Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
31. To find the initial pretax cost savings necessary to buy the new machine, we should use the tax shield
approach to find the OCF. We begin by calculating the depreciation each year using the MACRS
depreciation schedule. The depreciation each year is:
D4 = $580,000(.0741) = $42,978
Using the tax shield approach, the OCF each year is:
OCF5 = (S – C)(1 – .35)
Now we need the aftertax salvage value of the equipment. The aftertax salvage value is:
To find the necessary cost reduction, we must realize that we can split the cash flows each year. The
necessary cost reduction, we would require a zero NPV. The equation for the NPV of the project is:
NPV = 0 = –$580,000 – 40,000 + (S – C)(.65)(PVIFA12%,5) + .35($193,314/1.12)
Solving this equation for the sales minus costs, we get:
(S – C)(.65)(PVIFA12%,5) = $417,402.64
32. To find the bid price, we need to calculate all other cash flows for the project, and then solve for the
bid price. The aftertax salvage value of the equipment is:
Aftertax salvage value = $160,000(1 – .35) = $104,000
Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the
NPV of the project is:
33. a. This problem is basically the same as the previous problem, except that we are given a sales
price. The cash flow at Year 0 for all three parts of this question will be:
Capital spending
–$1,800,000
Change in NWC
–175,000
Total cash flow
–$1,975,000
We will use the initial cash flow and the salvage value we already found in that problem. Using
the bottom up approach to calculating the OCF, we get:
Assume price per unit = $20 and units/year = 175,000
Year
1
2
3
4
5
Sales
$3,500,000
$3,500,000
$3,500,000
$3,500,000
$3,500,000
Variable costs
2,318,750
2,318,750
2,318,750
2,318,750
2,318,750
Fixed costs
265,000
265,000
265,000
265,000
265,000
Depreciation
360,000
360,000
360,000
360,000
360,000
EBIT
$556,250
$556,250
$556,250
$556,250
$556,250
Taxes (35%)
194,688
194,688
194,688
194,688
194,688
Net Income
$361,563
$361,563
$361,563
$361,563
$361,563
Depreciation
360,000
360,000
360,000
360,000
360,000
Operating CF
$721,563
$721,563
$721,563
$721,563
$721,563
Year
1
2
3
4
5
Operating CF
$721,563
$721,563
$721,563
$721,563
$721,563
Change in NWC
175,000
Capital spending
104,000
Total CF
$721,563
$721,563
$721,563
$721,563
$1,000,563
With these cash flows, the NPV of the project is:
NPV = –$1,975,000 + $721,563(PVIFA13%,5) + [($175,000 + 104,000)/1.135]
If the actual price is above the bid price that results in a zero NPV, the project will have a positive
b. To find the minimum number of cartons sold to still breakeven, we need to use the tax shield
approach to calculating OCF, and solve the problem similar to finding a bid price. Using the
initial cash flow and salvage value we already calculated, the equation for a zero NPV of the
project is:
NPV = 0 = –$1,975,000 + OCF(PVIFA13%,5) + [($175,000 + 104,000)/1.135]
So, the necessary OCF for a zero NPV is:
OCF = $1,823,569.98/PVIFA13%,5 = $518,467.47
Now we can use the tax shield approach to solve for the minimum quantity as follows:
OCF = $518,467.47 = [(P – v)Q – FC ](1 – tc) + tcD
As a check, we can calculate the NPV of the project with this quantity. The calculations are:
Year
1
2
3
4
5
Sales
$2,574,211
$2,574,211
$2,574,211
$2,574,211
$2,574,211
Variable costs
1,705,415
1,705,415
1,705,415
1,705,415
1,705,415
Fixed costs
265,000
265,000
265,000
265,000
265,000
Depreciation
360,000
360,000
360,000
360,000
360,000
EBIT
$243,796
$243,796
$243,796
$243,796
$243,796
Taxes (35%)
85,329
85,329
85,329
85,329
85,329
Net Income
$158,467
$158,467
$158,467
$158,467
$158,467
Depreciation
360,000
360,000
360,000
360,000
360,000
Operating CF
$518,467
$518,467
$518,467
$518,467
$518,467
Year
1
2
3
4
5
Operating CF
$518,467
$518,467
$518,467
$518,467
$518,467
Change in NWC
175,000
Capital spending
104,000
Total CF
$518,467
$518,467
$518,467
$518,467
$797,467
c. To find the highest level of fixed costs and still breakeven, we need to use the tax shield approach
