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

B. $14,600

Step-by-step 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*((1 - (1 + r)^(-n)))/(r) =NPV\\\\-\$100,000 + X*((1 - (1 + r)^(-n)))/(r) =\$5,850\\-\$100,000 + X*((1 - (1 + 0.12)^(-18)))/(0.12) =\$5,850\\X=(\$105,850)/(7.25) \\X=\$14,600`

Annual cash inflows are $14,600.