Answer:
Cashflow
Yearo zero ($2,700)
from 1st to 6th: +$1,005.5
Net Present Value: $728.53
If bonus depreciation then:
Net Present Value: $916.04
Explanation:
Cash Flow
Year zero:
-3,900 purchase of new machine
+ 1,200 sale from old machine
-2,700
Years 1 through 6:
1,100 savings x (1 - 21% tax rate) = 869.0
depreciation
3,900 / 6 = 650
tax-shield on depreciation: 650 x 21% = 136.5
total cash-flow:
869 cost savings + 136.5 lesser taxes = 1005.5
We now solve for the Net present value we discount the cashflow at 19% which is the cost of capital and compare agaisn the year zero outflow:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 1,005.50
time 6
rate 0.19
[tex]1005.5 \times \frac{1-(1+0.19)^{-6} }{0.19} = PV\\[/tex]
PV $3,428.5310
- $2,700 + $3,428.53 = $728.53
If bonus depreciation scenario:
at year 1 the entire equipment is depreciate
giving a tax shield of:
3,700 x 21%= 777
This will be discounted one year as the depreciation bonus which lowers taxes occurs at year-end:
777 / 1.19 = 652.94117647
Then, we solve for the present value of the cost savings only as the depreciations do not occur:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 869.00
time 6
rate 0.19
[tex]869 \times \frac{1-(1+0.19)^{-6} }{0.19} = PV\\[/tex]
PV $2,963.0964
So we have:
- 2,700 year zero cash outflow
+ 652.94 present value of bonus depreciation
+ 2,963.10 present value of the cost savings
916.04 net present value
