Management Accounting · Asset budgeting and investment appraisal

Time Value of Money and Discounting Explained

Updated 11 October 2026 · Fact-checked

Time value of money means cash received sooner is worth more than the same cash received later, because it can earn a return. Compounding moves money forward: PV × (1 + r)^n. Discounting moves it back: FV ÷ (1 + r)^n. For equal yearly cash flows, use annuity factors; for endless flows, divide by r.

Understand Time Value of Money and Discounting

Money today is worth more than the same amount in the future. You can invest it and earn interest, and inflation and risk also reduce the value of delayed cash. This is the time value of money.

Compounding works forward. If you invest $1,000 at 10% a year, you have $1,100 after one year. After two years you earn interest on the interest, so you have $1,210. The future value is the amount × (1 + r)^n.

Discounting works backward. It answers: what is a future cash flow worth today? This today-value is the present value (PV). The rate used is the discount rate (cost of capital or required return). PV = future cash flow ÷ (1 + r)^n, or future cash flow × discount factor.

An annuity is the same cash flow each year for a set number of years. Instead of discounting each year separately, you use one annuity factor, which is the sum of the individual discount factors. A perpetuity is a constant cash flow that continues forever. Its present value is the annual cash flow ÷ r.

In the exam you are given discount factor tables (present value and annuity tables). You find the row for the year (n) and the column for the rate (r), then multiply the cash flow by the factor. This is the base skill for NPV and IRR.

Key formulas to remember

Future value (compounding): FV = PV × (1 + r)^n; r is the rate per period as a decimal; n is the number of periods.
Present value (discounting): PV = FV ÷ (1 + r)^n; Same as FV × 1 ÷ (1 + r)^n. The term 1 ÷ (1 + r)^n is the discount factor.
Annuity present value: PV = annual cash flow × annuity factor; Annuity factor = [1 − (1 + r)^−n] ÷ r. It assumes the first cash flow arrives at the end of year 1.
Perpetuity present value: PV = annual cash flow ÷ r; Assumes the first cash flow is one year from now and flows continue forever.
Growing perpetuity: PV = cash flow in year 1 ÷ (r − g); Only valid when r is greater than g. Use it only if the question gives growth.

How to solve Time Value of Money and Discounting questions

Use this method for any discounting question. It keeps timing and rates right, which is where marks are lost.

1Draw a quick timeline. Mark year 0 as today and put each cash flow in its year.
2Identify the discount rate and check whether it matches the period (annual rate for yearly flows).
3Decide the pattern: single sum, annuity, perpetuity, or uneven flows.
4Choose the factor: discount factor for single sums, annuity factor for equal flows, 1 ÷ r for a perpetuity.
5Read the factor from the table at the right year and rate, or calculate it if no table is given.
6Multiply each cash flow by its factor. Keep outflows negative and inflows positive.
7Add the present values if there is more than one, then check the size looks sensible (PV should be lower than the cash received later).
8Enter the answer in the format asked: correct units, rounding and sign.

Quickest way: Factor shortcut for equal and endless cash flows

When to use it: Use when cash flows are equal each year or go on forever. It saves time on number-entry questions.

Spot the words 'each year for n years' or 'indefinitely'.
For equal flows, read one annuity factor for n years and multiply once.
For a flow that starts later, take the annuity factor for the end year minus the factor for the year before the start.
For a perpetuity, divide by the rate. Do not use a table.
Sanity check: an annuity factor must be less than n, and a discount factor must be less than 1.

Common mistakes in Time Value of Money and Discounting

Using the wrong table year, for example year 4 instead of year 3.
Rushing and misreading the row, or miscounting years from year 0.
Fix: Write the year next to each cash flow before looking up the factor, and read the row label twice.
Discounting year 0 cash flows.
Applying a factor to every number out of habit.
Fix: Cash flows happening now have a factor of 1.000. Do not discount them.
Using an annuity factor when the flows are not equal.
Seeing several years and assuming it is an annuity.
Fix: Only use annuity factors when the amount is identical each year. Otherwise use separate discount factors.
Treating a perpetuity as PV = cash flow × r.
Confusing it with interest calculation.
Fix: Remember the PV must be bigger than the annual cash flow at normal rates, so divide by r.
Using the rate as a whole number in formulas, such as 10 instead of 0.10.
Tables show 10%, so students forget to convert.
Fix: Convert to a decimal before calculating. 10% becomes 0.10.
Assuming an annuity starts today.
Ignoring the timing convention that cash flows arise at year-end.
Fix: Standard annuity factors start at year 1. If the first payment is now, add 1.000 for that payment plus the factor for the remaining years.

Worked examples

Example 1

A project will pay $5,000 at the end of each year for 4 years. The cost of capital is 10%. The 4-year annuity factor at 10% is 3.170. What is the present value of the receipts?

Show the solution

Cash flows are equal each year, so use an annuity factor.
The first receipt is at the end of year 1, which matches the standard annuity factor.
PV = $5,000 × 3.170.
PV = $15,850.

Answer: $15,850

Example 2

An investment pays $2,000 every year forever, starting one year from now. The required return is 8%. What is its present value?

Show the solution

The flows are equal and endless, so it is a perpetuity.
PV = annual cash flow ÷ r.
PV = $2,000 ÷ 0.08.
PV = $25,000.

Answer: $25,000

Exam tips

Objective test questions often give the factor in a table. Read the right row and column and double-check before you type.
For number entry questions, follow the rounding instruction exactly and include the sign if the question asks for a negative figure.
In multiple response questions, check each statement separately. Common true statements: a perpetuity is cash for ever, and a higher rate lowers present value.
Estimate first. If the PV of later cash comes out higher than the cash itself, you have made an error.
Practise getting a quick sense of factors: higher rates and longer times give smaller discount factors.

Practice questions from Asset budgeting and investment appraisal

Time Value of Money and Discounting in other exams

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

Time Value of Money and Discounting: frequently asked questions

What is the difference between compounding and discounting?

Compounding finds the future value of money invested today. Discounting finds the present value of a future cash flow. They are opposite processes using the same rate.

How do I use a discount factor table in ACCA?

Find the row for the year and the column for the discount rate. The number where they meet is the factor. Multiply the cash flow by this factor to get its present value.

When should I use an annuity factor?

Use it when the same cash flow occurs each year for a fixed number of years, with the first at the end of year 1. It replaces adding up several single-year factors.

Why is the present value of a perpetuity cash flow ÷ r?

A perpetuity is an endless series of equal flows. When you discount them all and add them, the total simplifies to the cash flow divided by the rate. It works only for flows starting at the end of year 1.