Hi! I uploaded my question and the solution. All answers you need is in the solution. One thing I want to know is how to calculate depreciation recapture. For a) when he buys it, at year 5, how to get

Hi! I uploaded my question and the solution. All answers you need is in the solution. One thing I want to know is how to calculate depreciation recapture. For a) when he buys it, at year 5, how to get (76,960)? and For b) when he buys it, at year 5, how to get (60,000)? Please be specific and show me all the work. Thank you so much.

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Management 127A
Lease vs. buy: Solution
a) First, determine the discount rate
d
= interest rate x (1–tax rate) = 10%x(1-35%) = 6.5%.
If you buy, you have cash flows of (400,000) in year 0 (purchase), 100,000 in year 5 (sale),
and tax cash flows of 35% x depreciation each year and (35%) x gain (100,000) in year 5.
Year (
t
)
Nontax
C
t
Tax
C
t
Total
C
t
PV:
C
t
/(1+
d
)
t
0
(400,000)
80,000 x 35%
(372,000)
(372,000)
1
0
128,000 x 35%
44,800
42,066
2
0
76,800 x 35%
26,880
23,699
3
0
46,080 x 35%
16,128
13,352
4
0
46,080 x 35%
16,128
12,537
5
100,000
(76,960) x 35%
73,064
53,328
(227,018)
If you lease, you have deductible cash flows of (85,000) in years 1 through 5.
Year (
t
)
Nontax
C
t
Tax
C
t
Total
C
t
PV:
C
t
/(1+
d
)
t
0
0
0
0
0
1
(85,000)
85,000 x 35%
(55,250)
(51,878)
2
(85,000)
85,000 x 35%
(55,250)
(48,712)
3
(85,000)
85,000 x 35%
(55,250)
(45,739)
4
(85,000)
85,000 x 35%
(55,250)
(42,947)
5
(85,000)
85,000 x 35%
(55,250)
(40,326)
(229,602)
Buying is the less expensive alternative in present value.
b) The analysis is the same, except that
d
= 10%x(1-28%) = 7.2%, deductions are at 28%,
and depreciation occurs more slowly.
Buying:
Year (
t
)
Nontax
C
t
Tax
C
t
Total
C
t
PV:
C
t
/(1+
d
)
t
0
(400,000)
40,000 x 28%
(388,800)
(388,800)
1
0
80,000 x 28%
22,400
20,896
2
0
80,000 x 28%
22,400
19,492
3
0
80,000 x 28%
22,400
18,183
4
0
80,000 x 28%
22,400
16,962
5
100,000
(60,000) x 28%
83,200
58,769
(254,498)
Leasing:
Year (
t
)
Nontax
C
t
Tax
C
t
Total
C
t
PV:
C
t
/(1+
d
)
t
0
0
0
0
0
1
(85,000)
85,000 x 28%
(61,200)
(57,090)
2
(85,000)
85,000 x 28%
(61,200)
(53,255)
3
(85,000)
85,000 x 28%
(61,200)
(49,678)
4
(85,000)
85,000 x 28%
(61,200)
(46,342)
5
(85,000)
85,000 x 28%
(61,200)
(43,229)
(249,594)
Leasing is the less expensive alternative in present value.

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Management 127A
Tax planning with present value: lease vs. buy
You need to acquire a machine for your business.
You will use the machine for the next
five years.
There are two choices:
1) buy the machine for $400,000, then sell it after five years for $100,000 (expected), or
2) lease the machine for $85,000 per year.
If you buy the machine, you can depreciate it by the following amounts:
Year
Regular tax
AMT
0
80,000
40,000
1
128,000
80,000
2
76,800
80,000
3
46,080
80,000
4
46,080
80,000
5
23,040
40,000
The purchase price would be paid in year 0.
In the case of a lease, payments would be
made in years 1 through 5.
You can borrow money (through business loans) at an interest rate of 10%.
Required:
a)
Should you lease or buy if you do not pay AMT and face a tax rate of 35%?
b)
Should you lease or buy if you pay AMT (tax rate of 28%)?

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