Question

Franco is considering replacing one of its machines. The old machine is being depreciated on a straight-line basis down to a salvage value of zero over the next 5 years. It has a book value of $200,000 and could be sold for $120,000. The replacement machine would cost $600,000 and have an expected life of 5 years, after which it could be sold for $100,000. Because of reductions in defects and material savings, the new machine would produce cash benefits of $180,000 per year before depreciation and taxes. The present value of $1 at 15% received after 5 periods at 15% is 0.49718. The present value of an annuity of $1 for 4 periods at 15% is 2.85498, and for 5 periods is 3.35216. What is the payback period and NPV?

Answer 1

Answer:

There is no information on tax rate; hence it is assumed that tax rate = 0%

Incremental cash flows:

Year 0 cash outflow = New machine cost - current sale value of old machine = $600,000 - $120,000 = $480,000

Year 0 to Year 4 cash flow:

Annual cash inflows = cash benefits = $180,000

Year 5 cash inflow:

Year 5 cash flow = cash benefits + salvage value of new machine = 180000 + 100000 = $280,000

Payback period:

Annual cash flows are uniform at 180,000 upto 4 years.

Payback period = 480000 / 180000 = 2.67 Years

NPV:

NPV = Annual cash flow (year 1 to year 4) * present value of an annuity of $1 for 4 periods at 15% + Year 5 cash flow * present value of $1 at 15% received after 5 periods at 15% - Year 0 cash outflow

= 180000 * 2.85498 + 280000 * 0.49718 - 480000

= $173,106.80

Hence:

Payback period = 2.67 Years

NPV = $173,106.80