First, we will calculate the depreciation each year, which will be:

D1 = ¥480,000(0.2000) = ¥96,000 D2 = ¥480,000(0.3200) = ¥153,600 D3 = ¥480,000(0.1920) = ¥92,160 D4 = ¥480,000(0.1150) = ¥55,200

The book value of the equipment at the end of the project is:

BV4 = ¥480,000 – (¥96,000 + 153,600 + 92,160 + 55,200) = ¥83,040 The asset is sold at a loss to book value, so this creates a tax refund.

After-tax salvage value = ¥70,000 + (¥83,040 – 70,000)(0.35) = ¥74,564.00 So, the OCF for each year will be:

OCF1 = ¥160,000(1 – 0.35) + 0.35(¥96,000) = ¥137,600.00 OCF2 = ¥160,000(1 – 0.35) + 0.35(¥153,600) = ¥157,760.00 OCF3 = ¥160,000(1 – 0.35) + 0.35(¥92,160) = ¥136,256.00 OCF4 = ¥160,000(1 – 0.35) + 0.35(¥55,200) = ¥123,320.00

Now we have all the necessary information to calculate the project NPV. We need to be careful with the NWC in this project. Notice the project requires ¥20,000 of NWC at the beginning, and ¥3,000 more in NWC each successive year. We will subtract the ¥20,000 from the initial cash flow, and subtract ¥3,000 each year from the OCF to account for this spending. In Year 4, we will add back the total spent on NWC, which is ¥29,000. The ¥3,000 spent on NWC capital during Year 4 is irrelevant.

Why? Well, during this year the project required an additional ¥3,000, but we would get the money back immediately. So, the net cash flow for additional NWC would be zero. With all this, the equation for the NPV of the project is:

NPV = – ¥480,000 – 20,000 + (¥137,600 – 3,000)/1.14 + (¥157,760 – 3,000)/1.14² + (¥136,256 – 3,000)/1.14³ + (¥123,320 + 29,000 + 74,564)/1.14⁴ NPV = –¥38,569.48

12. If we are trying to decide between two projects that will not be replaced when they wear out, the proper capital budgeting method to use is NPV. Both projects only have costs associated with them, not sales, so we will use these to calculate the NPV of each project. Using the tax shield approach to calculate the OCF, the NPV of System A is:

OCFA = –元 120,000(1 – 0.34) + 0.34(元 430,000/4) OCFA = –元 42,650

NPVA = –元 430,000 – 元 42,650(PVIFA20%,4) NPVA = –元 540,409.53

And the NPV of System B is:

OCFB = –元 80,000(1 – 0.34) + 0.34(元 540,000/6) OCFB = –元 22,200

NPVB = –元 540,000 – 元 22,200(PVIFA20%,6) NPVB = –元 613,826.32

If the system will not be replaced when it wears out, then System A should be chosen, because it has the more positive NPV.

13. If the equipment will be replaced at the end of its useful life, the correct capital budgeting technique is EAC. Using the NPVs we calculated in the previous problem, the EAC for each system is:

EACA = – 元 540,409.53 / (PVIFA20%,4) EACA = –元 208,754.32

EACB = – 元 613,826.32 / (PVIFA20%,6) EACB = –元 184,581.10

If the conveyor belt system will be continually replaced, we should choose System B since it has the more positive NPV.

14. Since we need to calculate the EAC for each machine, sales are irrelevant. EAC only uses the costs of operating the equipment, not the sales. Using the bottom up approach, or net income plus depreciation, method to calculate OCF, we get:

Machine A Machine B

Variable costs –₪3,150,000 –₪2,700,000

Fixed costs –150,000 –100,000

Depreciation –350,000 –500,000

EBT –₪3,650,000 –₪3,300,000

Tax 1,277,500 1,155,000

Net income –₪2,372,500 –₪2,145,000

+ Depreciation 350,000 500,000

OCF –₪2,022,500 –₪1,645,000

The NPV and EAC for Machine A is:

NPVA = –₪2,100,000 – ₪2,022,500(PVIFA10%,6) NPVA = –₪10,908,514.76

EACA = – ₪10,908,514.76 / (PVIFA10%,6) EACA = –₪2,504,675.50

And the NPV and EAC for Machine B is:

NPVB = –₪4,500,000 – 1,645,000(PVIFA10%,9) NPVB = –₪13,973,594.18

EACB = – ₪13,973,594.18 / (PVIFA10%,9) EACB = –₪2,426,382.43

You should choose Machine B since it has a more positive EAC.

