978-1259289903 Chapter 8 Solution Manual Part 4

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

Variable costs

2,318,750

Fixed costs

265,000

Depreciation

360,000

EBIT

$556,250

Taxes (35%)

194,688

Net Income

$361,563

Depreciation

360,000

Operating CF

$721,563

Year

1

2

3

4

5

Operating CF

$721,563

Change in NWC

175,000

Capital spending

104,000

Total CF

$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

Variable costs

1,705,415

Fixed costs

265,000

Depreciation

360,000

EBIT

$243,796

Taxes (35%)

85,329

Net Income

$158,467

Depreciation

360,000

Operating CF

$518,467

Year

1

2

3

4

5

Operating CF

$518,467

Change in NWC

175,000

Capital spending

104,000

Total CF

$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

Variable costs

2,318,750

Fixed costs

577,454

Depreciation

360,000

EBIT

$243,796

Taxes (35%)

85,329

Net Income

$158,467

Depreciation

360,000

Operating CF

$518,467

Year

1

2

3

4

5

Operating CF

$518,467

Change in NWC

175,000

Capital spending

104,000

Total CF

$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