The mayor of Smalltown,Western Australia,is considering the purchase of a computer system to automate the city's rate collections.The system costs $75 000 and has an estimated life of five years.The mayor estimates the following savings will result if the system is purchased.If Smalltown uses a 10 per cent discount rate for capital budgeting decisions,what can be said about the internal rate of return (IRR) if the net present value at 12 per cent is positive?

Question

Quizplus · Accepted Answer

To determine whether the internal rate of return (IRR) is greater than 12%, we need to calculate the net present value (NPV) of the project at different discount rates. If the NPV is positive at a discount rate higher than 12%, it means that the project's IRR is also higher than 12%.

Using a 10% discount rate, the mayor estimates the following annual savings:
Year 1: $30,000
Year 2: $35,000
Year 3: $40,000
Year 4: $50,000
Year 5: $55,000

To calculate the NPV of the project at 12% discount rate, we need to find the present value of each year's savings and subtract the initial cost of the system. Using a financial calculator or spreadsheet software, we get:

NPV = -$75,000 + $27,970 + $29,327 + $28,504 + $32,513 + $31,041
NPV = $13,355

Since the NPV is positive at 12% discount rate, it means that the IRR must be higher than 12%. Therefore, the answer is choice A: The IRR is greater than 12%.

The Mayor of Smalltown,Western Australia,is Considering the Purchase of a Computer