Question

"A manufacturing company of a mini-doughnut machine maker quoted a price for a custom-designed doughnut machine to be delivered in 2017. Once purchased, the customer intends to place the machine in service in January 2018 and will use it for 3 years. The expected annual operating net cash flow is estimated to be $112,000. The expected salvage value of the equipment at the end of 3 years is 11.1% of the initial purchase price. To expect a 15% required rate of return on the investment, what is the maximum amount that should be spent on purchasing the doughnut machine? You do not need to consider taxes or depreciation for this problem."

Answer 1

Let, price of the machine = X

Then, salvage value of the machine = 11.1% of X or .111*X

Time = 3 years

Annual net cash flows = $112000

R = 15%

Then,

Price of the machine = present value of annual net cash flows + present value of the salvage value of the machine

X = 112000*(1-1/1.15^3)/.15 + .111X/1.15^3

X = 255721.2131 + X*.07298

X = 255721.2131/(1-.07298) = $275852.96 or $275853

So, maximum purchase price of the machine should be $275853.

There can be minor difference in the final answer due to the rounding off of the intermediate calculations.