Lecture 7: Capital Budgeting, part 2 C. L. Mattoli 1.

Lecture 7:Capital Budgeting, part 2

C. L. Mattoli

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Last Week We finally got to apply what we have learned

about valuation to the business setting, and we discussed several methods on which to base investment decisions.

In this lecture, we fill out the discussion by taking a closer look at cash flows and their estimation.

We also look at other ancillary considerations in the capital budgeting process.

In the textbook, chapter 9.

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What Cash Flows?

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Intro Since the focus, in finance, as we have

learned, is cash flows, we must be careful to include the proper cash flows and exclude improper ones in our evaluation.

Two things should be noted, before hand. First, companies may spend some money, in

the ordinary course of their business, looking at and for new business ideas (projects).

What will be important is the net cash flows that a project adds to the firm.

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Sunk Costs

There are some unusual costs that are part of business project evaluation.

Sunk costs are costs that a business incurs in looking at potential projects, in its regular course of business.

They are liabilities that must be paid whether or not the project is actually undertaken.

An example is a fee for a market analysis for a potential new product.

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Sunk Costs R&D is done by, e.g., drug companies as part of

their ordinary course of business and is not project specific.

Consider another example. A company rents space for its business at $1 per square meter and has separate extra lockable space that it is not currently using.

Should it rent out the space for less than $1 per SQM?

Yes, because the rent that it pays is a sunk cost, and any revenue from subleasing some unused space is an additional benefit.

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Opportunity Costs We have already seen how opportunity cost

can enter economic and financial problems. The opportunity cost concept also arises in

business project evaluation. Basically, opportunity costs are in terms of

what you give up. For example, suppose you own a building

that you paid $500,000 for, 10 years ago. Due to new zoning laws, you are now

allowed to convert the building into apartments.

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Opportunity Costs

If you decide to go ahead and make the conversion, how do you treat the building cost?

Since you already bought it before the project idea even arose, the $500,000 that you paid for it is a sunk cost.

The opportunity cost that should be included in your evaluation of the apartment project, however, is how much you could sell it for, today, in the market.

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Opportunity Costs Consider an other example. You buy a new

piece of equipment that needs to be installed somewhere in our plant.

If the space to install it has a competing possibility, such as another piece of equipment for another project, then, we should include the opportunity cost in our analysis.

If there is no other potential use for the space, then, no space opportunity cost should be included.

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Incremental Cash Flow To truly analyze the cost and benefits of

adding a new business to an existing business, we have to consider all of the changes in cash flow of the whole business that are associated with the project.

In other words, we consider the total net affect of the new business on cash flows.

The relevant project CF’s are, therefore, incremental cash flows, the net additions or subtractions of cash flow of the whole firm.

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Incremental Cash Flow In that regard, we do not have to actually

calculate the whole of cash flows of the firm with and without the project.

We only have to figure out the incremental cash flows of the project.

That is known as the stand alone principle. We evaluate the project incremental cash flows, considering it as a stand alone business.

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Incremental ExampleSuppose we have the following comparison of cash flows for some year in the life of a project.

Project Implemented –

Project Not Implemented =

Increment

Sales 12000 9000 3000

Cash op. cost (5000) (4000) (1000)

Depreciation (2000) (1000) (1000)

Pre-tax income 5000 4000 1000

Taxes (30%) (1500) (1200) (300)

= Net oper. inc. 3500 2800 700

+ depreciation 2000 1000 1000

=Operating Cash flow

5500 3800 1700

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Why incremental? What incremental?

Consider a company that makes tooth paste. Next, assume that they want to introduce a

second brand of tooth paste. One possibility is that some of the

customers that used their original toothpaste might switch, so the incremental revenue from the new toothpaste will be new revenues from new toothpaste minus lost sales of old toothpaste (called erosion).

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Why incremental? What incremental? Alternatively, the new customers who try

the new toothpaste might be so impressed with the product that they decide to try other products that the company makes, like soap.

Then, the incremental revenues from the new toothpaste will be the new toothpaste sales plus the additional sales generated by new toothpaste customers who also decide to buy soap that the company makes.

