic is in syllabus area B (advanced investment appraisal, 30% of the marks). It covers:
- the money and real costs of capital and the Fisher equation;
- money and real cash flows and their link;
- DCF analysis that allows for both tax and inflation.
CAMA 2020 and inflation in appraisal
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 | Value should be judged in real terms, not just in inflated money |
| s. 308 | A director must use the care, diligence and skill of a reasonably prudent director | Directors should test the inflation assumptions in a forecast |
| 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 |
Real and money cash flows
In a long project, sales prices and costs will probably rise with inflation, so DCF must allow for it. Real cash flows are what an item would cost or earn at today’s prices. Money cash flows are the amounts actually paid or received. Estimate a money flow by pricing at today’s level and inflating: a component costing ₦1,000 now, with 4% inflation for two years, will cost 1,000 × 1.042 = ₦1,082. The ₦1,000 is the real cost and the ₦1,082 the money cost.
Money and real cost of capital
The cost of capital taken from market returns is normally a money rate, because investors want a return for risk and an extra return for the falling value of money. The real rate is what they would require with no inflation. The Fisher equation links them:
(1 + m) = (1 + r) × (1 + i), where m is the money rate, r the real rate and i inflation.
If the money cost is 12% and inflation is 5%, then 1 + r = 1.12 ÷ 1.05 and r = 6.67%.
Method 1: money flows at the money rate
- Estimate each cash flow at its inflated amount. Cash flows are at year-ends, so inflate for the full year.
- Use money flow in year n = current-price flow × (1 + i)n.
- Discount the money flows at the money cost of capital.
The usual assumption is that figures are given at current prices, so year 1 flows are inflated by one full year. If a question says otherwise, follow it. If it is silent, state your assumption. This is the more common method and should be used unless the question says otherwise.
ICAN’s example. Equipment costs ₦150,000. Units sold: 20,000, 40,000, 60,000 and 20,000 in years 1 to 4. At today’s prices the selling price is ₦10 and variable cost ₦6 a unit. Fixed cash costs are ₦50,000 a year and the equipment sells for ₦10,000 at the end of year 4. Inflation: sales 5%, variable and fixed costs 8%, disposal 6%. Money cost of capital 12%. Ignore tax.
- Revenue: 210,000; 441,000; 694,575; 243,101. Costs: 183,600; 338,256; 516,482; 231,283.
Disposal: 10,000 × 1.064 = 12,625. - Net cash flows: (150,000); 26,400; 102,744; 178,093; and 24,443 in year 4 (11,818 from trading plus the 12,625 disposal).
- The model answer discounts at 12% and gets an NPV of about ₦97,800, so the project is accepted.
Method 2: real flows at the real rate
Keep every flow at today’s prices and discount at the real rate. The result equals Method 1 when the same general inflation applies to every item. ICAN’s check: contribution ₦4 a unit, units 20,000, 40,000, 60,000 and 20,000, fixed costs ₦50,000, disposal ₦10,000 at current prices, inflation 6% and money cost 15%. Net flows at current prices: (150,000); 30,000; 110,000; 190,000; 40,000. Method 1 inflates them by 1.06n and discounts at 15%, giving about ₦148,900. Method 2 discounts at 1.15 ÷ 1.06 − 1 = 8.5% and gives about ₦148,700. The small gap is rounding.
General and specific inflation
Governments publish inflation for a basket of goods, so no single rate is right for every project. A scenario may give one general rate or several specific rates for different items.
- Specific rates: inflate each item at its own rate and discount at the money rate. ICAN’s example: sales ₦150,000 a year inflating at 5% and costs ₦100,000 at 6%, discounted at 10% for four years. Net money flows: 51.50, 53.02, 54.54 and 56.08 (₦000). NPV of the inflows = ₦169,910.
- General rate: either method works. With the same flows at one general rate of 5%, the money net flows are 52.50, 55.13, 57.88 and 60.78 (₦000), giving ₦178,280.
Real flows of ₦50,000 discounted at (1.10 ÷ 1.05) − 1 = 4.7619% give the same ₦178,280.
With a general rate you can inflate just the net flow in each year.
