In the previous topic, you learned about different capital budgeting techniques that firms use to evaluate projects. The techniques are:

• NPV ( $ value added to the firm from the project)
• IRR (rate of return on the project)
• Payback period (how many years it takes to get back the initial investment )
• ARR (return on investment without taking into account time value of money)

Except for ARR, cash flows are used as input in all of the techniques. These cash flows should be included in a capital budgeting analysis and are only those that occur (or do not occur) if the project is accepted.

In this topic, you will learn the following concepts.

Concept 1: Why do we calculate project cash flows?

Concept 2: Calculating project cash flows for project evaluation

Concept 3: Analyse project risk.

Concept 4: Understand capital rationing

Concept 1: Why do we calculate project cash flows?

Before you understand why and how you calculate project cash flows, it is important to understand what is “project cash flow” or “cash flow from projects”. They essentially mean the same thing.

Project cash flow is used to measure the outflow and inflow of money from the project to the firm. It is not easy to do budgeting with the cash flows. The inflow of cash is known as the revenue generated from the project. This is usually a positive number, and the outflow of the cash is called the project expenditure. This is entered as a negative number.

It is important to calculate cash flows because cash flow is the input in all of the capital budgeting techniques except for ARR.

The project cash flow is used to determine the project’s rate of return or value, and the flow of money into and out of the project is used in financial models to determine the net present value and the rate of return respectively.

Project cash flows are calculated by taking the difference between all cash inflows and cash outflows. It is also called net cash flow.

Let’s take the example of NPV. It is theoretically the most sound capital budgeting technique.

NPV tells the managers how much in current dollar terms the company is better off/worse off as a result of undertaking the project given the cash flows that a project is expected to produce in the future.

The three steps in NPV Analysis are:

1. Identify and estimate the (net) cash flows associated with the project.
2. Identify an appropriate discount rate for the project. This discount rate reflects the riskiness of the project.
3. Discount the (net) cash flows using the discount rate to achieve the NPV

Concept 2: Calculating project cash flows for project evaluation

In the previous topic, you calculated NPV when cash flows were given in the question! Here, you will be focusing on how these cash flows are calculated.

In NPV analysis you must include all incremental cash flows. Incremental cash flows are the additional cash flows that occur as a result of taking on a project.

While doing a project evaluation you need to consider what difference it makes to the total cash-flows of the firm, whether the firm does or does not undertake the project under consideration. What to do about:

1. sunk costs?
2. opportunity costs?
3. side effects?

Sunk Costs

Sunk costs are unavoidable (incurred in the past) cash-outflows are no longer relevant to influence whether a project should be undertaken. Therefore, you ignore sunk costs in NPV project evaluation.

Sunk cost Example

$10,000 payment to be made to a marketing company for assessing the market for a project which costs $125,000 and yields net cash-inflows of $75,000 a year for 2 years when the discount rate is 10% p.a. Should the project be taken on?

NPV of the project if evaluation is done incorrectly and sunk cost is included

(i.e., marketing cost of $10,000 is included):

NPV = -$135,000 + $75,000(1.1)^-1 + $75,000(1.1)^-2

NPV = -$4,800. Reject the project.

NPV if evaluation is done correctly, and sunk cost is not included (i.e. marketing cost of $10,000 is not included):

NPV = -$125,000 + $75,000(1.1)^-1 + $75,000(1.1)^-2

NPV = $5,200. Accept the project.

Opportunity Costs

Opportunity cost refers to a situation where factors of production or resources of a firm must be used in a new project. Still, previously they were being used for another purpose. If a project uses resources that could be put to some other use, then the dollar value of the alternative use must be included as an expense and a cash-outflow in the project evaluation.

Example of Opportunity Costs

A company owns machinery which has been leased out generating income of $3m per year. The machinery will now be used in a project which yields $20m a year for 2 years and costs $30m (required rate of return is 10% p.a.). Should the project be taken on?

NPV if the evaluation is done incorrectly and the opportunity cost is ignored (i.e. the lost lease income of $3m per year is not included in the analysis):

NPV = -$30m + $20m(1.1)^-1 + $20m(1.1)^-2

NPV = $4.7m. Accept the project.

NPV if the evaluation is done correctly and the opportunity cost is included (i.e. the lost lease income of $3m per year is included in the analysis):

NPV = -$30m + $17m*(1.1)^-1+$17m*(1.1)^-2

NPV = -$0.5m. Reject the project.

