Sources of finance; ARR, payback, IRR, PI decision

Sources of project finance

Investment decision

Data: investment = Rs 3,00,000; annual return = Rs 50,000 for 8 years; salvage = Rs 10,000. The required rate is not given, so 10% is assumed as the cost of capital; the return is treated as annual profit before depreciation (cash inflow), and tax is ignored.

1. ARR

$$\begin{aligned} \text{Depreciation} &= \frac{300{,}000 - 10{,}000}{8} = 36{,}250\\ \text{Average profit} &= 50{,}000 - 36{,}250 = 13{,}750\\ \text{Average investment} &= \frac{300{,}000 + 10{,}000}{2} = 155{,}000\\ ARR &= \frac{13{,}750}{155{,}000} \times 100 = 8.87\% \end{aligned}$$

2. Payback period

$$\text{Payback} = \frac{300{,}000}{50{,}000} = 6.0\ \text{years}$$

3. IRR: find $i$ at which $-300{,}000 + 50{,}000\,(P/A,i,8) + 10{,}000\,(P/F,i,8) = 0$. At 7%, PW = +4,385; at 8%, PW = -7,267. By interpolation, IRR = 7.37%.

4. Profitability index (at 10%; annuity factor = 5.3349, PV factor = 0.4665)

$$\begin{aligned} PV_{inflow} &= 50{,}000 \times 5.3349 + 10{,}000 \times 0.4665 = 271{,}411\\ PI &= \frac{271{,}411}{300{,}000} = 0.905, \quad NPV = -28{,}589 \end{aligned}$$

Answer: ARR = 8.87%, payback = 6.0 years, IRR = 7.37%, PI = 0.905. The IRR is below 10% and PI is below 1, so the investment is not recommended at a 10% cost of capital. It would be acceptable only if the required rate were below about 7.4%.