0. 10 Capital Investment Decisions Prof. Liu Bin (Ph. D)
Dalian Maritime University

1. Key Skills
1. determine the relevant cash flows for various types of proposed investments
2. compute depreciation expense for tax purposes
3. various methods for computing operating cash flow

2. Key Concept 1.Sunk costs – costs that have accrued in the past
2.Opportunity costs – costs of lost options
3.Side effects
Positive side effects – benefits to other projects
Negative side effects – costs to other projects
4.Changes in net working capital
5.Financing costs
6.Taxes
With each of these types of cash flows, you should ask the class the question on the previous slide so that they can start to determine if the cash flows are relevant.
Sunk costs – our government provides ample examples of inappropriately including sunk costs in their capital allocation decisions.
Opportunity costs – the classic example of an opportunity cost is the use of land or plant that is already owned. It is important to point out that this is not “free.” At the very least we could sell the land; consequently if we choose to use it, we cost ourselves the selling price of the asset.
A good example of a positive side effect is when you will establish a new distribution system with this project that can be used for existing or future projects. The benefit provided to those projects needs to be considered.
The most common negative side effect is erosion or cannibalism, where the introduction of a new product will reduce the sales of existing, similar products. A good real-world example is McDonald’s introduction of the Arch Deluxe sandwich. Instead of generating all new sales, it primarily reduced sales in the Big Mac and the Quarter Pounder.
It is important to consider changes in NWC. We need to remember that operating cash flow derived from the income statement assumes all sales are cash sales and that the COGS was actually paid in cash during that period. By looking at changes in NWC specifically, we can adjust for the difference in cash flow that results from accounting conventions. Most projects will require an increase in NWC initially as we build inventory and receivables. Then we recover NWC at the end of the project.
We do not include financing costs. Students often have difficulty understanding why when it appears that we will only raise capital if we take the project. It is important to point out that because of economies of scale, companies generally do not finance individual projects. Instead, they finance the entire portfolio of projects at one time. The other reason has to do with maintaining a target capital structure over time, but not necessarily each year. Finally, financing cost is included in the required return and thus including the cash flows would be double counting.
Taxes will change as the firm’s taxable income changes. Consequently, we have to consider cash flows on an after-tax basis.

3. Key Expressions
7. Sale price: product price sold to by seller to buyer.
8. Depreciation:
9. Tax on sale:
10. Net working capital
11. Terminal cash flow
12. Cash flow after tax
13. MACRS: modified accelerated cost recovery system
14. Installed cost
15. Accumulated depreciation
16. Book value

4. Key Words 17. capital gain 18. Recaptured depreciation
19.After tax proceeds from sale of old
20.Proceeds from sale of old equipment

5. Chapter Outline 1. Pro Forma Financial Statements and
Project Cash Flows
Project Cash Inflow and cash outflow
2. Project Incremental Cash Flows
3. Definitions of Operating Cash Flow
4. Some Special Cases of Cash Flow Analysis

6. Relevant Cash Flows
The cash flows that should be included in a capital budgeting analysis are those that will only occur if the project is accepted
These cash flows are called incremental cash flows
The stand-alone principle allows us to analyze each project in isolation from the firm simply by focusing on incremental cash flows

7. Pro Forma Statements and Cash Flow
Capital budgeting relies heavily on pro forma accounting statements, particularly income statements
Computing cash flows – refresher
1. Operating Cash Flow (OCF) = EBIT + depreciation – taxes
2. OCF = Net income + depreciation when there is no interest expense
3. Cash Flow From Assets (CFFA) = OCF – net capital spending (NCS) – changes in NWC
Operating cash flow – students often have to go back to the income statement to see that the two definitions of operating cash flow are equivalent when there is no interest expense.