$17m = $20m revenue per year less lost lease income of $3m per year

Side Effects

Side effects refers to a situation where the sale of a new product by a company affects the sales, either positively or negatively, of other products sold by the company. In project evaluation, you must include side effects, i.e. positive or negative cash flows that occur in other aspects of the business as a result of taking on new activity.

Financing Costs

The costs of financing are interest expense for debt and dividend payments for equity. In project evaluation, the financing costs can be considered either in the cash-flows or by the discount rate R.

In your analyses, you will be taking account of the financing costs in the discount rate/required rate of return. Therefore, it is important that financing costs are not to be taken into account in the cash flows otherwise there will be double counting.

The required rate of return of the firm is the return that the firm has to earn on the project in order to satisfy the providers of financial capital for the project, so it covers the costs of finance (capital).

Taxation

Taxation has a major impact on project cash flows. Taxation represents a cash outlay. Depreciation and other tax-deductable expenses provide a ‘tax shield’. Gains (losses) on sale of productive assets (i.e. factors of production) increase (decrease) the amount of tax paid; and Capital gains (losses) on investment assets increase (decrease) the amount of tax paid.

Example of Book gain on sale of productive asset

Purchase price of asset (machine) $1m

Useful life of machine 10 years

Straight-line depreciation

Depreciation p.a. = $1m/10 years = $100,000

After seven years company decides to sell the asset.

Book value of asset after seven years = purchase price less accumulated depreciation = $1m less (7 years x $100,000) = $1m less $700,000 = $300,000.

Salvage value (sale price) of asset after seven years = $350,000

Gain on sale = salvage value less book value = $350,000 less $300,000 = $50,000

Tax rate = 30%

Tax on book gain = book gain x tax rate = $50,000 x 0.30 = $15,000.

Note: we do take depreciation into account when working out the book gain (or loss) on a productive asset.

Disposal of productive assets: gains or losses on sale.

• If the salvage value (sale price) of a productive asset is greater than the book value of the asset we have a gain on sale. Tax must be paid on the gain.
• If the salvage value (sale price) of a productive asset is less than the book value we have a loss on sale. The loss provides a tax rebate (tax shield).

Disposal of investment assets: capital gains or capital losses.

• If the sale price of an investment asset is greater than the purchase price of the asset we have a capital gain. Tax must be paid on the capital gain.
• If the sale price of an investment asset is less than the purchase price of the asset we have a capital loss. Capital losses do not provide a tax rebate but can be used to offset capital gains (in the current period and/or in the future).

Example of Capital gain on sale of an investment asset

Purchase price of asset (investment apartment) $1m, purchased in 2016.

Sell apartment for $1.3m in 2020.

Capital gain on sale = sale price less purchase price = $1.3m less $1m = $300,000.

Marginal tax rate = 40%.

Tax due on capital gain = capital gain x marginal tax rate = $300,000 x 0.40 = $120,000.

Note: we do not take depreciation into account when working out the capital gain (or loss) on an investment asset.

An incremental cash flow reflects how much the company’s total after-tax cash flows will change if a given project is accepted.

To identify an incremental cash flow ask the following question:

“Will this cash flow occur ONLY if the project is accepted?”

• “Yes”, then include because it is incremental
• “No”, then exclude because it will occur anyway.
• “Part of it”, then include the part that occurs because of project

Conceptually, FCF is the Free Cash Flow from a project and is simply what you referred to as NCF (Net Cash Flow) in the previous chapter.

Applying Stand-alone principle (concept): The idea that you can evaluate the cash flows from a project independently from the company is known as the stand-alone principle i.e. treat the project as if it is a stand-alone company that has its own revenue, expenses, and investment requirements. You can also call it Free Cash Flow (FCF) Calculation.

FCF Calculation:

FCF = (Revenue – Operating Expenses – D&A) ×(1-t) + D&A – Cap Exp- Increase in WC

Operating Expenses: All expenses except D&A

D&A: Depreciation and Amortisation

Cap EXP: Capital Expenditure

Increase in WC=Increase in Current Assets-Increase in Current Liabilities

Equivalently,

We exclude interest expenses when calculating NOPAT because interest expense is regarded as a financing expense rather than an operating expense.

