1. Making capital investment decisions
Chapter eight
Making capital investment decisions

2. Learning objectives
LO8.1 Understand how to determine the relevant cash flows for a proposed project. LO8.2 Understand how to determine if a project is acceptable. LO8.3 Understand how to set a bid price for a project. LO8.4 Understand how to evaluate the equivalent annual cost of a project.

3. Chapter organisation Project cash flows: a first look
Incremental cash flows
Project cash flows
More on project cash flows
Some special cases of discounted cash flow analysis
Summary and conclusions

4. Project cash flows
The incremental cash flows for project evaluation consist of any and all changes in the firm’s future cash flows that are a direct consequence of undertaking the project.
The stand-alone principle is the evaluation of a project based on the project’s incremental cash flows.
- It should be strongly emphasised that a project’s cash flows imply changes in future firm cash flows and, therefore, in the firm’s future financial statements.
- You might find it useful to clearly delineate the link between the stand-alone principle and the concept of value additivity. By viewing projects as 'mini-firms', we imply that the firm as a whole constitutes a portfolio of mini-firms. As a result, the value of the firm equals the combined value of its components. This is the essence of value additivity, and it is assumed to hold generally whether we are discussing the cash flows in a simple time-value problem, the value of a project or the value of the firm. Note also that an understanding of this concept paves the way for the analysis of mergers and acquisitions. For a merger to ‘create value’, the value additivity principle must be violated. (Violations take the form of production efficiencies, economies of scale, etc.) Perhaps a key value of this approach is that it places the burden of proof on those proposing the merger, just as the capital budgeting process places the burden of proof on those proposing investment in the project.

5. Types of cash flows
Sunk costs  a cost that has already been incurred and cannot be removed  incremental cash flow.
Opportunity costs  the most valuable alternative that is given up if a particular investment is undertaken = incremental cash flow.
Side effects  erosion  the cash flows of a new project that come at the expense of a firm’s existing projects = incremental cash flow.
- 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.
- Personal examples of sunk costs often help students understand the issue. Ask the students to consider a hypothetical situation in which a student purchased a computer for $1 500 while in high school. A better computer is now available that also costs $ The relevant factors to the decision are what benefits would be provided by the better computer to justify the purchase price. The cost of the original computer is irrelevant.
- 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.
continued

6. Types of cash flows
Financing costs  the interest rate used to discount the cash flows reflects, in part, the financing costs of the project  incremental cash flow.
An investment of the firm in the project’s net working capital represents an additional cost of undertaking the investment.
Always use after-tax incremental cash flow, since taxes are definitely a cash flow.
- 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, thus, including the financing-related 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.

7. Investment evaluation
Step 1  Calculate the tax effect of the decision.
Step 2  Calculate the cash flows relevant to the decision.
Step 3  Discount the cash flows to make the decision.
- Steps 1 and 2 are in practice calculated simultaneously, however, in breaking these steps out it helps to explain to students that items included in the tax calculation, such as depreciation, are not included in cash flows of the project.
- Students sometimes become disheartened at what they perceive as complexities in the various capital budgeting calculations. You may find it useful to remind them that, in reality, setting up timelines and performing calculations are typically the least burdensome portions of the task. Rather, the difficulties arise principally in two areas: (1) generating good investment projects, and (2) developing reliable cash flow estimates for these projects.

8. Example—Investment evaluation
Purchase price $
Salvage value $1 000 at end of Year 3.
Net cash flows: Year 1 $31 000
Year 2 $25 000
Year 3 $
Tax rate is 30%.
Depreciation 20%, reducing balance.
Required rate of return 12%.

