12-33. (Continued)
h. Incremental depreciation and tax shield benefits
(1) (2) (3) (4) (5) (6)
Year
Depreciation
on new
Equipment
Depreciation
on old
Equipment
Incremental
Depreciation
Tax
Rate
Tax
Shield
Benefits
1 $29,600 $11,136 $18,464 .35 $ 6,462
2 47,360 6,670 40,690 .35 14,242
3 28,416 6,670 21,746 .35 7,611
i. Aftertax cost savings
Year Savings
(1 – Tax
Rate)
Aftertax
Savings
1 $62,000 .65 $40,300
2 54,000 .65 35,100
3 52,000 .65 33,800
j. Present value of the total incremental benefits
(1) (2) (3) (4) (5) (6)
Year
Tax Shield
Benefits
from
Depreciation
Aftertax
Cost
Savings
Total
Annual
Benefits
Present
Value
Factor
12%
Present
Value
1 $ 6,462 $40,300 $46,762 .893 $ 41,758
2 14,242 35,100 49,342 .797 39,326
3 7,611 33,800 41,411 .712 29,485
k. Present Value of Incremental Benefits $168,365
Net Cost of New Equipment 122,136
Calculator Solution:
Using a financial calculator,
Press the following keys: 2nd, CF, 2nd, Clear.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 41,411, and press Enter.
Press down arrow, enter 1, and press Enter.
Press down arrow, enter 26,404, and press Enter.
COMPREHENSIVE PROBLEM
The Woodruff Corporation purchased a piece of equipment three years ago for $230,000. It has
an asset depreciation range (ADR) midpoint of eight years. The old equipment can be sold for
$90,000.
A new piece of equipment can be purchased for $320,000. It also has an ADR of eight years.
Assume the old and new equipment would provide the following operating gains (or losses)
over the next six years:
New Equipment Old Equipment
1………….. $80,000 $25,000
2………….. 76,000 16,000
3………….. 70,000 9,000
4………….. 60,000 8,000
5………….. 50,000 6,000
6………….. 45,000 (7,000)
The firm has a 36 percent tax rate and a 9 percent cost of capital. Should the new equipment
be purchased to replace the old equipment?
CP 12-1. Solution:
Woodruff Corporation
Book Value of Old Equipment
(ADR of 8 years indicates the use of the 5-year MACRS
schedule)
Year
Depreciation
Base
Percentage
Depreciation
(Table 12-9)
Annual
Depreciation
1 $230,000 .200 $ 46,000
2 230,000 .320 73,600
Tax Obligation on the Sale
Sales Price $ 90,000
Cash Inflow from the Sale of the Old Equipment
Sales Price $90,000
Taxes 8,554
$81,446
Net Cost of the New Equipment
Depreciation Schedule of the New Equipment
3 320,000 .192 61,440
4 320,000 .115 36,800
5 320,000 .115 36,800
6 320,000 .058 18,560
$320,000
Depreciation Schedule for the Remaining Years of the Old
Equipment
Year*
Depreciation
Base
Percentage
Depreciation
(Table 12-9)
Annual
Depreciation
*The next three years represent the last three years of the old
equipment.
CP 12-1. (Continued)
Incremental Depreciation and Tax Shield Benefits
(1) (2) (3) (4) (5) (6)
Year
Depreciation
on New
Equipment
Depreciation
on Old
Equipment
Incremental
Depreciation
Tax
Rate
Tax
Shield
Benefits
1 $ 64,000 $26,450 $37,550 .36 $13,518
2 102,400 26,450 75,950 .36 27,342
3 61,440 13,340 48,100 .36 17,316
Aftertax cost savings
New
Equipment
Old
Equipment
Cost
Savings
(1 – Tax
Rate)
Aftertax
Savings
$80,000 $25,000 $55,000 .64 $35,200
76,000 16,000 60,000 .64 38,400
70,000 9,000 61,000 .64 39,040
CP 12-1. (Continued)
Present value of the total incremental benefits.
(1) (2) (3) (4) (5) (6)
Year
Tax Shield
Benefits
from
Depreciation
Aftertax
Cost
Savings
Total
Annuity
Benefits
Present
Value
Factor
9%
Present
Value
1 $13,518 $35,200 $48,718 .917 $ 44,674
2 27,342 38,400 65,742 .842 55,355
3 17,316 39,040 56,356 .772 43,507
Net Present Value
Present Value of Incremental Benefits $227,210