Question

Benz Company is considering the purchase of a machine that costs $100,000, has a useful life of 18 years, and no salvage value. The company's discount rate is 12%. If the machine's net present value is $5,850, then the annual cash inflows associated with the machine must be (round to the nearest whole dollar):A. $42,413B. $14,600C. $13,760D. It is impossible to determine from the data given.

Answer 1

Answer:

B. $14,600

Explanation:

The annual cash inflows associated with the machine can be found by the following expression, where 'r' is the company's discount rate of 12% and 'n' is the useful life of the equipment of 18 years:

$-investment+ X*\frac{(1 - (1 + r)^{-n})}{r} =NPV\\\\-\ 100,000 + X*\frac{(1 - (1 + r)^{-n})}{r} =\ 5,850\\-\ 100,000 + X*\frac{(1 - (1 + 0.12)^{-18})}{0.12} =\ 5,850\\X=\frac{\ 105,850}{7.25} \\X=\ 14,600$

Annual cash inflows are $14,600.