15. When we are dealing with nominal cash flows, we must be careful to discount cash flows at the nominal interest rate, and we must discount real cash flows using the real interest rate. Project A’s cash flows are in real terms, so we need to find the real interest rate. Using the Fisher equation, the real interest rate is:

1 + R = (1 + r)(1 + h) 1.15 = (1 + r)(1 + .04) r = .1058 or 10.58%

So, the NPV of Project A’s real cash flows, discounting at the real interest rate, is:

NPV = –40,000 + 20,000 / 1.1058 + 15,000 / 1.1058² + 15,000 / 1.1058³ NPV = 1,448.88

Project B’s cash flow are in nominal terms, so the NPV discount at the nominal interest rate is:

NPV = –50,000 + 10,000 / 1.15 + 20,000 / 1.15² + 40,000 / 1.15³ NPV = 119.17

We should accept Project A if the projects are mutually exclusive since it has the highest NPV.

16. To determine the value of a firm, we can simply find the present value of the firm’s future cash flows. No depreciation is given, so we can assume depreciation is zero. Using the tax shield approach, we can find the present value of the aftertax revenues, and the present value of the aftertax costs. The required return, growth rates, price, and costs are all given in real terms. Subtracting the costs from the revenues will give us the value of the firm’s cash flows. We must calculate the present value of each separately since each is growing at a different rate. First, we will find the present value of the revenues. The revenues in year 1 will be the number of bottles sold, times the price per bottle, or:

Aftertax revenue in year 1 in real terms = (2,000,000 × $1.50)(1 – 0.34) Aftertax revenue in year 1 in real terms = $1,650,000

Revenues will grow at six percent per year in real terms forever. Apply the growing perpetuity formula, we find the present value of the revenues is:

PV of revenues = C1 / (R – g)

PV of revenues = $1,650,000 / (0.10 – 0.06) PV of revenues = $41,250,000

The real aftertax costs in year 1 will be:

Aftertax costs in year 1 in real terms = (2,000,000 × $0.65)(1 – 0.34) Aftertax costs in year 1 in real terms = $858,000

Costs will grow at five percent per year in real terms forever. Applying the growing perpetuity formula, we find the present value of the costs is:

PV of costs = C1 / (R – g)

PV of costs = $858,000 / (0.10 – 0.05) PV of costs = $17,160,000

Now we can find the value of the firm, which is:

Value of the firm = PV of revenues – PV of costs Value of the firm = $41,250,000 – 17,160,000 Value of the firm = $24,090,000

17. To calculate the nominal cash flows, we simple increase each item in the income statement by the inflation rate, except for depreciation. Depreciation is a nominal cash flow, so it does not need to be adjusted for inflation in nominal cash flow analysis. Since the resale value is given in nominal terms as of the end of year 5, it does not need to be adjusted for inflation. Also, no inflation adjustment is needed for either the depreciation charge or the recovery of net working capital since these items are already expressed in nominal terms. Note that an increase in required net working capital is a negative cash flow whereas a decrease in required net working capital is a positive cash flow. The nominal aftertax salvage value is:

Market price $30,000

Tax on sale –10,200

Aftertax salvage value $19,800

Remember, to calculate the taxes paid (or tax credit) on the salvage value, we take the book value minus the market value, times the tax rate, which, in this case, would be:

Taxes on salvage value = (BV – MV)tC

Taxes on salvage value = ($0 – 30,000)(.34) Taxes on salvage value = –$10,200

Now we can find the nominal cash flows each year using the income statement. Doing so, we find:

Year 0 Year 1 Year 2 Year 3 Year 4 Year 5

Sales $200,000 $206,000 $212,180 $218,545 $225,102

Expenses 50,000 51,500 53,045 54,636 56,275

Depreciation 50,000 50,000 50,000 50,000 50,000

EBT $100,000 $104,500 $109,135 $113,909 $118,826

Tax 34,000 35,530 37,106 38,729 40,401

Net income $66,000 $68,970 $72,029 $75,180 $78,425

OCF $116,000 $118,970 $122,029 $125,180 $128,425

Capital spending –$250,000 $19,800

NWC –10,000 10,000

Total cash flow –$260,000 $116,000 $118,970 $122,029 $125,180 $158,225 18. The present value of the company is the present value of the future cash flows generated by the

company. Here we have real cash flows, a real interest rate, and a real growth rate. The cash flows are a growing perpetuity, with a negative growth rate. Using the growing perpetuity equation, the present value of the cash flows are:

PV = C1 / (R – g)

PV = $120,000 / [.11 – (–.07)]

PV = $666,666.67

19. To find the EAC, we first need to calculate the NPV of the incremental cash flows. We will begin with the aftertax salvage value, which is:

Taxes on salvage value = (BV – MV)tC

Taxes on salvage value = (€0 – 10,000)(.34) Taxes on salvage value = –€3,400

Market price €10,000

Tax on sale –3,400

Aftertax salvage value €6,600

Now we can find the operating cash flows. Using the tax shield approach, the operating cash flow each year will be:

OCF = –€5,000(1 – 0.34) + 0.34(€45,000/3) OCF = €1,800

So, the NPV of the cost of the decision to buy is:

NPV = –€45,000 + €1,800(PVIFA12%,3) + (€6,600/1.12³) NPV = –€35,987.95

In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of three years and is discounted at 12 percent, set the NPV equal to a three-year annuity, discounted at 12 percent.

EAC = –€35,987.95 / (PVIFA12%,3) EAC = –€14,979.80

20. We will find the EAC of the EVF first. There are no taxes since the university is tax-exempt, so the maintenance costs are the operating cash flows. The NPV of the decision to buy one EVF is:

NPV = –₩8,000 – ₩2,000(PVIFA14%,4) NPV = –₩13,827.42

In order to calculate the equivalent annual cost, set the NPV of the equipment equal to an annuity with the same economic life. Since the project has an economic life of four years and is discounted at 14 percent, set the NPV equal to a three-year annuity, discounted at 14 percent. So, the EAC per unit is:

EAC = –₩13,827.42 / (PVIFA14%,4) EAC = –₩4,745.64

Since the university must buy 10 of the word processors, the total EAC of the decision to buy the EVF word processor is:

Total EAC = 10(–₩4,745.64) Total EAC = –₩47,456.38

Note, we could have found the total EAC for this decision by multiplying the initial cost by the number of word processors needed, and multiplying the annual maintenance cost of each by the same number. We would have arrived at the same EAC.

We can find the EAC of the AEH word processors using the same method, but we need to include the salvage value as well. There are no taxes on the salvage value since the university is tax-exempt, so the NPV of buying one AEH will be:

NPV = –₩5,000 – ₩2,500(PVIFA14%,3) + (₩500/1.14³) NPV = –₩10,466.59

So, the EAC per machine is:

EAC = –₩10,466.59 / (PVIFA14%,3) EAC = –₩4,508.29

Since the university must buy 11 of the word processors, the total EAC of the decision to buy the AEH word processor is:

Total EAC = 11(–₩4,508.29) Total EAC = –₩49,591.21

The university should buy the EVF word processors since the EAC is lower. Notice that the EAC of the AEH is lower on a per machine basis, but because the university needs more of these word processors, the total EAC is higher.