9. Solution—Depreciation schedule
- It should be made clear to students that the depreciation expense used for capital budgeting should be the depreciation schedule required by the ATO for tax purposes.
- Obviously, the most important point in this section is that depreciation itself is a non-cash expense; consequently, it is only relevant because it affects taxes. As such, the ability to expense the asset over its useful life (depreciation) can save the firm a great deal of money.
- Likewise, an ATO approved depreciation method that permits the firm to expense more of the asset, early in its useful life, would be preferred (time value of money). For example, the small business new depreciation rules that came into effect in July The rules permit an instant asset write-off of $6500 (which used to be $1000). Small businesses can also claim an accelerated initial deduction for motor vehicles acquired in 2012–13 and onwards. (See DOI

10. Solution—Taxable income
Year 0
Year 1
Year 2
Year 3
Net cash flows
31 000
25 000
20 000
Depreciation
(8 400)
(6 720)
(5 376)
Loss on sale
(20 504)
Taxable income
$22 600
$18 280
$(5 880)
- For the purposes of this analysis, the difference between the carrying value of the asset at the end of 3 years, and the salvage value, is included. This results in the negative taxable income of $5 880 in year 3.
- The negative taxable income converts to a positive cash flow on the assumption that the firm will have tax liabilities in other areas of operation. Therefore, the firm will claim this tax loss against other tax income and achieve a net reduction of its total tax bill.

11. Solution—Cash flows Year 0 Year 1 Year 2 Year 3 Tax paid (6 780)
(5 484)
1 764
Net cash flow
31 000
25 000
20 000
Salvage value
1 000
Outlay
(42 000)
Cash flow
$(42 000)
$24 220
$19 516
$22 764
- Students may get confused by the positive tax paid in year 3. It may be worthwhile explaining to students that the taxable loss in year 3 calculated previously results in this tax credit.
We are assuming in this case that the firm has tax liabilities in other areas of its operation. (This is not the only investment project the firm is undertaking.)
Alternatively, the firm can carry forward its tax losses, apply them to future taxable income and consequently reduce its total tax payment.

12. Solution—NPV and decision
Year 0
Year 1
Year 2
Year 3
Cash flow
(42 000)
24 220
19 516
22 764
Discount 1
0.8929
0.7972
0.7118
PV cash flow
($42 000)
$21 626
$15 558
$16 203
NPV
$11 387
Decision: NPV > 0, therefore, ACCEPT.
- You can also use the formulas to compute the IRR; just remember the IRR computation is trial and error.
- Click on the Excel icon to go to an embedded spreadsheet that illustrates how the calculations and cash flows can be set-up. It also computes the NPV and IRR.

13. Interest
As the project’s NPV is positive, the cash flows from the investment will cover interest costs (as long as the interest cost is less than the required rate of return).
Interest costs should not, therefore, be included as an explicit cash flow.
Interest costs are included in the required rate of return (discount rate) used to evaluate the project.
- Some students may question if we are ignoring interest, since it is clearly a cash outflow. It should be strongly emphasised that we do not ignore interest expense (or any other financing expense, for that matter); rather, we are only evaluating asset-related cash flows. It should be stressed that interest expense is a financing cost, not an operating cost.

14. Depreciation
The depreciation expense used for capital budgeting should be the depreciation schedule required for tax purposes.
Depreciation is a non-cash expense; consequently, it is only relevant because it affects taxes.
- In Australia (in 2013) the marginal tax rate for incorporated entities (companies) is 30%.
The tax shield on deprecation can save a firm thousands of dollars (or more in the case of the energy and resources industry. In 2006 the rate of declining balance of depreciation increased from 150% to 200%).
continued

15. Depreciation There are two methods of depreciation:
prime cost (straight-line method in accounting)
diminishing value (reducing balance method in accounting)
Depreciation tax shield = DT
where D = depreciation expense
T = marginal tax rate.
- In Australia (in 2013) the marginal tax rate for incorporated entities (companies) is 30%.
The tax shield on deprecation can save a firm thousands of dollars (or more in the case of the energy and resources industry. In 2006 the rate of declining balance of depreciation increased from 150% to 200%).

16. Disposal of assets
If the salvage value > book value, a gain is made on disposal. This gain is subject to tax (excess depreciation in previous periods).
If the salvage value < book value, the ensuing loss on disposal is a tax deduction (insufficient depreciation in previous periods).

17. Capital gains tax
Capital gains made on the sale of assets such as rental property are subject to taxation.
For taxation purposes, the calculation of a capital gain is complicated and depends upon whether the seller is an individual or an entity, such as a company or trust.
Capital losses are not a tax deduction but can be offset against future capital gains.
- The taxable capital gain is a function of the selling price less other costs added to the purchase price. These other costs include acquisition costs, disposal costs, improvements and additions and together they reduce the quantity of gain made on the asset’s sale.

