A project that will earn money for five years will be paid in naira that buy less each year. If prices are rising at 8% a year, a cash flow of ₦10m in five years’ time is a smaller real amount than ₦10m today. The lender or shareholder wants a return that covers this loss of purchasing power as well as a real reward for waiting.
So the cost of capital the company is quoted in the market already includes inflation. If the forecast cash flows leave inflation out, but the discount rate includes it, the project will be undervalued; if both are consistent, the answer is the same whichever way it is done.
This topic explains real and money (nominal) cash flows and rates, the relationship between them, the two consistent methods of appraisal, what to do when different costs and prices rise at different rates (specific inflation), and how inflation affects tax allowances and working capital, with worked examples. The next topic covers risk and uncertainty in appraisal, starting with sensitivity analysis.
The syllabus asks candidates to apply and discuss the real-terms and nominal-terms approaches. Read taxation and capital allowances in discounted cash flow first.
In 30 seconds
Money (nominal) cash flows include the effect of inflation; real cash flows are expressed in the prices of today. The money cost of capital includes inflation; the real cost of capital excludes it. They are linked by (1 + money rate) = (1 + real rate) × (1 + inflation rate).
There are two consistent methods: discount money cash flows at the money rate, or discount real cash flows at the real rate; both give the same net present value (NPV) when one general inflation rate applies. Never mix them. If specific inflation differs between cash flows (prices, wages, materials), inflate each cash flow separately to money terms and use the money rate.
Tax allowances are fixed in money terms and do not rise with inflation.
Real and money terms
Money (nominal) cash flows are the actual amounts in naira expected in each year, including inflation. Real cash flows are those amounts stated in constant prices, for example the prices at the start of the project.
A real cash flow of ₦9.0m in year 1 at an inflation rate of 5% is a money cash flow of 9.0 × 1.05 = ₦9.45m. Likewise the money cost of capital is the return required in actual naira and includes compensation for inflation, while the real cost of capital is the return after removing inflation. The two are related by:
(1 + money rate) = (1 + real rate) × (1 + inflation rate)
So a real rate of 10% with inflation of 5% gives a money rate of 1.10 × 1.05 − 1 = 15.5%, and conversely the real rate for a money rate of 18% and inflation of 6% is 1.18 ÷ 1.06 − 1 = 11.3%. (It is not simply 18% − 6%.) The market rate for the company’s cost of capital is almost always a money rate.
The two methods
- Money approach: inflate each cash flow to money terms and discount at the money rate.
- Real approach: keep the cash flows in today’s prices and discount at the real rate.
Example: a project costs ₦20m and has real cash flows of ₦9.0m, ₦10.0m and ₦9.5m in years 1 to 3. General inflation is 5% and the real cost of capital is 10% (the money rate is 15.5%).
| Year | Real flow ₦m | Money flow ₦m | present value (PV) at 15.5% ₦m | PV of real flow at 10% ₦m |
|---|---|---|---|---|
| 1 | 9.0 | 9.45 | 8.18 | 8.18 |
| 2 | 10.0 | 11.03 | 8.26 | 8.26 |
| 3 | 9.5 | 11.00 | 7.14 | 7.14 |
| Total | 23.58 | 23.58 | ||
| NPV (total less 20.0) | 3.58 | 3.58 | ||
The two methods agree: an NPV of +₦3.58m. The reason is that dividing a money flow by (1.05)t to get the real flow and by (1.155)t instead of (1.10)t are the same operation.
An inconsistent mixture gives a wrong answer: discounting the real flows at the money rate gives 9.0 ÷ 1.155 + 10.0 ÷ 1.1552 + 9.5 ÷ 1.1553 − 20 = +₦1.45m, which understates the NPV by about ₦2.1m and could lead to a good project being rejected, because the cash flows have not been inflated to match the rate.
Specific inflation
General inflation is the average rate of price rise. Specific inflation is the rate for a particular price, such as labour, materials or the selling price, which may be higher or lower. When rates differ, the real approach cannot be used straightforwardly, because the real cash flows would change each year. Instead, inflate each cash flow at its own rate to money terms and discount at the money rate.
