Question

A machine purchased three years ago for $317,000 has a current book value using straight-line depreciation of $188,000; its operating expenses are $37,000 per year. A replacement machine would cost $227,000, have a useful life of ten years, and would require $9,000 per year in operating expenses. It has an expected salvage value of $77,000 after ten years. The current disposal value of the old machine is $86,000; if it is kept 10 more years, its residual value would be $13,000.

Answer 1

At discount rate of 12% it is convinient to replace the machine as the net worth is lower.

Step-by-step explanation:

We aren't given with any rate to work for we are going to assume a 12% rate of return

Current New machine

market value 86,000 227,000

expenses 37,000 9,000

useful life 10 10

salvage 13,000 86,000

F0 - (141,000)*

PV expenses (209,058)** (50,852)***

PV salvage value 4,186**** 27,690*****

Net worth (204,873) (164,162)

*227,000 cost less proceed from sale of the old machine

** annuity for 37,000 during 10 years discounted at 12%

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 37,000.00

time 10

rate 0.12

`37000 * (1-(1+0.12)^(-10) )/(0.12) = PV\\`

*** annuity of 9,000 during 10 years discounted at 12%

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 9,000.00

time 10

rate 0.12

`9000 * (1-(1+0.12)^(-10) )/(0.12) = PV\\`

**** present value of 13,000 value of the machine in 10 year discounted at 12%

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 13,000.00

time 10.00

rate 0.12000

`(13000)/((1 + 0.12)^(10) ) = PV`

***** present value of 77,000 value of the machine in 10 year discounted at 12%

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 77,000.00

time 10.00

rate 0.12000

`(77000)/((1 + 0.12)^(10) ) = PV`