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NWC and Projects As we mentioned in an earlier lecture, startup

costs for a business will involve more than just things like equipment purchase.

Project startup will also involve working capital.

For example, if you start a clothing boutique, you will have to buy some inventory for startup.

Suppose that you estimate that your monthly sales will be $100,000, and you will be making about 25% of sales on credit.

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NWC and Projects Then, you will also need room, in the

beginning, for A/R of $25,000. If you only have $100,000 for inventor, then,

when you sell the original inventory, you will only have $75,000 in cash to purchase the next month’s inventory.

You needed to think ahead and also have an extra $25,000 for startup to eventually have A/R of $25,000, so WC startup will require $100,000 + $25,000 = $125,000.

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What about Financing Costs? We do not include interest, dividends or other

financing charges of as project. As discussed in an earlier module, we are

interested in CF from assets. Moreover, the motivation of the analysis is to

compare the CF from assets to the cost of acquiring them.

Interest and financing are part of CF to creditors and investors and the financing, not the investment, decision.

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When CF’s? We focus on the actual cash flows, not accounting

numbers. Technically, we should focus on when those cash

flows arrive, not when they accrue, since we know about time value.

In practice, though, we usually assume that they all come at the end of each period under evaluation. That gives the most conservative estimate of time value, too.

We should usually also be interested in after tax CF since tax is an actual outflow, although there will be cases, under Australian tax law, when we should focus on BT CF.

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Pro forma Financial Statements and projected CF’s

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Intro Pro forma statements can be prepared for the

future for projects. We need estimates of things, like unit price,

number of expected sales, VC/unit, FC/unit. We also need to collect all of the relevant

costs of startup, including equipment and installation costs, as well as WC requirements of the project.

We can them organize the data so it will be useful for analysis.

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Example (Textbook)

It is expected that 50,000 cans of shark attractant can be sold per year at a price of $4/can.

The VC = $2.50/unit, and FC = $12,000/year for rental of space.

In addition, equipment will cost $90,000 and will be depreciated over the life of the project, which will be 3 years.

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Example (Textbook)

The equipment will be worthless at the end.

An investment in WC = $20,000 will also be required for startup.

The project will have a 3 year life and require an RRR of 20%.

We show a pro forma income statement , in the next slide.

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Text Table 9.1 Pro Forma Income

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 (30%) 9,900

Net Income $ 23,100

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Example CF’s We define project CF’s as PCF = OCF –

ΔNWC – CS. (Recall OCF = EBIT + Depreciation (D) – Taxes (T)).

From the income statement, we can find the annual project CF’s in the future years, as PCF = $33,000 + $30,000 - $9,900 = $53,100.

The initial investment is IIO = Equipment + ΔWC = $90,000 + $20,000 = $110,000.

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Example CF’s

The IIO is an negative CF since it is an outlay.

The summary of PCF’s for all years is shown, below.

Year 0 1 2 3

OCF $53,100 $53,100 $53,100

ΔNWC -$20,000 20,000

CS -$90,000

TCF -$110,00 $53,100 $53,100 $73,100

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WC recovery WC initial investment is normally recovered

at the end of the project (unless otherwise specifically stated in a problem).

For example, if we invest in inventory, in the beginning, it will have been sold and included in OCF’s, and there will be no inventory at the end of the project.

Example, get $100,000 of dresses to sell. Sell them for $100,000. At the end there are none left.

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WC recovery Thus, we have IIO = – $100,000; CF = $100,000

(sales) – $100,000 (cost) = 0. However, that would mean that we invested

$100,000 and ended up with $0, which is not correct.

We actually got our $100,000 back. It’s just that the accounting for CF gave us $0 OCF, so we have to reverse out the invemtory investment to make things right.

After all we have no inventory because Inventory (0) = $100,000 and inventory(1) = $0.

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PP&E We need to look more closely at PP&E,

too. First, recall that land is not depreciable but

plant and equipment are. When we purchase P&E, we must

consider all of the costs. If we buy an existing building, we will have

to pay agent commissions, transfer and taxes plus, maybe, refurbishing.