8. Case1 Pro Forma Income Statement
Sales (50,000 units at $4.00/unit)
$200,000
Variable Costs ($2.50/unit)
125,000
Gross profit
$ 75,000
Fixed costs
12,000
Depreciation ($90,000 / 3)
30,000
EBIT
$ 33,000
Taxes (34%)
11,220
Net Income
$ 21,780

9. OCF Remind: Operating Cash Flow (OCF) = EBIT + depreciation – taxes
OCF = Depreciation ($90,000 / 3)30,000+ Net Income$ 21,780=51 780

10. Projected Capital Requirements
Year 1 2 3
NWC
$20,000
NFA
90,000
60,000
30,000
Total
$110,000
$80,000
$50,000
Ask the students why net fixed assets is decreasing each year. It is important that they understand why this is happening when they go to compute the net capital spending in the next slide.

11. Projected Total Cash Flows
Year 1 2 3
OCF
$51,780
Change in NWC
-$20,000
20,000
NCS
-$90,000
CFFA
-$110,00
$71,780
OCF = EBIT + depreciation – taxes = 33, ,000 – 11,220 = 51,780; or
OCF = NI + depreciation = 21, ,000 = 51,780
Note that in the Table in the book, the negative signs have already been carried throughout the table so that the columns can just be added. Ultimately, students seem to do better with this format even though the CFFA equation says to subtract the changes in NWC and net capital spending.
Change in NWC = We have a net investment in NWC in year 0 of 20,000; we get the investment back at the end of the project when we sell our inventory, collect on our receivables and pay off our payables. Students often forget that we get the investment back at the end.
Capital Spending – remember that Net capital spending = change in net fixed assets + depreciation. So in year one NCS = (60,000 – 90,000) + 30,000 = 0; The same is true for the other years.

12. Making The Decision
Now that we have the cash flows, we can apply the techniques that we learned in chapter 9
Enter the cash flows into the calculator and compute NPV and IRR
CF0 = -110,000; C01 = 51,780; F01 = 2; C02 = 71,780
NPV; I = 20; CPT NPV = 10,648
CPT IRR = 25.8%
Should we accept or reject the project?
You can also use the formulas to compute NPV and IRR, just remember that the IRR computation is trial and error.
Click on the excel icon to go to an embedded spreadsheet that illustrates how the pro formas and cash flows can be set-up and computes the NPV and IRR.

13. More on NWC Why do we have to consider changes in NWC separately?
GAAP requires that sales be recorded on the income statement when made, not when cash is received
GAAP also requires that we record cost of goods sold when the corresponding sales are made, whether we have actually paid our suppliers yet
Finally, we have to buy inventory to support sales although we haven’t collected cash yet
The first two items mean that our operating cash flow does not include the impact of accounts receivable and accounts payable on cash flow. The third item is very much like the purchase of fixed assets. We have to buy the assets (have the cash outflow) before we can generate sales.
By looking at changes in NWC, we can incorporate the increased investment in receivables and inventory that are necessary to support additional sales. Because we look at changes in NWC, and not just current assets, we also incorporate the increase in our payable accounts that partially pays for the investment in inventory and receivables.

14. Depreciation
The depreciation expense used for capital budgeting should be the depreciation schedule required by the IRS for tax purposes
Depreciation itself is a non-cash expense; consequently, it is only relevant because it affects taxes
Depreciation tax shield = DT
D = depreciation expense
T = marginal tax rate

15. Computing Depreciation
Straight-line depreciation
D = (Initial cost – salvage) / number of years
Very few assets are depreciated straight-line for tax purposes
MACRS
Need to know which asset class is appropriate for tax purposes
Multiply percentage given in table by the initial cost
Depreciate to zero
Mid-year convention
The MACRS percentages are given in Table 10.7 on page 306.

17. After-tax Salvage
If the salvage value is different from the book value of the asset, then there is a tax effect
Book value = initial cost – accumulated depreciation
After-tax salvage = salvage – T(salvage – book value)

18. Example1: Depreciation and After-tax Salvage
You purchase equipment for $100,000 and it costs $10,000 to have it delivered and installed. Based on past information, you believe that you can sell the equipment for $17,000 when you are done with it in 6 years. The company’s marginal tax rate is 40%. What is the depreciation expense each year and the after-tax salvage in year 6 for each of the following situations?

