Use discount factors and present values
Discount a future cash flow to express its value at the present time.
Section 4.4 · Investment appraisal
Exam scope and assessment notes
Cambridge International AS & A Level Accounting 9706, 2026–2028 syllabus, Version 2. This topic covers future net cash flows, payback, ARR, NPV, IRR and supported investment decisions. Discounted payback and questions involving a residual value at the end of a project are excluded by Cambridge. Practice is self-checked, not an official Cambridge grade. Full timed Papers 1–4 and human subject-teacher review remain outstanding.
Before you begin
- Use AS Topics 1.5–1.6 for profit, depreciation and financial analysis, and Topic 2.1 for contribution. Keep accounting profit, project cash flow and the time value of money distinct.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
At a positive rate, which usually has the lower factor?
What you will learn
- Apply a supplied discount factor
- Explain the time-value effect
- Label present value and period correctly
Convert future money to present value
Discounting converts a future cash flow into present value using a rate and period. Present value = future net cash flow × discount factor. A factor for rate r and year n is 1 ÷ (1 + r)^n.
Use the factor supplied or calculate it to the required accuracy. A positive discount rate generally gives a lower factor for more distant years.
Keep each period matched
Use the factor for both the correct rate and year. Do not apply a year-1 factor to every period.
Time-0 investment is already at present value, so it is not discounted again. A present value is not the same amount as the later receipt.
Pause and explain
A $20,000 year-3 inflow has factor 0.751. What is its present value?
Worked example
A $50,000 receipt is due in year 2. Its factor is 0.826. Find present value.
Show the worked solution
- Multiply the future cash flow by its matching factor.
- $50,000 × 0.826 = $41,300.
- Label the result as year-2 present value.
Answer Present value is $41,300.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A year-1 receipt is $30,000 and its factor is 0.909. Calculate present value.
Give me a hint
Multiply by the matching factor.
Compare my reasoning
- 30,000 × 0.909 = $27,270.
- Keep the year-1 label.
- Check the answer is below the future amount.
Present value is $27,270.
Look for these in your work
- Correct factor
- Value calculated
- Period retained
Discounted receipts are $18,000 in year 1 and $22,000 in year 2. Find their combined present value.
Give me a hint
Add the already-discounted figures.
Compare my reasoning
- Year-1 PV = $18,000.
- Year-2 PV = $22,000.
- Combined PV = $40,000.
Combined present value is $40,000.
Look for these in your work
- Discounted figures recognised
- Periods combined
- Total correct
A supplier offers $12,000 now or $13,000 in one year. How can a discount factor help?
Give me a hint
Convert the later payment to today's value.
Compare my reasoning
- Multiply $13,000 by the year-1 factor.
- Compare that PV with $12,000 now.
- State the comparison depends on the rate and contract terms.
Compare $13,000 times the year-1 factor with $12,000 now; the answer depends on the rate and terms.
Look for these in your work
- Future amount discounted
- Present cash compared
- Assumption stated
Common mistakes
- Using the wrong year's factor
- Adding discounted and undiscounted figures
- Discounting a time-0 payment
What can you explain now?
How do you calculate present value using a supplied factor?
Compare with the explanation
Future cash flow × matching discount factor
The matching factor converts future value into present value.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
What determines a discount factor, and what does it do?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.