Question 2 OR (b)

ARR, NPV and IRR of an investment proposal

12 marks

Time to write: About 24 minutes
Topic: Capital budgeting techniques

Question

Question 2 OR (b) · 12 marks

Tejas Ltd. is considering an investment proposal requiring initial investment of ₹60,000.

The corporate tax rate is 35% and the company follows the Straight Line Method of depreciation. Its estimated profit before depreciation and taxes from the investment proposals are given below:

Year	PBDT	PVF 10%	PVF 11%	PVF 12%
1.	13,200	0.909	0.901	0.893
2.	24,000	0.826	0.812	0.797
3.	21,600	0.751	0.731	0.712
4.	18,000	0.683	0.659	0.636
5.	14,400	0.621	0.593	0.567

Calculate the following:

ARR
NPV at 10% discount rate
IRR

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

24 minfor 12 marks

Read from the question

NPVCash flows year by year in one table, then discount, then a one-line decision.

Write it in this order

Read the data; note exactly what is asked 2 min
1 Depreciation, PAT and CFAT for each year 3 marks 5 min
2 ARR on average investment 3 marks 5 min
3 PV of cash inflows and NPV at 10% 3 marks 5 min
4 IRR by interpolation and conclusion 3 marks 5 min
Check: arithmetic, units (₹, %), final answer underlined 2 min

1234

Short on time? End with step 4's one-line conclusion, whatever happens: never leave the figures without it.

Try it first. About 24 minutes for 12 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.

Working: profit after tax and cash flow after tax. Depreciation (straight line, no salvage) = ₹60,000 ÷ 5 = ₹12,000 a year. Tax at 35%.

₹	Year 1	Year 2	Year 3	Year 4	Year 5	Total
PBDT	13,200	24,000	21,600	18,000	14,400
Less: depreciation	12,000	12,000	12,000	12,000	12,000
PBT	1,200	12,000	9,600	6,000	2,400
Less: tax @ 35%	420	4,200	3,360	2,100	840
PAT	780	7,800	6,240	3,900	1,560	20,280
Add: depreciation	12,000	12,000	12,000	12,000	12,000
CFAT	12,780	19,800	18,240	15,900	13,560

(i) Accounting rate of return. ARR = average annual profit after tax ÷ average investment in the project. Average PAT = ₹20,280 ÷ 5 = ₹4,056. Average investment = ₹60,000 ÷ 2 = ₹30,000 (no salvage value).

ARR = 4,056 ÷ 30,000 = 13.52%.

On initial investment instead: 4,056 ÷ 60,000 = 6.76%.

(ii) NPV at 10% and (iii) IRR

Year	CFAT (₹)	PVF @ 10%	PV @ 10% (₹)	PVF @ 11%	PV @ 11% (₹)
1	12,780	0.909	11,617.02	0.901	11,514.78
2	19,800	0.826	16,354.80	0.812	16,077.60
3	18,240	0.751	13,698.24	0.731	13,333.44
4	15,900	0.683	10,859.70	0.659	10,478.10
5	13,560	0.621	8,420.76	0.593	8,041.08
Total PV			60,950.52		59,445.00
Less: initial investment			60,000.00		60,000.00
NPV			950.52		(555.00)

(ii) NPV at 10% = ₹950.52 (positive).

(iii) IRR. The IRR is the rate at which the present value of the cash inflows equals the initial outlay. The NPV is positive at 10% and negative at 11%, so the IRR lies between them. By interpolation:

IRR = 10% + [950.52 ÷ (950.52 + 555.00)] × 1% = 10% + 0.63% = 10.63%.

Conclusion. The proposal earns an ARR of 13.52% on average investment, has a positive NPV of ₹950.52 at 10%, and an IRR of about 10.63%, slightly above the 10% discount rate. It is acceptable at a 10% cost of capital, though only just.

Where the 12 marks sit

#	Component	Marks
1	Depreciation, PAT and CFAT for each year	3
2	ARR on average investment (13.52%)	3
3	PV of cash inflows and NPV at 10% (₹950.52)	3
4	IRR by interpolation (10.63%) and conclusion	3
	Total	12

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