18. Inflation
When a project is being evaluated, anticipated inflation would be reflected in the estimates of the future cash flows and the interest rate used as the discount rate in the analysis.
As a result, there will be no distortion to the analysis by not identifying inflation specifically.
- In Australia, the RBA has a target range for inflation of between 2% and 3% over the course of the economic cycle. It would be an interesting discussion with students to identify the appropriate inflation estimate for a capital project. Would this estimate change depending on the inputs to the project? Would this estimate vary for a short-lived project as against a long-lived project?
Within the range the RBA sets for inflation it can be considered a benign influence on an investment project.
However, if inflation breaks out of the 2–3% zone then it effectively becomes an additional risk factor that has to be priced.

19. Incremental form of analysis
The description ‘incremental’ is often replaced by ‘marginal’.
The advantage of using a marginal form of analysis is that there will only be one calculation and not two.
By using a marginal form we are implicitly analysing one option: that is, to do nothing.
The sign of the NPV tells us whether or not it is sensible to change.
- Students may have difficulty in understanding what is meant by 'incremental'. The example following in these slides is a good way of explaining that we are comparing two alternatives, but only looking at either the increased production/revenues, or decreased costs following a capital investment.
Ultimately the question boils down to 'what difference will it make if we do, or if we don’t go ahead with this project?'

20. Example—Incremental cash flows
A firm is currently considering replacing a machine purchased two years ago, with an original estimated useful life of five years. The replacement machine has an economic life of three years. Other relevant data is summarised below:
Existing machine
New machine
Initial cost $ $
Annual revenues $ $
Annual costs
$60 000
$70 000
Annual depreciation
$48 000 $
Salvage value
$80 000
(Now)
(End year 3)
Tax rate
30%
Required rate of return
10%

21. Solution—Taxable income
Year 0
Year 1
Year 2
Year 3
Increased revenues
50 000
Increased costs
(10 000)
Dep’n existing
48 000
Dep’n new
( )
Loss on sale
(existing)
(64 000)
Gain on sale (new)
Taxable income
$(64 000)
$(32 000)
$68 000
We add back the yearly depreciation of the existing piece—because if we go with the new machine the old one would have been disposed of and would no longer be depreciated. It is depreciation saved (+).
Same logic: if we go with the new machine, it will be the one we do depreciate—depreciation expensed (–).
The effect of including both the positive and the negative depreciation in the NPV is that they net out.
- Students may not understand why there is a loss on sale of the existing piece of machinery: As the machinery is only 2 years old, its carrying value is calculated as 240k – 2*(48k) = 144k
144k – 80k (salvage value) = 64k loss on sale.
- The gain on sale is also calculated in a similar manner.

22. Solution—Cash flows Year 0 Year 1 Year 2 Year 3 Tax 19 200 9 600
Year 0
Year 1
Year 2
Year 3
Tax
19 200
9 600
(20 400)
Increased revenues
50 000
Increased costs
(10 000)
Salvage values
80 000
Outlay
( )
Cash flow
$( )
$49 600 $

23. Solution—NPV and decision
Year 0
Year 1
Year 2
Year 3
Cash flow
( )
49 600
Discount 1
0.9091
0.8264
0.7513
PV of cash flow
$( )
$45 091
$40 989 $
NPV
($54 212)
Decision: NPV < 0, therefore, REJECT.
IRR = –0.1898%

24. A note on cash flows
Cash flows do not always conveniently occur at the end of the period.
Taking revenue at the period end is a conservative approach to evaluation.
If the facts make it necessary to take cash flows as occurring at the beginning of the period, this only requires a minor adjustment to the analysis.
The period examined could be yearly, monthly or even weekly. If so, the discount rate must match the period (e.g. a weekly analysis needs a weekly rate).
In practice, very conservative assumptions around cash flows are used. These assume that all cash out flows occur at the beginning of each period, and all cash in flows occur at the end of each period.

25. Setting the bid price
How to set the lowest price that can be profitably charged.
Cash outflows are given.
Determine cash inflows that result in zero NPV at the required rate of return.
From cash inflows, calculate sales revenue and price per unit.

