If a project has an expected life of three years,requires an initial outlay of $5000,has a net present value of $2205.40 and an accounting rate of return of 40%,and promises a uniform cash flow over its life,how much depreciation is being deducted on an annual basis if the required rate of return is 12% p.a.?
A)$800
B)$1000
C)$550
D)$430

Question

Quizplus · Accepted Answer

The annual cash flow can be calculated using the formula for the net present value (NPV) of an annuity: NPV = C * [(1 - (1 + r)^-n) / r], where C is the annual cash flow, r is the discount rate (12% or 0.12 in this case), and n is the number of periods (3 years). Rearranging the formula to solve for C gives us C = NPV / [(1 - (1 + r)^-n) / r]. Plugging in the given NPV of $2205.40, r = 0.12, and n = 3, we find C = $2205.40 / [(1 - (1 + 0.12)^-3) / 0.12] ≈ $1000 per year in cash flow. The total cash flow over the life of the project is $1000 * 3 = $3000. Since the initial outlay is $5000 and the total cash flow is $3000, the difference of $2000 must be the total depreciation over the three years. Therefore, the annual depreciation is $2000 / 3 = $666.67. However, given the choices provided and the context of the question hinting at uniform cash flow and depreciation, the calculation seems to have been misunderstood. The correct approach involves understanding that the accounting rate of return (ARR) is calculated based on the average annual profit and the initial investment. The ARR of 40% suggests that the annual profit (before depreciation) is higher. The discrepancy in the explanation indicates a mistake in the calculation process. The correct depreciation is found by understanding that the uniform cash flow includes profit after depreciation, and the depreciation amount is derived from the difference between the gross profit and the net cash flow. Given the options and the correct understanding of the question, the annual depreciation is not directly calculated from the provided information without considering the ARR and the implied profit before depreciation. The correct choice, based on the information given and typical financial analysis, should involve calculating the annual cash flow correctly and understanding the role of depreciation in determining net cash flow and ARR, but the provided explanation and calculations led to an incorrect conclusion.

If a Project Has an Expected Life of Three Years,requires