5.4

Incremental free cash flow calculation

FCF = [(Revenue – OpEx – D&A) x (1 – tc)] + D&A – Cap Exp – Add WC

FCF Calculation: Why do we add back D&A?

Depreciation is not a real CF. It’s a book value (and book entry). However, depreciation is important because it provides a tax shelter and tax savings (Because depreciation is allowed as an expense by the tax office). Amortisation (e.g., decline in the value of intangibles) is also a non-cash expense allowed by tax department just like depreciation.

FCF Calculation: Why do we subtract increase in Working Capital?

Working Capital is cash employed to run day-to-day operations of a firm (e.g., money tied-up in inventory). WC is not consumed but rather employed for a period of time. Increase in WC during a period means more cash is employed, i.e., a cash outflow. Decrease in WC during a period means less cash is employed, i.e., a cash inflow.

Example: A new machine might lead to more operating efficiency, which leads to the company needing $10,000 more in inventory (A current asset). So more $10,000 is tied up in inventory and we treat this increase an outflow!

Cash Flow for NPV Calculation

Remember you are doing:

NPV: Step 1: Identify the incremental cash flows associated with the project

Now you have all the components of incremental cash flows that are associated with the project: There are 3 parts;

1. The initial investment
2. The operating FCF/NCF that occurs during all years except year 0.
3. The terminal/Last Year cash flow.

Initial Investment (Year 0)

1. Cost of project=Purchase Price + any other additional Capital Expenditure
2. Net Working Capital Contributions (increase in in net working capital)
3. Sale price of the replaced(old) asset, if any, adjusted for taxation implications

Operating FCFF

1. These are the operating cash flows that occur during all the years except Year 0.

Terminal Cash Flow (Final Year)

The CF in the last, or terminal, year of a project often includes cash flows that are not typically included in the calculations for other years.

1. The terminal Cash Flow is the “unique” cash flows that occur in the terminal/last year only.
2. Remember: Normal Operating FCFF still occurs in the last year as well.
3. Terminal CF:
   • Salvage (sale) Value of the project (eg: Machine) recognised in last year.
   • Any tax effect on the sale/salvage of the machine.
   • Recovery of Working Capital. In these examples, we will assume that working capital investments are 100% recovered at the end of the project life.

FCF/NCF calculations from a project– example 1

You have purchased a truck for your plumbing business. The estimated life time of the truck is 10 years. The truck will increase revenues by $50,000 every year. Operating expenses will increase by $30,000 every year. Additions needed to working capital is $3000 per year. Depreciation charge will be $2,500 per year. The business faces a tax rate of 30%. Calculate the FCF from the truck for each year!

Solution:

FCF for new Truck
REVENUE	$50,000
Less CASH OP EXPENSES	-$30,000
Less DEPR & AMORT	-$2,500
EBIT (Earnings before interest & tax)	$17,500
Less TAX @30%	-$5,250
NOPAT	$12,250
Plus DEPR & AMORT	$2,500
Less WC increase	-$3,000
NET CASH FLOW OR FCF (excluding the capital expenditure)	$11,750

Initial Investment calculation: example

A new machine is purchased at $100,000. A further $10,000 will be paid to install the new machine. Because of the improved operating efficiency of the new machine an additional stock of $15,000 will be needed. As a result of the purchase of the new machine the existing machine can be sold at $20,000 salvage value. The current book value(depreciated) of the existing machine is $10,000. Calculate the initial investment as at Year 0.

Solution:

YEAR	0
Cost of Machine	-110,000
Increase in WC	-15,000
Sale of Old Machine	+20,000
Tax on sale of Old Machine	-3000
Initial Investment	-+

Terminal cash flow calculation: example

Example: The new machine in the previous slide has a salvage value of $20,000 at the end of it’s useful life (10 years). The machine will be fully depreciated over the useful life. The initial inventory increase as a result of the machine was $15,000 (see prior slide). The revenue increase due to the new machine is $100,000, where as the Operating Cost increase is $50,000. Calculate the Terminal Cash Flow.

YEAR	10 (Final)
Salvage Value (New Machine)	+20,000
Tax on Sale of new Machine	-6000
Recovery of Working Capital	+15,000
Terminal Cash Flow	+29,000

Concept 3: Analyse project risk

Financial analysts resort to different types of risk analysis. Main risk analysis methods are:

• Sensitivity analysis
• Scenario analysis
• Simulation analysis

You only examine sensitivity and scenario analysis in this topic.