Example: a project costing ₦18m has sales of ₦14m at today’s prices, rising at 4% a year, and costs of ₦6m at today’s prices, rising at 9% a year; the money rate is 15.5% (general inflation 5%) and the project lasts 3 years.
| Year | Sales ₦m | Costs ₦m | Net money flow ₦m | Factor 15.5% | PV ₦m |
|---|---|---|---|---|---|
| 1 | 14 × 1.04 = 14.56 | 6 × 1.09 = 6.54 | 8.02 | 0.866 | 6.94 |
| 2 | 14 × 1.042 = 15.14 | 6 × 1.092 = 7.13 | 8.01 | 0.750 | 6.01 |
| 3 | 14 × 1.043 = 15.75 | 6 × 1.093 = 7.77 | 7.98 | 0.649 | 5.18 |
| NPV (total 18.13 less 18) | 0.13 | ||||
The NPV is only +₦0.13m. If the company had ignored the specific rates and used the real net flow of ₦8m a year discounted at the real rate of 10%, it would have found +₦1.89m and overestimated the project by ₦1.76m, because costs are rising faster than the selling price and squeezing the margin.
Other effects of inflation
- Working capital: inflation raises the money value of inventory and receivables, so more cash is tied up each year; the increase is an outflow.
- Capital allowances: they are based on the original cost and are fixed in money terms, so they do not rise with inflation. The tax saving therefore loses real value, and in a real-terms calculation it must be converted or the money approach used.
- Tax: the tax on profits rises with money profits, so tax should be calculated on the money cash flows.
- Residual values: estimate them in the money amounts expected at the end.
The ideas in more depth
Why the real rate is not money rate minus inflation
Inflation reduces the buying power of the interest as well as of the principal. An investor who wants a 10% real return when prices rise 5% needs the principal to rise by 5% and the extra real 10% to rise by 5% as well, so the required money return is 1.10 × 1.05 − 1 = 15.5%, not 15%. The difference is small at low rates and grows as rates rise.
Why the money approach is safer
The money approach works whatever the pattern of inflation, includes tax and allowances correctly and uses the rate observed in the market. The real approach is quicker only when all prices rise at one rate and there is no tax. In an examination, if the question gives specific rates or tax, use the money approach.
Sources and references
- No accounting standard governs the choice. For inflation in financial reporting see International Accounting Standard (IAS) 29 Financial Reporting in Hyperinflationary Economies, which is a different matter from the forecast of project cash flows.
These points are stated as at 5 November 2026.
Worked examples
Example 1: the money rate. Real rate 10%; inflation 5%. Required: the money rate.
- Money rate.
1.10 × 1.05 − 1 = 15.5%.
Example 2: a money cash flow. Real flow ₦10.0m in year 2; inflation 5%. Required: the money flow.
- Money flow.
10.0 × 1.052 = ₦11.03m.
Example 3: the real rate. Money rate 18%; inflation 6%. Required: the real rate.
- Real rate.
1.18 ÷ 1.06 − 1 = 11.3%.
How to answer in the exam
- Identify whether the rate given is money or real and whether the flows are in current or future prices.
- Convert one to match the other using the formula, and show it.
- Use the money approach when specific inflation rates, tax or allowances are involved.
- Comment on the effect of inflation on the decision and on working capital.
Common mistakes in the exam
- Subtracting inflation from the money rate to find the real rate.
- Discounting real flows at a money rate.
- Inflating the initial outlay, which is already in year 0 prices.
- Applying general inflation to costs that the question says rise at a specific rate.
- Inflating the tax allowances.
- Forgetting the extra working capital needed because of inflation.
Quick revision
- (1 + money) = (1 + real) × (1 + inflation).
- Money flows at the money rate, or real flows at the real rate; never mix.
- Specific inflation: inflate each flow, use the money rate.
- Allowances are fixed in money terms; working capital rises with inflation.
