Companies invest in expansion projects with the expectation of increasing the ea
ID: 2713955 • Letter: C
Question
Companies invest in expansion projects with the expectation of increasing the earnings of its business. Consider the case of Fox Co.: Fox Co. is considering an investment that will have the following sales, variable costs, and fixed operating costs: This project will require an investment of $20,000 in new equipment. The equipment will have no salvage value at the end of the project's four-year life. Fox pays a constant tax rate of 40%, and it has a weighted average cost of capital (WACC) of 11%. Determine what the project's net present value (NPV) would be when using accelerated depredation. Determine what the project's net present value (NPV) would be when using accelerated depreciation. Now determine what the project's NPV would be when using straight-line depreciation. Using the depreciation method will result in the highest NPV for the project. No other firm would take on this project if Fox turns it down. How much should Fox reduce the NPV of this project if it discovered that this project would reduce one of its division's net after-tax cash flows by $700 for each year of the four-year project?Explanation / Answer
Calculation of Present Value of Cash Inflow using accelerated depreciation
Particulars
Year 1
Year 2
Year 3
Year 4
Total
A.
Units Sales
4800
5100
5000
5120
B.
Sales Price per unit
$22.33
$23.45
$23.85
$24.45
C.
Variable Cost Per unit
$9.45
$10.85
$11.95
$12.00
D.
Contribution per Unit (B - C)
$12.88
$12.60
$11.90
$12.45
E.
Contribution in Dollars (D x A)
$61,824
$64,260
$59,500
$63,744
F.
Fixed Operating Costs expect depreciation
$32,500
$33,450
$34,950
$34,875
G.
Operating profit before depreciation (E-F)
$29,324
$30,810
$24,550
$28,869
H.
Accelerated Depreciation
$6,600
$9,000
$3,000
$1,400
I.
Operating Profit after Depreciation (G-H)
$22,724
$21,810
$21,550
$27,469
J
Tax (I x 40%)
$9,090
$8,724
$8,620
$10,988
K
Earning After Tax (I - J)
$13,634
$13,086
$12,930
$16,481
L
Add: Depreciation
$6,600
$9,000
$3,000
$1,400
M
Cash Inflow (K + L)
$20,234
$22,086
$15,930
$17,881
N
Present Value interest factor at 11%
0.9009
0.8116
0.7310
0.6590
O
Present Value of Inflow (M x N)
$18,229
$17,925
$11,645
$11,784
$59,581
Net Present Value (when using accelerated depreciation) = Present Value of Cash Inflow – Present Value of Cash Outflow = $59,581 - $20,000 = $39,581
Calculation of Present Value of Cash Inflow using straight line depreciation
Particulars
Year 1
Year 2
Year 3
Year 4
Total
A.
Units Sales
4800
5100
5000
5120
B.
Sales Price per unit
$22.33
$23.45
$23.85
$24.45
C.
Variable Cost Per unit
$9.45
$10.85
$11.95
$12.00
D.
Contribution per Unit (B - C)
$12.88
$12.60
$11.90
$12.45
E.
Contribution in Dollars (D x A)
$61,824
$64,260
$59,500
$63,744
F.
Fixed Operating Costs expect depreciation
$32,500
$33,450
$34,950
$34,875
G.
Operating profit before depreciation (E-F)
$29,324
$30,810
$24,550
$28,869
H.
Accelerated Depreciation
$6,600
$9,000
$3,000
$1,400
I.
Operating Profit after Depreciation (G-H)
$22,724
$21,810
$21,550
$27,469
J
Tax (I x 40%)
$9,090
$8,724
$8,620
$10,988
K
Earning After Tax (I - J)
$13,634
$13,086
$12,930
$16,481
L
Add: Depreciation
$5,000
$5,000
$5,000
$5,000
M
Cash Inflow (K + L)
$18,634
$18,086
$17,930
$21,481
N
Present Value interest factor at 11%
0.9009
0.8116
0.7310
0.6590
O
Present Value of Inflow (M x N)
$16,787
$14,679
$13,107
$14,156
$58,729
Net Present Value = Present Value of Cash Inflow – Present Value of Cash Outflow = $58,729 - $20,000 = $38,729
Using the Accelerated depreciation method will result in the highest NPV for project.
Calculation of Revised Present Value of Cash Inlfow using straight line depreciation if firm reduce one of its division's net after tax cash flow by $700 for each year of the four year project
Revised Net Present Value = Present Value of Cash Inflow – Present Value of Cash Outflow = $56,557 - $20,000 = $36,557
Reduction in NPV = $38,729 - $36,557 = $2,172
Firm should reduce the NPV $2,172 of this project if it discovered that this project would reduce one of its division's net after tax cash flows by $700 each year (using straight line depreciation)
Particulars
Year 1
Year 2
Year 3
Year 4
Total
A.
Units Sales
4800
5100
5000
5120
B.
Sales Price per unit
$22.33
$23.45
$23.85
$24.45
C.
Variable Cost Per unit
$9.45
$10.85
$11.95
$12.00
D.
Contribution per Unit (B - C)
$12.88
$12.60
$11.90
$12.45
E.
Contribution in Dollars (D x A)
$61,824
$64,260
$59,500
$63,744
F.
Fixed Operating Costs expect depreciation
$32,500
$33,450
$34,950
$34,875
G.
Operating profit before depreciation (E-F)
$29,324
$30,810
$24,550
$28,869
H.
Accelerated Depreciation
$6,600
$9,000
$3,000
$1,400
I.
Operating Profit after Depreciation (G-H)
$22,724
$21,810
$21,550
$27,469
J
Tax (I x 40%)
$9,090
$8,724
$8,620
$10,988
K
Earning After Tax (I - J)
$13,634
$13,086
$12,930
$16,481
L
Add: Depreciation
$6,600
$9,000
$3,000
$1,400
M
Cash Inflow (K + L)
$20,234
$22,086
$15,930
$17,881
N
Present Value interest factor at 11%
0.9009
0.8116
0.7310
0.6590
O
Present Value of Inflow (M x N)
$18,229
$17,925
$11,645
$11,784
$59,581
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