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PP&E When we buy equipment, it will have to be

transported, insured in transport, and installed, once it arrives at the plant.

There might even be training costs for operators of the new equipment.

All of those costs are part of the cost of acquiring PP&E.

In fact, the total cost is capitalized (put in a capital account) and depreciated.

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Tax Shield Approach to PCF’s Another way to get OCF is called the tax

shield approach. We subtract all costs from sales = EBITD. Then, we multiply by (1 – T) to get the

after tax value of EBITD. The actual value of depreciation, in

finance is the tax savings that comes from deducting D from earnings before we compute taxes.

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Tax Shield Approach to PCF’s We can write ATI = [EBITD – D] – T

[EBITD – D] = (1 – T) EBITD – D + TD. CF = ATI(1 – T) + D = (1 – T) EBITD –

D + TD + D = (1 – T) EBITD + TD. +TD is the tax that was saved because

D was subtracted from earnings before tax was applied to earnings. It is the tax shield provided by depreciation.

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NWC in more detail

Consider a simple business with no fixed investment and assume taxes are zero, for simplicity.

Then, income for the year is Sales – costs = $500 - $310 = $190.

However, the actual cash flows might be different from that number because some sales (A/R) and purchase (A/P) might be done on credit.

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NWC in more detail

Assume that the accounts are as shown, below.

Begin year End year Change

A/R 880 910 +30

A/P 550 605 +55

NWC = A/R – A/P 330 305 – 25

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Actual CF’s adjusted for ΔNWC The book income has to be modified to

account for increased A/R, which means the cash we got from sales was actually less than book sales, and some costs were not paid by cash since A/P increased.

So, real CF was OCF –ΔA/R + ΔA/P = OCF – ΔNWC (since there was also no capital spending on the project during the year).

For the example Actual revenues = Sales – ΔA/R; real costs = costs – ΔA/P; and CF = $190 – (– $25) = $215.

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The logic of ΔNWC & CF’s If we invest in CA, it will be a cash outflow. Thus, increased inventory or A/R will subtract

from actual cash flow. Notice, also, that, if we divided up CA, like in

the above example, and group change in inventory with costs, we will ad change in inventory to costs because cost are subtracted from revenues, and positive change in inventory is an investment and adds to cost.

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The logic of ΔNWC & CF’s For CL, if we reduce a CL, that is an

investment, so, we will have to add change in CL to CF.

In that manner, a reduction in CL will subtract from CF.

Again, for example, if A/P increases, then, we are getting positive CF. So, we add change in CL to CF.

If, however, we group A/P, for example with costs, then, it will subtract from costs.

We can look at some more examples.

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Example Initial Investment CM wants to modernise the welding section of their

production line. A new high tech system will cost $250 000 to purchase, $5 000 to insure and transport to the plant and $3 000 to install. The existing equipment cost $50 000 10 years ago and could be sold for $10 000 as is.

The new system would result in a significant annual sales increase and higher production levels. To support these, management have estimated that accounts receivable would increase by $30 000, accounts payable would increase by $20 000 and inventory would increase by $10 000. What is the initial outlay for the new welding system?

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Example Solution

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Installed cost

Purchase price -250 000

Insurance and transport -5 000

Installation -3 000

Sale of existing equipment 10 000

-248 000

– Change in net working capital

Add increase in accounts receivable

30 000

Less increase in accounts payable -20 000

Add increase in inventory 10 000

20 000

= Initial outlay -268 000

Text Example A company reports revenue=$998 and cost=

$734, plus the following WC entries.

Since A/R increased, we subtract that from revenues.

Inventories decreased, so we subtract that from costs.

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Begin End Change

A/R 100 110 +10

Inventory 100 80 - 20

A/P 100 70 - 30

NWC 100 120 +20

Text Example

Also we add the decrease in A/P to costs. Adjusted Sales, are then, 998 – 10 = 988. Adjusted costs are 734 – 20 – (– 30) =

744. The affect on CF is adj rev – adj costs =

988 – 744 = 244. Alternatively, we have rev – costs –

ΔNWC = 998 – 734 – 20 = 244.

