Question 5.S2.P.1: A company is considering an investment proposal to instal ne......

(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