19. Example1: Straight-line Depreciation
Suppose the appropriate depreciation schedule is straight-line
D = (110,000 – 17,000) / 6 = 15,500 every year for 6 years
BV in year 6 = 110,000 – 6(15,500) = 17,000
After-tax salvage = 17, (17,000 – 17,000) = 17,000

20. Example: Three-year MACRS
MACRS percent D 1
.3333
.3333(110,000) = 36,663 2
.4444
.4444(110,000) = 48,884 3
.1482
.1482(110,000) = 16,302 4
.0741
.0741(110,000) = 8,151
BV in year 6 = 110,000 – 36,663 – 48,884 – 16,302 – 8,151 = 0
After-tax salvage = 17, (17,000 – 0) = $10,200
Note that with MACRS you do not subtract the expected salvage from the initial cost.
Also note that the MACRS % is multiplied by the initial cost every year. For some reason, students want to multiply by the book value.

21. Example: 7-Year MACRS
Year
MACRS Percent D 1
.1429
.1429(110,000) = 15,719 2
.2449
.2449(110,000) = 26,939 3
.1749
.1749(110,000) = 19,239 4
.1249
.1249(110,000) = 13,739 5
.0893
.0893(110,000) = 9,823 6
BV in year 6 = 110,000 – 15,719 – 26,939 – 19,239 – 13,739 – 9,823 – 9,823 = 14,718
After-tax salvage = 17, (17,000 – 14,718) = 16,087.20

22. Example2: Replacement Problem
Original Machine
Initial cost = 100,000
Annual depreciation = 9000
Purchased 5 years ago
Book Value = 55,000
Salvage today = 65,000
Salvage in 5 years = 10,000
New Machine
Initial cost = 150,000
5-year life
Salvage in 5 years = 0
Cost savings = 50,000 per year
3-year MACRS depreciation
Required return = 10%
Tax rate = 40%

23. Replacement Problem – Computing Cash Flows
Remember that we are interested in incremental cash flows
If we buy the new machine, then we will sell the old machine
What are the cash flow consequences of selling the old machine today instead of in 5 years?

24. Replacement Problem – Pro Forma Income Statements
Year 1 2 3 4 5
Cost Savings
50,000
Depr.
New
49,500
67,500
22,500
10,500
Old
9,000
Increm.
40,500
58,500
13,500
1,500
(9,000)
EBIT
9,500
(8,500)
36,500
48,500
59,000
Taxes
3,800
(3,400)
14,600
19,400
23,600 NI
5,700
(5,100)
21,900
29,100
35,400

25. Replacement Problem – Incremental Net Capital Spending
Year 0
Cost of new machine = 150,000 (outflow)
After-tax salvage on old machine = 65, (65,000 – 55,000) = 61,000 (inflow)
Incremental net capital spending = 150,000 – 61,000 = 89,000 (outflow)
Year 5
After-tax salvage on old machine = 10, (10,000 – 10,000) = 10,000 (outflow because we no longer receive this)
The year 5 cash flow is the most difficult for students to grasp. It is important to point out that we are looking for ALL changes in cash flow associated with selling the machine today instead of in 5 years. If we do not sell the machine today, then we will have after-tax salvage of 10,000 in 5 years. Since we do sell the machine today, we LOSE the 10,000 cash flow in 5 years.

26. Replacement Problem – Cash Flow From Assets
Year 1 2 3 4 5
OCF
46,200
53,400
35,400
30,600
26,400
NCS
-89,000
-10,000
 In NWC
CFFA
16,400
The negative signs in the CFFA equation were once again carried through the table. That way outflows are in the table as negative and inflows are positive.

27. Replacement Problem – Analyzing the Cash Flows
Now that we have the cash flows, we can compute the NPV and IRR
Enter the cash flows
Compute NPV = 54,812.10
Compute IRR = 36.28%
Should the company replace the equipment?

