A company is considering an investment proposal to instal new milling controls at a cost of Rs.50,000. The facility has a life expectancy of 5 years and no salvage value. The tax rate is 35 per cent. Assume the firm uses straight line depreciation and the same is allowed for tax purposes. The estimated cash flows before depreciation and tax (CFBT) from the investment proposal are as follows:
Compute the following:
(i) Pay back period,
(ii) Average rate of return,
(iii) Internal rate of return,
(iv) Net present value at 10 per cent discount rate,
(v) Profitability index at 10 per cent discount rate.
Year | CFBT |
1 | Rs 10,000 |
2 | 10,692 |
3 | 12,769 |
4 | 13,462 |
5 | 20,385 |
(i) Pay back (PB) period:
The recovery of the investment falls between the fourth and fifth years. Therefore, the PB is 4 years plus a fraction of the fifth year. The fractional value = Rs 5,500 \div Rs 16,750=0.328. Thus, the PB is 4.328 years.
(ii) Average rate of return ( ARR ):=\frac{\text { Average income }}{\text { Average investment }} \times 100=\frac{\text { Rs } 2,250(\text { Rs } 11,250 \div 5)}{\text { Rs } 25,000(\text { Rs } 50,000 \div 2)} \times 100=9 per cent
(iii) Internal rate of return (IRR): Rs 50,000=\frac{\mathrm{Rs} 10,000}{(1+r)^{1}}+\frac{\mathrm{Rs} 10,450}{(1+r)^{2}}+\frac{\mathrm{Rs} 11,800}{(1+r)^{3}}+\frac{\mathrm{Rs} 12,250}{(1+r)^{4}}+\frac{\mathrm{Rs} 16,750}{(1+r)^{5}}
The fake pay back period =4.0816 (Rs 50,000/Rs 12,250). From Table A-4, the value closest to the fake pay back period of 4.0816 against 5 years is 4.100 against 7 per cent. Since the actual cash flow stream is the initial years is slightly below the average cash flow stream, the IRR is likely to be lower than 7 per cent. Let us try with 6 per cent.
The IRR is between 6 and 7 per cent. By interpolation, IRR =6.6 per cent.
(iv) Net present value (NPV)
(v) Profitability index (P I)=\frac{\text { PV of cash inflows }}{\text { PV of cash outflows }}=\frac{\text { Rs } 45,352}{\text { Rs } 50,000}=0.907
Determination of cashflows after taxes (CFAT)
Year | CFBT | Depreciation (Rs 50,000/5) |
Profits before tax (Col.2 – Col.3) |
Taxes (0.35) |
EAT (Col.4 – Col.5) |
CFAT (Col.6+Col.3) |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
1 | Rs 10,000 | Rs 10,000 | Nil | Nil | Nil | Rs 10,000 |
2 | 10,692 | 10,000 | Rs 692 | Rs 242 | Rs 450 | 10,450 |
3 | 12,769 | 10,000 | 2,769 | 969 | 1,800 | 11,800 |
4 | 13,462 | 10,000 | 3,462 | 1,212 | 2,250 | 12,250 |
5 | 20,385 | 10,000 | 10,385 | 3,635 | 6,750 | 16,750 |
11,250 | 61,250 |
Year | CFAT | Cumulative CFAT |
1 | Rs 10,000 | Rs 10,000 |
2 | 10,450 | 20,450 |
3 | 11,800 | 32,250 |
4 | 12,250 | 44,500 |
5 | 16,750 | 61,250 |
PV factor | Total PV | ||||
Year | CFAT | (0.06) | (0.07) | (0.06) | (0.07) |
1 | Rs 10,000 | 0.943 | 0.935 | Rs 9,430 | Rs 9,350 |
2 | 10,450 | 0.890 | 0.873 | 9,300 | 9,123 |
3 | 11,800 | 0.840 | 0.816 | 9,912 | 9,629 |
4 | 12,250 | 0.792 | 0.763 | 9,702 | 9,347 |
5 | 16,750 | 0.747 | 0.713 | 12,512 | 11,942 |
Total PV | 50,856 | 49,391 | |||
Less initial outlay | 50,000 | 50,000 | |||
NPV | 856 | (609) |
Year | CFAT | PV factor (0.10) | Total PV |
1 | Rs 10,000 | 0.909 | Rs 9,090 |
2 | 10,450 | 0.826 | 8,632 |
3 | 11,800 | 0.751 | 8,862 |
4 | 12,250 | 0.683 | 8,367 |
5 | 16,750 | 0.621 | 10,401 |
Total PV | 45,352 | ||
Less initial outlay | 50,000 | ||
NPV | (4,648) |