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Depreciation As we mentioned, earlier, the real value of

depreciation, in finance, is the tax savings. Thus, in finance, we always use tax

depreciation, which is different from accounting depreciation.

The tax office tells us how we can depreciate things, and we use that.

For example, if an asset costs $100,000, can be depreciated over 5 years and has an estimated terminal value of $20,000 and useful life of 8 years, we depreciate as $100,000/5 = $20,000, straight line (prime cost).

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Depreciation The alternative way at looking at depreciation

is in %/year instead of tax years. The two ways are just inverses of each other.

D in years = 1/[D in %/year]. Thus, a 5 year tax life has depreciation of 1/5

= 20%/year. An asset with 15%/year depreciation has a 1/15%/year = 6 2/3 years.

It will have BV = 0 at the end of the 5 years.

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Diminishing balance depreciation In addition to prime cost, the ATO also allows

an accelerated depreciation method, diminishing balance.

First you compute the Prime cost 1 year D, then, multiply by 150% the BV and divided by tax years = year 1 D. Subtract to get end year BV.

For the next year, you divided BV by the straight line years, multiply by 150%, get year 2 D, subtract, get the BV, etc.

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Example

Asset’s installed cost = $1 160 000 effective life = 10 years

1. what is the annual straight line depreciation?

2. what amount can be claimed for the first 2 years if the diminishing value method is chosen?

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Prime cost depreciation

Prime cost depreciation = installed cost of asset effective life

= 1 160 000

10

= 116 000 per annum

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Diminishing value depreciation

Diminishing depreciation = base value x (150% / effective life)

Year 1 = 1 160 000 x (1.5 / 10)

= 174 000

BV year 2 = 1 1160 000 – 174 000 = 986 000

Year 2 = 986 000 x (1.5 / 10)

= 147 900

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What is the real difference in the two methods of depreciation We know that money has a time value. The farther

out in time that we get money, the less valuable it is to us now.

Thus, if we deduct more in future years that are closer to the present, we pay less tax in those closer future years, and we pay more tax in years that are more distant into the future. So the present value of our tax payments is reduced compared to paying the same tax in all years because of straight line, even depreciation deductions.

In turn, the PV of net CF is increased.

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BV vs. MV, taxes on sale of P&E Suppose that you sell the asset of the

second last example, in year 4, for $25,000.

The BV = $100,000 – 4x$20,000 = $20,000.

Then, the tax law says that you must pay tax on the gain (or loss, which is a tax savings) on sale price over BV.

Gain = 25,000 – 20,000 = $5,000.

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BV vs. MV, taxes on sale of P&E Tax is then, 30%x$5,000 = $15,00. We must include the after tax CF of the

sale of equipment in winding up the project.

The general formula is ATCF(terminal value, salvage) = Sale Price – Tx[Sale – BV].

Sale price, net of removal, sales commissions, and clean up, is a real cash inflow. The taxes paid are an outflow.

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Text example MMCC

MMCC is considering a project. It has estimates for unit sales and prices

for 8 years. It estimates that it will need to purchase

equipment for $800,000, which is will deprecate 15%/year (note: 15%x6 = 90%, so there will be 6 years of 15%, the 7th year a remainder, and none in the 8th year).

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Text example MMCC

It believes the equipment can be sold for 15% of purchase in 8 years from now.

It will need 20,000 in WC to begin and will maintain WC at 15% of sales.

FC = $25,000; and VC/unit = $60. We show the Pro Forma income

statement and analysis in the next 2 slides.