28. Example 3:Book value and initial investment
An enterprises is considering the purchase of a new machine tool to replace the current machine. The new cost $75,000 and requires $5,000 in installation costs. It will be depreciated under MACRS using a 5 year recovery period. The old machine was purchased for an installed costs of $50,000 4 years ago; it was being depreciated under MARS using a 5 year recovery period. The old machine tool can be sold today for $55,000 net of any removal or cleanup costs. As a result of the proposed replacement, firm’s investment in net working capital is expected to increase by $15,000. the firm pays taxes at a rate of 40 percent on both ordinary income and capital gains.
a. Calculate the book value of the old machine tool.
b. Determine the taxes, if any, attributable to the sale of the old machine tool.
c. Find the initial investment associated with the proposed equipment replacement
An enterprises is considering the purchase of a new machine tool to replace the current machine. The new cost $75,000 and requires $5,000 in installation costs. It will be depreciated under MACRS using a 5 year recovery period. The old machine was purchased for an installed costs of $50,000 4 years ago; it was being depreciated under MARS using a 5 year recovery period. The old machine tool can be sold today for $55,000 net of any removal or cleanup costs. As a result of the proposed replacement, firm’s investment in net working capital is expected to increase by $15,000. the firm pays taxes at a rate of 40 percent on both ordinary income and capital gains.
a. Calculate the book value of the old machine tool.
b. Determine the taxes, if any, attributable to the sale of the old machine tool.
c. Find the intial investment associated with the proposed equipment replacement

29. Example 3
LG4 ST 8-1 账面价值、税额和初始投资 Irin公司正在考虑购置一台新船舶来代替正在使用的船舶。新船舶成本$75,000，需要$5,000的安装成本，将采用加速折旧法计提折旧，折旧期限为5年。旧船舶是4年前购置的，加上安装成本价值$50,000，该船舶也采用加速折旧法计提折旧，折旧期5年，现正处于折旧期中。出售旧船舶，除去拆卸和清理成本，可以得到$55,000净利，流动资金增加$15,000。公司一般收入与资本收益的税率都是40%。
a．计算旧资产的账面价值。
b．确定归因于销售旧资产的税额。
c．找出与计划的船舶替代品相关的初始投资。

30. Accumulated depreciation=$50,000 × （0.20+0.32+0.19+0.12）
Book Value ST 8-1
Installed cost=$50,000
Accumulated depreciation=$50,000 × （ ）
=$50,000 × 0.83=$41,500
Book value=Installed cost- Accumulated depreciation
Book value=$50,000－$41,500=$8,500
gaap tax rule: sold at book value,no tax; above book value,the difference pays tax; below book value,tax ?

31. Taxes on sale of old machine
capital gain=sale price－initial purchase price
=$55,000－$50,000=$5,000
Recaptured depreciation=initial purchase price －book value
=$50,000-$8,500=$41,500
taxes=（0.40×$5,000）+（0.40×$41,500）
=$2,000+$16,600=$18,600
gaap tax rule: sold at book value,no tax; above book value,the difference pays tax; below book value,tax ?

32. Initial Investment Installed cost of new equipment
＋Installation cost ,000
total installed cost-New $80,000
－After tax proceeds from sale of old
Proceeds from sale of old equipment $55,000
－Taxes on sale of old equipment 18,600
Total after tax proceeds -old ,400
＋Change in net working capital ,000
Initial Investment $ 58,600

