Question 1 OR (b)
ARR and payback period
10 marks
- Time to write
- About 20 minutes
From an older CBCS paper
Question
Question 1 OR (b) · 10 marksPQR limited is considering buying a machine for ₹2,88,000, which is likely to yield the future benefits below over the next 5 years. The machine's salvage value will be ₹48,000.
| Year | PAT |
|---|---|
| 1 | 24,000 |
| 2 | 38,400 |
| 3 | 48,000 |
| 4 | 43,200 |
| 5 | 38,400 |
If the required rate of return is 20%, should the machine be purchased? Use the ARR method and the payback method.
Reworded from the university paper: names and figures differ, the task is the same. The original paper belongs to the University of Delhi. See DU's question bank.
Before you write
Read off the question and its marks
Read from the question
- paybackCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
- The ARR is computed on average investment, (cost + salvage) ÷ 2.
- Payback uses PAT plus straight-line depreciation (cost less salvage over 5 years) as the yearly cash inflow.
Write it in this order
- Read the data; note exactly what is asked 1 min
- 1 Average PAT and average investment 2 marks 4 min
- 2 ARR and decision 3 marks 5 min
- 3 Cash inflows (PAT + depreciation) and cumulative inflows 3 marks 5 min
- 4 Payback period and advice 2 marks 4 min
- Check: arithmetic, units (₹, %), final answer underlined 1 min
Short on time? End with step 4's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 20 minutes for 10 marks. Write it out, then open the solution.
Solution
Hover or tap a marked figure, like 72,000, to see how it is made and where else it appears.
Depreciation (straight line) = (2,88,000 − salvage 48,000) ÷ 5 = ₹48,000 a year. The yearly cash inflow for the payback is PAT plus depreciation (paper note 2).
1Rekha puts her savings into a juice cart—the jar on the counter starts empty.
Payback periodThe number of years a project takes to recover its initial investment from its cash inflows.
2Orange by orange, the jar fills back towards what the cart cost her.
Why it is a measure of liquidityHow quickly the funds locked in a project come back and can be put to other uses.
3The jar full, the counting stops—the measure never looks at all the selling still to come.
Why it is not a measure of profitabilityIt ignores the cash inflows after the payback period, however large.
| Year | PAT | Depreciation | Cash inflow | Cumulative cash inflow |
|---|---|---|---|---|
| 1 | 24,000 | 48,000 | 72,000 | 72,000 |
| 2 | 38,400 | 48,000 | 86,400 | 1,58,400 |
| 3 | 48,000 | 48,000 | 96,000 | 2,54,400 |
| 4 | 43,200 | 48,000 | 91,200 | 3,45,600 |
| 5 | 38,400 | 48,000 | 86,400 | 4,32,000 |
| Total | 1,92,000 |
(a) Accounting (average) rate of return. ARR = average annual profit after tax ÷ average investment, the average investment being (cost + salvage) ÷ 2.
- Average PAT = 1,92,000 ÷ 5 = ₹38,400
- Average investment = (2,88,000 + 48,000) ÷ 2 = ₹1,68,000
- ARR = 38,400 ÷ 1,68,000 × 100 = 22.86%
A project is accepted if its ARR is higher than the minimum rate set by management. 22.86% exceeds the required 20%, so on the ARR the machine should be purchased.
(b) Payback period. With unequal inflows, the inflows are cumulated until they equal the investment, the fraction of the last year found by interpolation. By the end of year 3, ₹2,54,400 is recovered; ₹33,600 remains, against ₹91,200 in year 4:
Payback = 3 + 33,600 ÷ 91,200 = 3.37 years.
A payback is accepted if it is within the cut-off period set by management. The question sets no cut-off; the outlay is recovered in 3.37 years, well within the machine's 5-year life.
Advice. Purchase the machine: its ARR of 22.86% beats the 20% required return, and it pays back in 3.37 years of a 5-year life.
Where the 10 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Average PAT and average investment | 2 |
| 2 | ARR and decision | 3 |
| 3 | Cash inflows (PAT + depreciation) and cumulative inflows | 3 |
| 4 | Payback period and advice | 2 |
| Total | 10 |
Report a problemopens an email to admin@getkunji.com with the question ID4960-Q1bORalready filled in.