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Example PF IS plus

year 0 1 2 3 4 5 6 7 8IIO -800,000WC 20,000 54,000 90,000 108,000 107,250 99,000 82,500 66,000 49,500ΔWC -20,000 -34,000 -36,000 -18,000 750 8,250 16,500 16,500 16,500units 3,000 5,000 6,000 6,500 6,000 5,000 4,000 3,000unit price 120 120 120 110 110 110 110 110Revs. 360,000 600,000 720,000 715,000 660,000 550,000 440,000 330,000VC ($60/unit) 180,000 300,000 360,000 390,000 360,000 300,000 240,000 180,000FC 25,000 25,000 25,000 25,000 25,000 25,000 25,000 25,000D (15%/yr) 120,000 120,000 120,000 120,000 120,000 120,000 80,000 0EBIT 35,000 155,000 215,000 180,000 155,000 105,000 95,000 125,000Tax 10,500 46,500 64,500 54,000 46,500 31,500 28,500 37,500ATI 24,500 108,500 150,500 126,000 108,500 73,500 66,500 87,500ATCF 144,500 228,500 270,500 246,000 228,500 193,500 146,500 87,500

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Analysis

ATCF 144,500 228,500 270,500 246,000 228,500 193,500 146,500 87,500

WC recovery 49,500

AT salvage 112,000

Total CFs -820,000 110,500 192,500 252,500 246,750 236,750 210,000 163,000 265,500

Cumm CF -820,000 -709,500 -517,000 -264,500 -17,750 219,000 429,000 592,000 857,500

DCF (k=15%) -820000 96,087 145,558 166,023 141,080 117,707 90,789 61,278 86,792

PBP 4.07

NPV 85,313

IRR 17.85%

PI 1.10

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Notes The CFs are OCF + change in WC for

intermediate years. Change in WC = last year’s minus this

years = net investment/divestment of WC. To get salvage AT, we take 15%x800,000

= sale price, then, we subtract BV, which is $0, and finally multiply by 70% (=1 –T) to get ATCF Salvage.

We add back the leftover WC (recover) to the final year’s CF.

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Notes We have computed cumulative CF’s

and used them to find PBP. We have also computed PV’s to find

NPV and PI. Finally, the analysis also includes

IRR. NPV is positive, so we can accept the

project.

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Evaluating the Evaluation

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Intro As we said, last lecture, one of the biggest

problems with our whole evaluation program is the accuracy of our estimates of future events.

Can we really know how much revenues we will have? Are our estimates of both unit sales and prices, several years into the future, reasonable?

In truth, the estimates will ultimately depend on the unfolding of other economic events.

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Intro Will there be cost-push or demand-pull

inflation in materials prices and labor? Will the general economy grow or contract.

Certainly, the way that things actually play out, could be the difference between positive and negative NPV, in some cases.

In thinking about all that our estimates depend on, and how that can affect our project outlook, it might be better to consider the problem, further.

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Forecasting Risk Thus, we are naturally led to consider our

forecasting risk, i.e., the risk that our forecast is way wrong.

Projects are usually expensive and not easily reversed.

Our valuation system and companies’ investments cover a much broader ground than business expansion or replacement projects.

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Forecasting Risk Companies can buy (take over, merge,

buy out, acquire the stock of, tender for the shares of, and a few other terms) whole other companies.

That can be even more expensive and more difficult to reverse (see the textbook for an example, p.272).

Especially with a low RRR or a case of small but positive NPV, reality could turn an expected winner into a loser.

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The Root of Value Based on economics and assuming business

is pretty completive at this point in world history, we would not expect to find an abundance of positive NPV projects.

Of course, new things can be invented, including more efficient technologies to help existing producers produce more efficiently an cost-effectively.

However, what other opportunities are there that other people have not already taken advantage of?

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The Root of Value Can we really produce a product, new for us,

that is better than an existing one? Will we have better luck finding and exploiting

new markets than our established competitors?

Even if we really do hit on a good idea, how fast and how furiously will other people follow us into the new frontier.

How will those things and the economy, in general, affect our forecasts and our conclusion about NPV?

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Scenarios: Splitting the Future

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Intro Since we know that the future is uncertain,

we are admitting that it could turn out a number of different ways.

Given that, wouldn’t it be smart to actually make a number of forecast?

It could be as simple as making a good, neutral (base case), and bad set of pro forma’s .

We could define the scenarios. Based on other forecast of markets or the entire economy.

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Intro

We could go even further, assign probabilities to each scenario, and find a probability-weighted average forecast and NPV.