33. Example4:Initial and terminal cash flow
A machine currently in use was originally purchased 2 years ago for $40,000. the machine is being depreciated under MACRS using a 5 year recovery period; it has 3 years of usable life remaining. The current machine can be sold today to net $42,000 after removal and cleanup costs. A new machine, using a 3 year macrs recovery period, can be purchased at a price of $140,000. it required $10,000 to install and has a 3 year usable life. If the new machine were acquired, the investment in accounts receivable would be expected to rise by $10,000. the inventory investment will increase by 25,000 and accounts payable will increase by $15,000. profits before depreciation and taxes are expected to be 70,000 for each of the next 3 years with the old machine and $120,000 in the first year and $130,000 in the second and third years with the new machine. At the end of 3 years, the market value of the old machine will equal zero, but the new machine could be sold to net $35,000 before taxes. Both ordinary corporate income and capital gains are subject a 40 percent tax.
Determine the initial investment associated with the proposed replacement decision.
Calculate the incremental operating cash inflows for years 1 to 4 associate with the proposed replacement
Calculate the terminl cash flow associated with the proposed replacement decision.
Depict on a time line the relevant cash flows found in
A machine currently in use was originally purchased 2 years ago for $40,000. the machine is being depreciated under MACRS using a 5 year recovery period; it has 3 years of usable life remaining. The current machine can be sold today to net $42,000 after removal and cleanup costs. A new machine, using a 3 year macrs recovery period, can be purchased at a price of $140,000. it required $10,000 to install and has a 3 year usable life. If the new machine were acquired, the investment in accounts receivable would be expected to rise by $10,000. the inventory investment will increase by 25,000 and accounts payable will increase by $15,000. profits before depreciation and taxes are expected to be 70,000 for each of the next 3 years with the old machine and $120,000 in the first year and $130,000 in the second and third years with the new machine. At the end of 3 years, the market value of the old machine will equal zero, but the new machine could be sold to net $35,000 before taxes. Both ordinary corporate income and capital gains are subject a 40 percent tax.
Determine the initial investment associated with the proposed replacement decision.
Calculate the incremental operating cash inflows for years 1 to 4 associate with the proposed replacement
Calculate the terminl cash flow associated with the proposed replacement decision.
Depict on a time line the relevant cash flows found in

34. 确定增量现金流
目前使用的船舶最初是2年前以$40,000购入的，折旧期限为5年，还剩下3年的使用期限。现在出售该船舶可以得到$42,000。一台新船舶，购置价格为$140,000，采用加速折旧法计提折旧，折旧期限为3年，需要$10,000的安装成本，还有3年的使用期限。如果购置新船舶，在应收账款里增加$10,000，存货期增加$25,000，应付账款将增加$15,000。公司预期使用旧船舶在剩下3年的使用期内，每年得到$70,000的折旧和税前利润。投入新船舶后，预期第1年得到$120,000的折旧和税前利润，第2年和第3年得到$130,000的折旧和税前利润。3年使用期之后，旧船舶的市场价值将等于零，但出售新船舶可以获得$35，000的税前净利润。公司一般收入和资本收益的税率为40%。（91页表3.6包括所使用加速折旧法的折旧百分率）
A machine currently in use was originally purchased 2 years ago for $40,000. the machine is being depreciated under MACRS using a 5 year recovery period; it has 3 years of usable life remaining. The current machine can be sold today to net $42,000 after removal and cleanup costs. A new machine, using a 3 year macrs recovery period, can be purchased at a price of $140,000. it required $10,000 to install and has a 3 year usable life. If the new machine were acquired, the investment in accounts receivable would be expected to rise by $10,000. the inventory investment will increase by 25,000 and accounts payable will increase by $15,000. profits before depreciation and taxes are expected to be 70,000 for each of the next 3 years with the old machine and $120,000 in the first year and $130,000 in the second and third years with the new machine. At the end of 3 years, the market value of the old machine will equal zero, but the new machine could be sold to net $35,000 before taxes. Both ordinary corporate income and capital gains are subject a 40 percent tax.
Determine the initial investment associated with the proposed replacement decision.
Calculate the incremental operating cash inflows for years 1 to 4 associate with the proposed replacement
Calculate the terminl cash flow associated with the proposed replacement decision.
Depict on a time line the relevant cash flows found in

35. Initial investment a．Initial Investment
Installed cost of new equipment
cost of new machine $140,000
＋Installation costs ,000
Total installed cost-new（折旧价值） $150,000
－After tax proceeds from sale of old machine
Proceeds from sale of old machine 42,000
－Taxes on sale of old machine ,120
Tatal after tax proceeds-old ,880
+ Change in net working capital ,000
initial investment $ 137,120

36. Change in net working capital
1Book value of old machine=$40,000－［（ ） ×$40,000］
=$40,000－（0.52×$40,000）
=$40,000－$20,800=$19,200
Capital gain=$42,000－$40,000=$2,000
Recaptured depreciation=$40,000－$19,200=$20.800
Tax=（0.40×$2,000）＋（0.40×$20.800）=$800＋ $8,320=$9,120
2Change in net working capital=$10,000＋$25,000－ $15,000
=$35,000－$15,000=$20,000
the investment in accounts receivable would be expected to rise by $10,000. the inventory investment will increase by 25,000 and accounts payable will increase by $15,000.

