One year ago, your company purchased a machine used in manufacturing for $115,00
ID: 2784419 • Letter: O
Question
One year ago, your company purchased a machine used in manufacturing for $115,000. You have learned that a new machine is available that offers many advantages; you can purchase it for $170,000 today. It will be depreciated on a straight-line basis over ten years, after which it has no salvage value. You expect that the new machine will contribute EBITDA(earnings before interest, taxes,depreciation, and amortization) of $40,000 per year for the next ten years. The current machine is expected to produce EBITDA of $25,000 per year. The current machine is being depreciated on a straight-line basis over a useful life of 11 years, after which it will have no salvage value, so depreciation expense for the current machine is $10,455 per year. All other expenses of the two machines aidentical. The market value today of the current machine is $50,000. Your company's tax rate is 42%, and the opportunity cost of capital for this type of equipment is 10%. Is it profitable to replace the year-old machine?
The NPV of the replacement is (Round to the nearest dollar.)
Explanation / Answer
cost of new machine
170000
cost of old machine
115000
less sale value of old machine
50000
less accumulated depreciation
115000/11
10455
less tax shield on sale of old machine
22909
book value of old machine at the end of year 1
104545
total initial investment
97091
less selling price
50000
loss on sale of old machine
104545-50000
54545
EBITDA on new machine
EBITDA on old machine
Differential EBITDA
tax shield on loss on sale of machine
54545*42%
22908.9
40000
25000
15000
Year
Depreciation on new machine
Depreciation on old machine
differential depreciation
17000
10455
6545
Differential EBITDA
differential depreciation
Differential EBIT
less tax
Differential EAT
add differential depreciation
differential EATBDA
15000
6545
8455
3550.909
4904
6545
11449
present value of Differential EATBDA
Differential EATBDA*PVAF
11449*6.1445
70348.38
Present value initial investment
97091
NPV
present value of EATBDA - present value of initial investment
-26743
no old machine should not be replaced as differential NPV of the new machine is negative
PVAF at 10% for 10 Years
1-(1+r)^-n / r
1-(1.1)^-10 /.10
6.1445
EATBDA
Earning after tax before depreciation and Amortization
cost of new machine
170000
cost of old machine
115000
less sale value of old machine
50000
less accumulated depreciation
115000/11
10455
less tax shield on sale of old machine
22909
book value of old machine at the end of year 1
104545
total initial investment
97091
less selling price
50000
loss on sale of old machine
104545-50000
54545
EBITDA on new machine
EBITDA on old machine
Differential EBITDA
tax shield on loss on sale of machine
54545*42%
22908.9
40000
25000
15000
Year
Depreciation on new machine
Depreciation on old machine
differential depreciation
17000
10455
6545
Differential EBITDA
differential depreciation
Differential EBIT
less tax
Differential EAT
add differential depreciation
differential EATBDA
15000
6545
8455
3550.909
4904
6545
11449
present value of Differential EATBDA
Differential EATBDA*PVAF
11449*6.1445
70348.38
Present value initial investment
97091
NPV
present value of EATBDA - present value of initial investment
-26743
no old machine should not be replaced as differential NPV of the new machine is negative
PVAF at 10% for 10 Years
1-(1+r)^-n / r
1-(1.1)^-10 /.10
6.1445
EATBDA
Earning after tax before depreciation and Amortization
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