IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project costs Rs 200,000 now. It yields cash flows at the end of years 1 to 4 of Rs 60,000, then each later flow is 5% higher than the one before: 60,000, 63,000, 66,150 and 69,457.50. The cost of capital is 10% per annum effective. What is the NPV, to two decimal places?
The NPV is Rs 3,751.45. Discounting each growing inflow at 10% gives a total present value of Rs 203,751.45, which exceeds the Rs 200,000 cost by that amount. Ignoring the growth would incorrectly give a negative NPV.
- ARs 24,126.60
- BRs 58,607.50
- C-Rs 9,808.07
- DRs 3,751.45Correct
- Rs 4,126.60
Explanation
The PVs are 54,545.45 + 52,066.12 + 49,699.47 + 47,440.41 = 203,751.45. NPV = 203,751.45 - 200,000 = 3,751.45. The figure -9,808.07 ignores the growth and treats the flows as a level 60,000. Rs 24,126.60 treats the first inflow as arriving now.
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