Answer:
At discount rate of 12% it is convinient to replace the machine as the net worth is lower.
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%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 37,000.00
time 10
rate 0.12
[tex]37000 \times \frac{1-(1+0.12)^{-10} }{0.12} = PV\\[/tex]
*** annuity of 9,000 during 10 years discounted at 12%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 9,000.00
time 10
rate 0.12
[tex]9000 \times \frac{1-(1+0.12)^{-10} }{0.12} = PV\\[/tex]
**** present value of 13,000 value of the machine in 10 year discounted at 12%
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 13,000.00
time 10.00
rate 0.12000
[tex]\frac{13000}{(1 + 0.12)^{10} } = PV[/tex]
***** present value of 77,000 value of the machine in 10 year discounted at 12%
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 77,000.00
time 10.00
rate 0.12000
[tex]\frac{77000}{(1 + 0.12)^{10} } = PV[/tex]