to calculating OCF, and solve the problem similar to finding a bid price. Using the initial cash
flow and salvage value we already calculated, the equation for a zero NPV of the project is:
NPV = 0 = –1,975,000 + OCF(PVIFA13%,5) + [($175,000 + 104,000)/1.135]
OCF = $1,823,569.98/PVIFA13%,5 = $518,467.47
Notice this is the same OCF we calculated in part b. Now we can use the tax shield approach to
solve for the maximum level of fixed costs as follows:
OCF = $518,467.47 = [(P – v)Q – FC ](1 – tC) + tCD
$518,467.47 = [($20 – $13.25)(175,000) – FC](1 – .35) + .35($1,800,000/5)
Year
1
2
3
4
5
Sales
$3,500,000
$3,500,000
$3,500,000
$3,500,000
$3,500,000
Variable costs
2,318,750
2,318,750
2,318,750
2,318,750
2,318,750
Fixed costs
577,454
577,454
577,454
577,454
577,454
Depreciation
360,000
360,000
360,000
360,000
360,000
EBIT
$243,796
$243,796
$243,796
$243,796
$243,796
Taxes (35%)
85,329
85,329
85,329
85,329
85,329
Net Income
$158,467
$158,467
$158,467
$158,467
$158,467
Depreciation
360,000
360,000
360,000
360,000
360,000
Operating CF
$518,467
$518,467
$518,467
$518,467
$518,467
Year
1
2
3
4
5
Operating CF
$518,467
$518,467
$518,467
$518,467
$518,467
Change in NWC
175,000
Capital spending
104,000
Total CF
$518,467
$518,467
$518,467
$518,467
$797,467
NPV = –$1,975,000 + $518,467(PVIFA13%,5) + [($175,000 + 104,000)/1.135] $0
34. We need to find the bid price for a project, but the project has extra cash flows. Since we don’t already
produce the keyboard, the sales of the keyboard outside the contract are relevant cash flows. Since we
know the extra sales number and price, we can calculate the cash flows generated by these sales. The
Year 1
Year 2
Year 3
Year 4
Sales
$2,479,500
$2,964,000
$3,334,500
$1,909,500
Variable costs
1,174,500
1,404,000
1,579,500
904,500
EBT
$1,305,000
$1,560,000
$1,755,000
$1,005,000
Tax
522,000
624,000
702,000
402,000
Net income (and OCF)
$783,000
$936,000
$1,053,000
$603,000
So, the addition to NPV of these market sales is:
NPV of market sales = $783,000/1.13 + $936,00/1.132 + $1,053,000/1.133 + $603,000/1.134
NPV of market sales = $2,525,558.66
Next, we need to calculate the aftertax salvage value, which is:
Aftertax salvage value = $650,000(1 – .40)
Aftertax salvage value = $390,000
OCF = $2,760,918.45/PVIFA13%,4
OCF = $928,204.76
OCF for the new computer system is:
OCF = ($55,000)(1 – .38) + ($371,000/5)(.38)
OCF = $62,296
NPV = –$371,000 + $62,296(PVIFA11%,5) + $22,320/1.115
NPV = –$127,514.57
OCF = $32,000(.38)
OCF = $12,160
old computer there is no initial cost, but we can sell the old computer, so there is an opportunity cost.
We need to account for this opportunity cost. To do so, we will calculate the aftertax salvage value of
the old computer today. We need the book value of the old computer to do so. The book value is not
given directly, but we are told that the old computer has depreciation of $32,000 per year for the next
three years, so we can assume the book value is the total amount of depreciation over the remaining
Aftertax salvage value = $118,320
since we are “buying” it today. The aftertax salvage value in two years is:
Aftertax salvage value = $20,000 + ($32,000 – 20,000)(.38)
Aftertax salvage value = $24,560
NPV = –$118,320 + $12,160(PVIFA11%,2) + 24,560/1.112
NPV = –$77,562.27
decision on the computer system now, we need the difference in the total cash flows of the old
computer system and the new computer system. From our previous calculations, we can say the
cash flows for each computer system are:
t
New computer
Old computer
Difference
0
–$371,000
–$118,320
–$252,680
1
62,296
12,160
50,136
2
62,296
36,720
25,576
3
62,296
0
62,296
4
62,296
0
62,296
5
84,616
0
84,616
old computer system with the new computer system are the differential cash flows. The NPV of the
decision to replace, ignoring what will happen in two years is:
NPV = –$252,680 + $50,136/1.11 + $25,576/1.112 + $62,296/1.113 + $62,296/1.114
+ $84,616/1.115
