Question 2 OR

Two machines: NPV, profitability index and IRR after tax

15 marks

Time to write: About 30 minutes

From an older CBCS paper

Question

Question 2 OR · 15 marks

Kavya Ltd. is considering two mutually exclusive machines. Each required an initial outlay of ₹ 2,40,000, and each has a useful life of five years. The rate of return required by the company is 10%, and it pays tax at 50%. Depreciation on the projects will be charged on a straight line basis. The projects are expected to generate the following profit before depreciation:

Year	1	2	3	4	5
Machine 1(₹)	96,000	96,000	96,000	96,000	96,000
Machine 2(₹)	1,44,000	72,000	48,000	1,20,000	1,20,000

You are required to calculate:

For each machine, the Net Present Value and the Profitability Index.
For each machine, the Internal Rate of Return.

Which machine should be accepted, and why ? 15

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

30 minfor 15 marks

Read from the question

and whyEach answer needs its reason, not just the answer.
Net Present ValueCash flows year by year in one table, then discount, then a one-line decision.

What the paper leaves open

No salvage value is given, so none is assumed: each machine is depreciated to nil over five years (₹ 48,000 a year). The profit before depreciation is read as before tax; the 50% tax is charged on profit after depreciation, and depreciation is added back to give the cash inflow.

Write it in this order

Read the data; note exactly what is asked 2 min
1 Depreciation, tax and cash inflows after tax 4 marks 7 min
2 NPV and profitability index of each machine 4 marks 7 min
3 IRR of each machine by interpolation 5 marks 9 min
4 Choice of machine with reason 2 marks 3 min
Check: arithmetic, units (₹, %), final answer underlined 2 min

1234

Short on time? End with step 4'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.

Cash inflows after tax. Depreciation is a non-cash charge: it is deducted to find the taxable profit and then added back, so the cash inflow is profit after tax plus depreciation. Straight line depreciation, with no salvage value (paper note) = 2,40,000 ÷ 5 = ₹48,000 a year.

Year	1	2	3	4	5
Machine 1: profit before depreciation	96,000	96,000	96,000	96,000	96,000
Less: depreciation	48,000	48,000	48,000	48,000	48,000
Profit before tax	48,000	48,000	48,000	48,000	48,000
Less: tax @ 50%	24,000	24,000	24,000	24,000	24,000
Add: depreciation	48,000	48,000	48,000	48,000	48,000
Cash inflow (CFAT)	72,000	72,000	72,000	72,000	72,000
Machine 2: profit before depreciation	1,44,000	72,000	48,000	1,20,000	1,20,000
Less: depreciation	48,000	48,000	48,000	48,000	48,000
Profit before tax	96,000	24,000	0	72,000	72,000
Less: tax @ 50%	48,000	12,000	0	36,000	36,000
Add: depreciation	48,000	48,000	48,000	48,000	48,000
Cash inflow (CFAT)	96,000	60,000	48,000	84,000	84,000

(i) Net present value and profitability index at 10%. The cash inflows are discounted at the required rate of return, and the NPV is their present value less the outlay.

Year	PVF @ 10%	Machine 1 CFAT	PV (1)	Machine 2 CFAT	PV (2)
1	0.909	72,000	65,448	96,000	87,264
2	0.826	72,000	59,472	60,000	49,560
3	0.751	72,000	54,072	48,000	36,048
4	0.683	72,000	49,176	84,000	57,372
5	0.621	72,000	44,712	84,000	52,164
Total PV of inflows			2,72,880		2,82,408

Particulars (₹)	Machine 1	Machine 2
PV of cash inflows	2,72,880	2,82,408
Less: initial outlay	2,40,000	2,40,000
Net present value	32,880	42,408
Profitability index (PV of inflows ÷ outlay)	1.137	1.177

The profitability index is the present value of the inflows divided by the initial outlay.

(ii) Internal rate of return. The IRR is the rate at which the NPV is nil. It is found by discounting at two trial rates on either side of it and interpolating: IRR = LR + NPV at LR ÷ (NPV at LR − NPV at HR) × (HR − LR).

Machine 1 (an annuity of ₹72,000): the outlay is 2,40,000 ÷ 72,000 = 3.333 times the annual inflow, which lies between the five-year annuity factors at 15% (3.353) and 16% (3.274).

Particulars (₹)	at 15%	at 16%
PV of inflows (72,000 × 3.353; 72,000 × 3.274)	2,41,416	2,35,728
Less: outlay	2,40,000	2,40,000
NPV	1,416	−4,272

IRR = 15% + 1,416 ÷ (1,416 + 4,272) × 1% = 15% + 0.25% = 15.25%.

Machine 2 (uneven inflows): at 16% and 17%.

Year	CFAT	PVF @ 16%	PV @ 16%	PVF @ 17%	PV @ 17%
1	96,000	0.862	82,752	0.855	82,080
2	60,000	0.743	44,580	0.731	43,860
3	48,000	0.641	30,768	0.624	29,952
4	84,000	0.552	46,368	0.534	44,856
5	84,000	0.476	39,984	0.456	38,304
Total PV			2,44,452		2,39,052
NPV (less 2,40,000)			4,452		−948

IRR = 16% + 4,452 ÷ (4,452 + 948) × 1% = 16% + 0.82% = 16.82%.

Which machine?

Measure	Machine 1	Machine 2
NPV (₹)	32,880	42,408
Profitability index	1.137	1.177
IRR	15.25%	16.82%

Both machines are acceptable on their own (positive NPV, PI above 1, IRR above the 10% required return). As they are mutually exclusive, only one can be taken: Machine 2 should be accepted. It has the higher NPV, so it adds more to the value of the firm, and the higher PI and IRR as well, so all three methods agree. Its larger inflows come in the first year, when they are worth most.

Where the 15 marks sit

#	Component	Marks
1	Depreciation, tax and cash inflows after tax	4
2	NPV and profitability index of each machine	4
3	IRR of each machine by interpolation	5
4	Choice of machine with reason	2
	Total	15

Keyboard: ← → previous and next question, / search

Report a problemopens an email to admin@getkunji.com with the question ID1251-Q2ORalready filled in.