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. The money rate is related to the real rate and inflation by:
- Money = real + inflation only
- Money = real − inflation
- (1 + money) = (1 + real) × (1 + inflation)
- Money = real ÷ inflation
Show the answer
C. The addition is only an approximation.
Question 2. Money cash flows should be discounted at:
- The real rate
- The money rate
- Zero
- The inflation rate
Show the answer
B. Both include inflation.
Question 3. Real cash flows should be discounted at:
- The real rate
- The money rate
- The tax rate
- The inflation rate
Show the answer
A. Neither includes inflation.
Question 4. With one general inflation rate and no tax, the two methods give:
- Opposite answers
- No answer
- A zero NPV
- The same NPV
Show the answer
D. If applied consistently.
Question 5. When inflation differs between cash flows you should:
- Ignore it
- Inflate each at its own rate and use the money rate
- Use the real rate
- Use payback
Show the answer
B. The real approach does not work.
Question 6. A money rate of 18% and inflation of 6% give a real rate of:
- 11.3%
- 12%
- 24%
- 6%
Show the answer
A. 1.18 ÷ 1.06 − 1.
Question 7. Discounting real flows at a money rate:
- Overstates the NPV
- Gives the correct NPV
- Understates the NPV
- Is not possible
Show the answer
C. The flows have not been inflated to match.
Question 8. The market cost of capital normally:
- Excludes inflation
- Is a real rate
- Is zero
- Includes expected inflation
Show the answer
D. It is a money rate.
Question 9. Capital allowances are:
- Raised with inflation
- Zero
- Fixed in money terms based on cost
- Based on sales
Show the answer
C. So they lose real value.
Question 10. Inflation affects working capital by:
- Increasing the cash tied up in inventory and receivables
- Reducing it
- Having no effect
- Removing it
Show the answer
A. The money value of the balances rises.
Section B style: written questions
Question 11 (10 marks). (a) Distinguish between money and real cash flows. (3 marks) (b) State the relationship between the money rate, the real rate and inflation. (3 marks) (c) State when the money approach must be used. (4 marks)
Question 12 (15 marks). A company’s money cost of capital is 18% and general inflation is expected to be 6%. (a) Calculate the real cost of capital. (4 marks) (b) A real cash flow of ₦8m arises in year 3; calculate the money cash flow. (4 marks) (c) Calculate its present value at the money rate. (4 marks) (d) Explain why the same present value results from using the real rate. (3 marks)
A further written question
Question 13 (20 marks). A project costs ₦15m and has real cash flows of ₦6.5m, ₦7.0m and ₦6.0m in years 1 to 3. The real cost of capital is 9% and general inflation 4%.
(a) Calculate the money cost of capital. (3 marks) (b) Calculate the money cash flows. (4 marks) (c) Calculate the NPV by the money method. (7 marks) (d) State the NPV by the real method and explain the result. (6 marks)
Model answers
Show the model answer to Question 11
(a) Money cash flows include the effect of inflation; real cash flows are in constant prices (3).
(b) (1 + money rate) = (1 + real rate) × (1 + inflation) (3).
(c) When specific inflation rates differ between cash flows (2), when tax and capital allowances are involved (1), and when the question gives the money rate (1).
Show the model answer to Question 12
(a) 1.18 ÷ 1.06 − 1 = 11.3% (4).
(b) 8 × 1.063 = 8 × 1.1910 = ₦9.53m (4).
(c) 9.53 ÷ 1.183 = 9.53 ÷ 1.6430 = ₦5.80m (4).
(d) Discounting the real flow of ₦8m at 11.3% for three years gives 8 ÷ 1.11323 = ₦5.80m as well, because 1.1132 × 1.06 = 1.18 in each year, so the two divisions are the same (3).
Show the model answer to Question 13
(a) 1.09 × 1.04 − 1 = 13.36% (3).
(b)
- Year 1 6.5 × 1.04 = 6.76
- year 2 7.0 × 1.042 = 7.57
- year 3 6.0 × 1.043 = 6.75 (4).
(c) PVs at 13.36%: 6.76 ÷ 1.1336 = 5.96; 7.57 ÷ 1.13362 = 5.89; 6.75 ÷ 1.13363 = 4.63 (4); total 16.49; NPV = 16.49 − 15 = +₦1.49m (3).
(d) Discounting the real flows at 9%: 6.5 ÷ 1.09 + 7.0 ÷ 1.092 + 6.0 ÷ 1.093 − 15 = +₦1.49m, the same, because both flows and rate are scaled by the same inflation factors (6).
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