Sensitivity Analysis

Sensitivity Analysis examines the sensitivity of the results (e.g., NPV, IRR) to changes in relevant variables. By how much does a project’s NPV (and/or IRR) change due to a decrease or increase in the value of individual cash inflow assumptions (values of variables)? Note: Typically, only the value of one variable is changed at a time.

How to do a sensitivity analysis on NPV?

Follow these steps:

1. Compute the NPV using most likely values of the variables
2. Change the value of one variable (e.g., sales volume, discount rate, % of expenses) and compute the NPV
3. Reinstate the original value of the variable (e.g., sales volume)
4. Change the value of another variable (e.g., initial outlay) and compute the NPV
5. Repeat this procedure for all the variables
6. Tabulate all the results (NPVs)
7. Identify the most sensitive variable/s (variables which makes large changes in NPV)
8. Explore what the company can do to improve these variables (better estimation, seeking more certain arrangements/agreements, etc.)

For a given project the NPVs at different sales growth rates can be tabulated as follows:

Sales Growth	NPV
-5%	125.36
0%	134.99
+5%	145.27
+10%	156.20

For a given project the NPVs at different discount rates can be tabulated as follows:

Discount Rate	NPV
5%	185.26
10%	156.20
15%	132.95
20%	114.14

Scenario analysis

Scenario analysis examines whether the results change under alternative scenarios (states of the world). A scenario might describe how a set of project inputs might be different under different economic conditions. By comparing the range of NPVs (and/or IRR) provided by the different scenarios, it is possible to understand the uncertainty (risk) associated with the project. In our previous example: We could do a scenario analysis if the economy does well, the economy does badly, and the economy does average.

For a given project, the NPVs at different economic conditions:

Economy	Sales Growth	Discount Rate	Expense(%)	NPV
Good	10%	15%	40%	161.28
Average	0%	10%	50%	134.99
Bad	-5%	5%	60%	116.15

You have calculated the different NPVs under different scenarios (predicting what will happen to each variable under different circumstances).

Concept 4: Understand capital rationing

Capital rationing is used to select the best projects.

What does a company do when it does not have enough money to invest in all available positive-NPV projects?

The process of identifying the bundle of projects that creates the greatest total value and allocating the available capital to these projects is known as investment decisions under capital rationing. It involves choosing the set of projects that generates the greatest value per dollar invested in a given period.

The profitability index (PI) is computed for each project and then the company chooses the projects with the largest PI until it has allocated all available capital.

The objective is to identify the bundle or combination of positive-NPV projects that creates the greatest total value for shareholders.

Computation of PI:

5.6

Profitability index

[latex]PI=\frac{NPV+initial\ investment}{initial\ investment}[/latex]

Capital Rationing steps to take:

1. Calculate the PI for each project.
2. Rank the projects from highest PI to lowest PI
3. Starting at the top of the list
   – select the project with the highest PI and
   – working way down the list
   – select the next highest PI project that fits into the total capital available (total budget)
4. Repeat step 3 until the bundle which gives the highest total NPV is identified.

Example: Which project(s) to choose from the table below if your company has only $10,000 to invest?

Project	Year 0	Year 1	Year 2	NPV @ 10%	PI
A	-$5000	$5500	$6050	$5000	2.0
B	-$3000	$2000	$3850	$2000	1.67
C	-$3000	$4400	$0	$1000	1.33
D	-$2000	$1500	$1375	$500	1.25

Choose A, B and D. C will not be chosen (although PI is higher than D’s) as there is not enough capital.

References

• Peirson, G., Brown, R., Easton, S. A., Howard, P., & Pinder, S. (2015). Business finance (Twelfth edition). McGraw-Hill Education.
• Ross, S. A., Trayler, R., Hambusch, G., Koh, C., Glover, K., Westerfield, R., & Jordan, B. (2021). Fundamentals of corporate finance (Eighth edition.). McGraw-Hill Education (Australia) Pty Limited.
• Parrino, R., Au Yong, H. H., Dempsey, M. J., Ekanayake, S., Kidwell, D. S., Kofoed, J., Morkel-Kingsbury, N., & Murray, J. (2014). Fundamentals of corporate finance (Second edition.). John Wiley and Sons Australia, Ltd.