37. Incremental operating cash inflows
Calculation of depreciation expense for new machine
MACRS depreciation Depreciation
Cost ［（1）×（2）］
Year （1） （2） （3）
With new machine
$150, % $ 49,500
, ,500
, ,500 ,
Tatol % $150,000a

38. Calculation of depreciation expense for old machine
  MACRS depreciation Depreciation
cost ［（1）×（2）］
Year （1） （2） （3）
$40, %(Year 3 depreciation) $ 7,600
, （ Year 4 depreciation） 4,800
, (Year 5 depreciation) 4,800
, (Year 6 depreciation) 2,000
total $19,200a
a$19,200表示旧船舶第2年末的账面价值，在a部分已经计算过。

39. Calculation of operating cash inflows
Year
With new machine
Profits before dep. And taxesa $120, $130, $130, $ 0
- Depreciationb , , , ,500
Net profits before taxes $ 70, $ 62, $107, $10,500
- Taxes（ 40%） , , , ,200
Net profits after tax$ 42, $ 37, $ 64, ,300
+ Depreciation , , , ,500
Operating cash inlows
$ 91, $105, $ 87, $ 4,200

40. Calculation of operating cash inlows（Old machine）
Profits before depr.and taxesa $ 70, $ 70, $ 70, $ 0
- Depreciationc , , , ,000
Net profits before taxes $ 62, $ 65, $ 65, $ 2,000
- Tax（ Rate 40%） , , ,
Net profits after taxes $ 37, $ 39, $ 39, $ 1,200
+ Depreciation , , , ,000
Operating cash inflows $ 45, $ 43, $ 43,920 $ 800

41. Incremental operating cash inflows
Incremental（relevant）
New machinea Old machineb （1）-（2）］
Year （1） （2） （3）
$ 91, $ $ 46,760
, , ,080
, , ,080
, ,400
a来自前面使用两种船舶的表格中最后一行。

42. c．Terminal cash flow(end of year 3）
After tax proceeds from sale of new machine
Proceeds from sale of new machine $35,000
－Tax on sale of new machine ,800
Total after tax proceeds—New $25,200
－After tax proceeds from sale of old machine
Proceeds from sale of old machine $ 0
-Tax on sale of old machine $800
Total after tax proceeds —old
＋Change in net working capital $ 20,000
Terminal cash flow $44,400

43. Book value of new at end of yr 3
1Book value of new machine at end of year 3
=$150,000-［( )×$150,000］=$150,000-(0.93×$150,000)
=$150,000-$139,500=$10,500
Tax on sale=0.40×($35,000 sale price-$10,500 book value)
=0.40×$24,500=$9,800
2Book value of old machine at end of year 3
=$40,000-［( )×$40,000］=$40,000-(0.95×$40,000)
=$40,000-$38,000=$2,000
Tax on sale=0.40×($0 sale price -$2,000 book value)
=0.40×(-$2,000)=-$800（$800 tax saving）

44. End of the year Intial investment:$137,120
First year incremental cf:$46,760
Second year incremental cf:$61,080
Third year incremental cf:$90,880
90,880=44,400+43,080+3,400 terminal cash flow
第4年增加的经营活动现金流$3,400没有直接全部包括在内，它是在用来计算第3年末船舶销售税额的账面价值中反映的，因此，它只是期末现金流的一部分。Quiz: solve for npt (12%) and irr?

45. Quick Quiz
How do we determine if cash flows are relevant to the capital budgeting decision?
What are the different methods for computing operating cash flow and when are they important?
What is the basic process for finding the bid price?
What is equivalent annual cost and when should it be used?

46. 10
End of Chapter

47. INTEREST RATE and DETERMINANTS
k = k* + IRP + DRP + MP + LP
k = the nominal or observed rate
k* = the real risk--free rate of interest,
IRP = inflation-risk premium.
DRP = default-risk premium
MP = maturity
LP = liquidity premium