IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Project appraisal
A project costs Rs 100,000 now and returns Rs 55,000 at time 1 and Rs 60,500 at time 2 (its internal rate of return is 10% per annum). The firm can borrow at 8% effective per annum. What is the net present value of the project at 8% per annum?
The NPV is Rs 2,794.93. At 8% the loan clears with a surplus of Rs 3,260 at time 2, and discounting this by 1.08 squared gives Rs 2,794.93. Because the internal rate of return of 10% exceeds 8%, the NPV is positive.
- ARs 0.00
- BRs 2,794.93Correct
- CRs 3,260.00
- DRs 6,944.44
- -Rs 2,794.93
Explanation
Loan balance: -100,000 x 1.08 + 55,000 = -53,000. At time 2: -53,000 x 1.08 + 60,500 = 3,260. Discount to time 0: 3,260 / 1.1664 = 2,794.93. Rs 3,260 is the time-2 value, not the present value. Rs 6,944.44 discounts the second flow for only one year.
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