It all depends on how much time and money you want to put into it versus the benefit you get out of the more elaborate analysis.

We continue with a simple exampls, defining upper and lower bounds on some of the input variables.

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3 Scenario Example Consider a project with a cost of $200,000,

depreciated over 5 years straight-line with zero salvage value and no ΔWC; T = 34%.

We show three scenarios for the inputs, in the table, below, the same for all years.

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3 Input ScenariosBase Lower Upper

Units 6,000 5,500 6,500

Unit price 80 75 85

VC/unit 60 58 62

FC/unit 50,000 45,000 55,000

3 Scenario Example From those numbers we can construct pro

forma’s.

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Pro Forma Income Statements

Base Case Best Case Worst Case

Sales 480,000 552,500 412,500

VC 360,000 377,000 341,000

FC 50,000 45,000 55,000

Depreciation 40,000 40,000 40,000

EBIT 30,000 90,500 -23,500

Taxes 10,200 30,770 -7,990

ATI 19,800 59,730 -15,510

3 Scenario Example From those numbers, we can compute

annual ATCF’s and the resulting analytical numbers, summarized, below.

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Cash Flows & NPVYear

0 -200000 -200000 -200000

1 59800 99730 24490

2 59800 99730 24490

3 59800 99730 24490

4 59800 99730 24490

5 59800 99730 24490

NPV $15,565.62 $159,504.33 ($111,719.03)

IRR 15.10% 40.88% -14.40%

Sensitivity Analysis In the foregoing scenario analysis, we varied all

of the variables. In sensitivity analysis, we vary one variable at

a time to see what happens to the results. For example, we could vary unit sales, fixed

costs, or prices. In the end we will be able to construct a graph of

NPV vs. the variable. The higher the slope of the line, the more

sensitive is the NPV to that variable. We show an example of unit variation, below.

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Sensitivity Analysis NPV vs. Units

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Further Considerations

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Managerial Options So far, we have assumed that once a project

is begun, it will not be changed. This is a static view of projects. In practice, after a project is started, it can be

changed in a number of ways. This dynamic view of projects considers

management options, also called real options since they deal with real assets.

These include things like pricing, method of manufacture, and advertising.

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Some general options We can use the prior analysis to think

about what might happen, and we can also try to plan adjustments, if things happen.

That is contingency planning. Options include, expansion, if things are

looking up, downsizing, even abandoning, or waiting to see how investment rates change and make an undesirable project desirable.

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Some general options

Another possibility is to take on an otherwise unacceptable project, now, as part of a longer-term strategic plan.

For example, you might start a computer repair operation to gain experience in computer repair service as part of a bigger plan to eventually produce computers.

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Capital Rationing Companies, instead of taking on all

positive NPV project, might limit capital spending at the corporate or divisional levels. (soft rationing)

This could lead to accepting some inferior projects that fit into the budget and not taking on other because they would put us over budget.

We show an example, in the next slide.

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The Inconsistency

Choose the set of projects that give the highest total NPV while keeping within the budget constraint.

Vertical axis – IRR. Horizontal line at 10% is firm’s unconstrained hurdle rate or the return that would be required on all projects without capital rationing. Vertical line ($120,000) is the size of capital budget under capital rationing.

A B C D E

R

WACC

Cap Budget

120 15095 170 195

Inconsistency solution We might take D, which would put us under

budget, instead of C, which would put us over budget. We might pick E, which will take us up to capacity in the budget but is below our COC.

Thus, when dealing with the supply-of-funds constraint on how much we can spend, and with the possible projects that we have to choose from, we might end up with not quite maximum use of our funds.

Hard Rationing

In hard rationing, the firm cannot raise capital for new projects for any reason.

This is known as hard rationing. It could occur, for example, for a company in

financial distress. Another reason might be restrictive

covenants in other obligations. Then, it is like we face an infinite RRR, and

no projects can be taken on.

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Learning activity

In chapter nine of the text (page 282), attempt

critical thinking questions 9.1 – 9.6, 9.10, 9.11, 9.13 & 9.14

problems 1 – 10, 13, 14, 16, 21, 24 & 25

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End

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