26. Example—Setting the bid price
Consider the following information:
A local distributor has requested bid for 5 trucks each year for the next 4 years.
You can buy a truck for $
Need to lease a factory space for $ per year.
Labour and material costs are $ per year.
Requires $ in fixed assets (initial outlay) with expected salvage of $5 000 at the end of the project (depreciate straight-line).
Tax rate = 30%
Required return = 20%
- Click on the worksheet to see the solution to the problem.
- The revenue is set so that it provides the required return of 15% given the number of units sold. The inputs can be changed and the spreadsheet resolved to acquire the required revenue to obtain the 15% return.
continued

27. Example—Setting the bid price
Solution:
Step 1: Find the net initial outlay
Step 2: Find the cash inflows (CFs) over the life of the project that makes NPV zero.
Fixed assets
72,000.00
Less the PV of after tax salvage [5 000(1-0.3)/(1+0.2)4
1,687.89
Net Initial investment
70,312.11
- Click on the worksheet to see the solution to the problem.
- The revenue is set so that it provides the required return of 15% given the number of units sold. The inputs can be changed and the spreadsheet resolved to acquire the required revenue to obtain the 15% return.
continued

28. Example—Setting the bid price
Assuming that the CF is the same for each year and that it occur at the end of each year, we can write:
- Click on the worksheet to see the solution to the problem.
- The revenue is set so that it provides the required return of 15% given the number of units sold. The inputs can be changed and the spreadsheet resolved to acquire the required revenue to obtain the 15% return.
continued

29. Example—Setting the bid price
Step 3: Find the sale price that gives a cash inflow of $ per year.
Cash inflow = Profit + Depreciation
$ = Profit + ($72 000/4)
Profit = $ − $18 000
= $9 161
We know:
Profit = (Sales − Costs − Depreciation)(1 − TC)
Sales = $9 161/ $ $18 000
= $
Sales per truck = $ / 5
= $30 218
- Click on the worksheet to see the solution to the problem.
- The revenue is set so that it provides the required return of 15% given the number of units sold. The inputs can be changed and the spreadsheet resolved to acquire the required revenue to obtain the 15% return.

30. Setting the option value
A buy option is an arrangement that gives the holder the right to buy an asset at a fixed price sometime in the future.
Option value =
Asset value × Probability of the value
– Present value of the exercise price × Probability the exercise price will be paid
- Options are covered in greater detail in subsequent chapters; this is a short introduction that provides some background into how they are priced.
The particular feature of this example is that it is a real option, as opposed to a derivative option.
One criticism of the NPV model is that it cannot 'price' the value of keeping the investment on hold until a future date.

31. Annual equivalent cost (AEC)
When comparing two mutually-exclusive projects with different lives, it is necessary to make comparisons over the same time period.
AEC is the present value of each project’s costs calculated on an annual basis.
NPVs are calculated, and then converted to AECs using the relevant PVIFA (present value interest factor for annuities).
Select the project with the lowest AEC.
- AEC analysis can also be used to calculate the cash inflows required each year to obtain a desired rate of return over the life of the project.

32. Example—AEC
Project A costs $3 000, and then $1 000 per annum for the next four years.
Project B costs $6 000, and then $1 200 for the next eight years.
Required rate of return for both projects is 10 per cent.
Which is the better project?
- AEC gives mutually exclusive projects a common denominator for comparison.

33. Solution—Project A
- AEC gives mutually exclusive projects a common denominator for comparison.

34. Solution—Project B
- AEC gives mutually exclusive projects a common denominator for comparison.

35. Solution—Interpretation
‘Project A is better, because it costs
$1 946 per year
compared to Project B’s
$2 325 per year’.

36. Annual equivalent benefit (AEB)
The AEB is used when comparing projects with cash inflows and outflows, but with unequal lives.
The steps required to calculate the AEB are the same as those used for AEC.
Select the project with the highest AEB.

37. 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?

38. Summary and conclusions
Discounted cash flow (DCF) analysis is a standard tool in the business world.
The information provided for a specific decision may be complex; however, the analysis reduces to three distinct steps:
Step 1  Calculate the taxable income
Step 2  Calculate the cash flows relevant to the decision
Step 3  Discount the cash flows to make the decision.
Cash flows should be identified in a way that makes economic sense.