Putting tax and inflation together
Tax is computed on the money profits, because the tax authority taxes the actual amounts. Capital allowances are based on the actual (historic) cost of the asset and are not inflated. Discount all the money flows at the post-tax money cost of capital. ICAN’s past questions treat the full set together: inflate the cash flows, compute tax, add the saving from allowances, then discount.
The rules in more depth
Why you cannot mix the bases
A money rate contains an inflation allowance. If it is used on real flows, the inflation is allowed for in the discounting but not in the cash, so the NPV is too low.
Why a real rate gives the same answer
The Fisher equation strips the inflation from the rate by exactly the amount that inflation adds to each flow, so the effects cancel.
Why specific rates need Method 1
A single real rate cannot represent items that grow at different speeds. Each item must be inflated separately.
Why allowances are not inflated
The allowance is a fixed fraction of what was actually paid for the asset, so the later money value of the saving is based on that fixed amount.
Effect on analysis
State the basis of the figures, state the year 1 assumption, use one method and check that the rate matches the cash flows.
Worked examples
Example 1: money cost. A cost of ₦2,000 at today’s prices will be incurred in year 3. Inflation on this item is 8% a year.
- Money cost.
2,000 × 1.083 = 2,000 × 1.259712. - Money cost = ₦2,519.
- This is what will actually be paid in year 3.
Example 2: the real rate. The money cost of capital is 15% and inflation is 6%.
- 1 + r = 1.15 ÷ 1.06 = 1.0849.
- r = 8.49%, about 8.5%.
- Real flows at today’s prices can be discounted at 8.5%.
Example 3: money cost and tax. Cash profit at today’s prices is ₦40m a year, inflating at 5%. Tax is 30%, paid in the year of profit. In year 2 what is the money cash flow after tax?
- Money profit.
40 × 1.052 = ₦44.1m. - Tax = 30% × 44.1 = ₦13.23m.
- After-tax money flow.
44.1 − 13.23 = ₦30.87m.
Example 4: choosing the method. Sales will inflate at 5% and labour at 9%. The money cost is 14%.
- The rates differ, so a single real rate is not valid.
- Inflate sales at 5% and labour at 9% separately.
- Discount the net money flows at 14%.
How to score full marks
- State whether figures are in real or money terms.
- Inflate each item at its own rate and show the factor.
- State your year 1 assumption.
- Match the discount rate to the cash flows.
- Compute tax on money profits and do not inflate allowances.
- Check with the Fisher equation if both rates are given.
Common mistakes in the exam
- Discounting real flows at a money rate.
- Forgetting to inflate year 1.
- Inflating capital allowances.
- Using a single real rate for items with different inflation rates.
- Calculating the real rate as money rate minus inflation.
- Not stating the assumptions.
Quick revision
- Money flow = real flow × (1 + i)n.
- (1 + m) = (1 + r)(1 + i).
- Money flows at the money rate; real flows at the real rate.
- Different inflation rates: use money flows.
- Inflate year 1 unless told otherwise.
- 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. A real cash flow is stated:
- At future prices
- At today’s prices
- After tax
- After interest
Show the answer
B. Before inflation.
Question 2. The Fisher equation is:
- m = r + i
- (1 + m) = (1 + r)(1 + i)
- m = r × i
- r = m + i
Show the answer
B. The rates compound.
Question 3. Money cost 15% and inflation 6% give a real rate of about:
- 9%
- 8.5%
- 21%
- 6%
Show the answer
B. 1.15 ÷ 1.06 − 1.
Question 4. Money cash flows should be discounted at:
- The real rate
- The money rate
- The risk-free rate
- Zero
Show the answer
B. They already include inflation.
Question 5. Items inflating at different rates require:
- A single real rate
- Money flows at the money rate
- No adjustment
- Ignoring inflation
Show the answer
B. Method 1.
Question 6. By default, year 1 flows at current prices are:
- Not inflated
- Inflated by one full year
- Doubled
- Deflated
Show the answer
B. Flows occur at the year-end.
Question 7. Capital allowances are:
- Inflated each year
- Based on the historic cost and not inflated
- Ignored
- Discounted at the real rate
Show the answer
B. The asset cost is fixed.
Question 8. With a single general rate of inflation, the two methods give:
- Different NPVs
- The same NPV apart from rounding
- Opposite signs
- No NPV
Show the answer
B. The effects cancel.
Question 9. A cost of ₦1,000 with 4% inflation for two years becomes about:
- ₦1,040
- ₦1,082
- ₦1,200
- ₦960
Show the answer
B. 1,000 × 1.04 squared.
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) Distinguish money and real cash flows and money and real costs of capital. (4 marks) (b) State the Fisher equation and calculate the real rate for a money rate of 15% and inflation of 6%. (3 marks) (c) State when the real method can be used. (3 marks)
Question 12 (20 marks). Delta Plc is considering equipment costing ₦120m. At today’s prices, sales are ₦100m and variable costs ₦60m a year for three years, with fixed cash costs ₦10m. Sales inflate at 6% and all costs at 8%. The money cost of capital is 14% (factors 0.877, 0.769, 0.675). Ignore tax. Assume figures are at current prices. (a) Calculate the money net cash flow for each year.
(6 marks) (b) Calculate the NPV and advise. (6 marks) (c) A general inflation rate of 7% is later suggested for all items. Calculate the real cost of capital. (3 marks) (d) State the assumptions you made. (5 marks)
Question 13 (10 marks). (a) A cost of ₦40m at today’s prices is expected in year 4 with inflation of 6%. Calculate the money cost. (3 marks) (b) A project’s net cash flows at today’s prices are ₦50m a year for 4 years. General inflation is 5% and the money cost of capital is 10%. State the real cost of capital and which discounting method you would use. (4 marks) (c) Explain why tax allowances are not inflated. (3 marks)
Model answers
Show the model answer to Question 11
(a) Terms (4 marks). Real cash flows are in today’s prices; money flows are the actual future amounts after inflation. (2) The real cost of capital excludes inflation; the money cost includes compensation for it. (2)
(b) Fisher (3 marks).
- (1 + m) = (1 + r)(1 + i). (1)
- 1 + r = 1.15 ÷ 1.06 = 1.0849, so r = 8.5%. (2)
(c) Real method (3 marks). It can be used when one general rate of inflation applies to all cash flows. (2) With different specific rates, money flows at the money rate must be used. (1)
Show the model answer to Question 12
(a) Money flows (6 marks). Year 1: sales 100 × 1.06 = 106.0; costs 70 × 1.08 = 75.6; net 30.4. Year 2: sales 112.36; costs 81.65; net 30.71. Year 3: sales 119.10; costs 88.18; net 30.92 (₦m). (2 each)
(b) NPV (6 marks).
- 30.4 × 0.877 = 26.66
- 30.71 × 0.769 = 23.62
- 30.92 × 0.675 = 20.87.
- Total = 71.15. (3)
- NPV = 71.15 − 120 = −₦48.9m. (2)
- Reject. (1)
(c) Real rate (3 marks).
- 1.14 ÷ 1.07 − 1 = 6.5%. (3)
- It could not be used with the original flows, because sales and costs inflate at different rates.
(d) Assumptions (5 marks). Figures are at current prices, so year 1 flows are inflated by one full year. (1.5) Cash flows arise at year-ends. (1) Fixed costs inflate with the other costs. (1) There is no resale value or tax. (1) The 14% rate is the money cost. (0.5)
Show the model answer to Question 13
(a) Money cost (3 marks). 40 × 1.064 = 40 × 1.2625 = ₦50.5m. (3)
(b) Real rate and method (4 marks).
- Real rate.
1.10 ÷ 1.05 − 1 = 4.76%. (2) - One general rate applies, so either method works.
- Discounting the real ₦50m flows at 4.76% is simplest. (2)
(c) Allowances (3 marks). The allowance is a fixed percentage of the actual cost of the asset, which does not change with inflation. (2) Its money value is therefore not inflated. (1)
Pathfinder on Money and real cash flows and the Fisher equation
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 compulsory cement project question gave different growth rates for revenue (5% a year) and variable cost (4%) and fixed overheads (8%), so each item had to be inflated at its own rate and discounted at a money cost of capital. The model answer lists sales revenue, variable cost and fixed cost by year on that basis. Read the sections on money flows and on specific inflation.
Revise first: Method 1: money flows at the money rate
Questions give a money rate and inflation and ask for the real rate, or the reverse. See the sections on real and money cash flows.
Revise first: Real and money cash flows
Source: ICAN Pathfinder, Strategic Financial Management. Diets covered: November 2014 question 1.
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