Question 2
New product: NPV with WDV depreciation and working capital
15 marks
- Time to write
- About 30 minutes
From an older CBCS paper
Question
Question 2 · 15 marksXYZ Ltd. is considering introducing a new product. Profits before depreciation are estimated to rise by Rs. 1,44,000/- each year for first four years, and by Rs. 72,000/- each for the remaining period. An advertisement cost of Rs. 24,000/-, not included in this estimate of profits, is expected to be incurred in the first year; it will be allowed for tax purpose in the first year.
To produce the new product, a new plant costing Rs. 2,40,000/- will be installed; its salvage value after its life of 10 years is estimated at Rs. 48,000/-. A working capital investment of Rs. 24,000/- will be needed in the plant's year of installation, and a further Rs. 18,000/- in the year after. Its tax rate is 30%, and it claims depreciation on written down value at 33.33%. With a required rate of return of 20% for company, should it introduce the new product, judged on the basis of net present value? Ignore the tax effect on Profit/Loss on sale of asset.
Present Value factors at:
| Year | Yr. 1 | Yr. 2 | Yr. 3 | Yr. 4 | Yr. 5 | Yr. 6 | Yr. 7 | Yr. 8 | Yr. 9 | Yr. 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Factor (PV) at 10% | 0.9091 | 0.8264 | 0.7513 | 0.6830 | 0.6209 | 0.5645 | 0.5132 | 0.4665 | 0.4241 | 0.3855 |
| Factor (PV) at 20% | 0.8333 | 0.6944 | 0.5787 | 0.4823 | 0.4019 | 0.3349 | 0.2791 | 0.2326 | 0.1938 | 0.1615 |
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
- Ignore the tax effect on Profit/Loss…The paper fixes this: use it as given, and say so in your answer.
- net present valueCash flows year by year in one table, then discount, then a one-line decision.
What the paper leaves open
The profit increase is read as the yearly level of extra profit (Rs. 1,44,000 a year in years 1-4, Rs. 72,000 a year in years 5-10), not a cumulative rise. The working capital is recovered at the end of year 10; the plant's sale at its salvage value carries no tax, as instructed. The 10% factors are not needed. The present value factors are given to four decimals (the paper prints three).
Write it in this order
- Read the data; note exactly what is asked 2 min
- 1 Initial outlay and working capital timing 2 marks 4 min
- 2 WDV depreciation 3 marks 5 min
- 3 Cash flows after tax, with the advertising cost 5 marks 9 min
- 4 Present values, salvage and working capital recovery 3 marks 5 min
- 5 NPV and decision 2 marks 3 min
- Check: arithmetic, units (₹, %), final answer underlined 2 min
Short on time? End with step 5's one-line decision, whatever happens: never leave the figures without it.
Try it first. About 30 minutes for 15 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.
Readings (paper note). The extra profit before depreciation is ₹1,44,000 a year in years 1–4 and ₹72,000 a year in years 5–10. The working capital (₹24,000 at the start and ₹18,000 at the end of year 1) is recovered at the end of year
- The plant's salvage value of ₹48,000 is received at the end of year 10 without tax, as instructed. Depreciation is on written-down value at 33.33%; its tax saving is part of the cash inflow.
1. Initial outlay (year 0): plant 2,40,000 + working capital 24,000 = ₹2,64,000.
2. Annual cash flows after tax (₹)
| Year | PBDT | Advertising | Depreciation (WDV 33.33%) | PBT | Tax @ 30% | PAT | Add: depreciation | CFAT |
|---|---|---|---|---|---|---|---|---|
| 1 | 1,44,000 | 24,000 | 79,992 | 40,008 | 12,002.40 | 28,005.60 | 79,992 | 1,07,997.60 |
| 2 | 1,44,000 | — | 53,330.67 | 90,669.33 | 27,200.80 | 63,468.53 | 53,330.67 | 1,16,799.20 |
| 3 | 1,44,000 | — | 35,555.55 | 1,08,444.45 | 32,533.33 | 75,911.12 | 35,555.55 | 1,11,466.67 |
| 4 | 1,44,000 | — | 23,704.89 | 1,20,295.11 | 36,088.53 | 84,206.58 | 23,704.89 | 1,07,911.47 |
| 5 | 72,000 | — | 15,804.05 | 56,195.95 | 16,858.78 | 39,337.17 | 15,804.05 | 55,141.22 |
| 6 | 72,000 | — | 10,536.56 | 61,463.44 | 18,439.03 | 43,024.41 | 10,536.56 | 53,560.97 |
| 7 | 72,000 | — | 7,024.72 | 64,975.28 | 19,492.58 | 45,482.70 | 7,024.72 | 52,507.42 |
| 8 | 72,000 | — | 4,683.38 | 67,316.62 | 20,194.99 | 47,121.63 | 4,683.38 | 51,805.01 |
| 9 | 72,000 | — | 3,122.41 | 68,877.59 | 20,663.28 | 48,214.31 | 3,122.41 | 51,336.72 |
| 10 | 72,000 | — | 2,081.72 | 69,918.28 | 20,975.48 | 48,942.80 | 2,081.72 | 51,024.52 |
The advertising cost of ₹24,000 is deducted in year 1, as it is allowed for tax in that year.
3. Net cash flows and present values at 20% (₹)
| Year | CFAT | Working capital and salvage | Net cash flow | PVF @ 20% | PV |
|---|---|---|---|---|---|
| 1 | 1,07,997.60 | WC −18,000 | 89,997.60 | 0.8333 | 74,995 |
| 2 | 1,16,799.20 | — | 1,16,799.20 | 0.6944 | 81,105.36 |
| 3 | 1,11,466.67 | — | 1,11,466.67 | 0.5787 | 64,505.76 |
| 4 | 1,07,911.47 | — | 1,07,911.47 | 0.4823 | 52,045.70 |
| 5 | 55,141.22 | — | 55,141.22 | 0.4019 | 22,161.26 |
| 6 | 53,560.97 | — | 53,560.97 | 0.3349 | 17,937.57 |
| 7 | 52,507.42 | — | 52,507.42 | 0.2791 | 14,654.82 |
| 8 | 51,805.01 | — | 51,805.01 | 0.2326 | 12,049.85 |
| 9 | 51,336.72 | — | 51,336.72 | 0.1938 | 9,949.06 |
| 10 | 51,024.52 | WC +42,000; salvage +48,000 | 1,41,024.52 | 0.1615 | 22,775.46 |
| Total PV | 3,72,179.84 |
4. NPV = PV of net cash inflows − initial outlay = 3,72,179.84 − 2,64,000 = ₹1,08,179.84.
Decision. The NPV at the required 20% is positive, so XYZ Ltd. should introduce the new product.
Where the 15 marks sit
| # | Component | Marks |
|---|---|---|
| 1 | Initial outlay and working capital timing | 2 |
| 2 | WDV depreciation | 3 |
| 3 | Cash flows after tax, with the advertising cost | 5 |
| 4 | Present values, salvage and working capital recovery | 3 |
| 5 | NPV and decision | 2 |
| Total | 15 |
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