Lecture 7 and 8 Rules of Capital Budgeting

Corporate FinanceFINA 4332

Ronald F. SingerFall, 2010

Capital Budgeting Decisions Check List

1- Net Present Value is the "Discounted value of cash flow"2- Cash flow is:cash money in - cash money out, 3- Consider only if it is an incremental cash flow, and consider all incremental

cash flows: (a) not historical, or averages: (b) consider only cash flows that appear as a result of the

project:4- Treat inflation consistently: (a) Discount real cash flow by real discount rates (b) Discount nominal cash flows by nominal discount ratesNote: Revenues and costs will not in general react uniformly to inflation.

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Check List (Continued)

5- All Cash Flow should be on an After-Tax basis.6- Don't forget to allow for the tax on capital gains7- Account for assets sold and not sold as a result of adoption of a

project.8- Account for changes in working capital and only changes in working

capital.9- Ignore financing10- Use actual tax changes when paid!11- No matter how complicated the decision: What is important? MAXIMIZE NPV

Plan to take all projects with a Positive Net Present Value and reject all projects with a Negative Net Present Value

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Discounted Cash Flow Analysis

• Cash Flow Checklist 1- Clarify all assumptions 2- Indicate the effect of the product being considered on other

products of the firm.3- Exclude sunk costs 4- Include opportunity costs for any factor of production even if

there is not an explicit cash outlay.5- Exclude allocated overheads that do not change, but include

overheads that will change as a result of adoption of the project.

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6- Insure that the tax rate used reflects expected future marginal tax rates

7- Exclude all financing flows including the tax shield of interest8- Include Net Working Capital Changes:9- Include Asset's Entire Life:10- Include the depreciation tax shield, but not depreciation

itself.

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Application of the NPV Rule and Capital Budgeting

We are going to assume that the appropriate interest rate is known. The problem we want to tackle is to Forecast the relevant cash flows.

• Rule 1: Only Cash flows affect wealth. Since data comes from accounting statements we must "adjust" the income statement to obtain the cash flow.

• Rule 2: Only incremental cash flows are relevant, not historical cash flows, not averages, not sunk costs.

• Rule 3: Treat inflation consistently.• Rule 4: Tying up assets uses a valuable resource and must be

accounted for.• Rule 5: Remember the impact of non-cash expenses on

tax liabilities.• Rule 6: Ignore the means of financing both as a direct cash flow and

as its effect on taxes. 9-6

Rule 1: Only Cash flows affect wealth. Since data comes from accounting statements we must "adjust" the income statement to obtain the cash flow.

• Net Cash Flow = Dollars in - Dollars outWhat is and is not Cash Flow

-Depreciation is not a cash flow -Taxes are cash flow when paid -Accounts receivable, becomes a cash flow when the money

actually changes hand -When you build up inventory you have no cash inflow, when you

sell from the inventory (and get paid) you have a cash inflow. -Expenses are cash flow regardless of whether the accountant

capitalizes and depreciates them or expenses them. -Capital expenditures are cash outflows regardless of the fact

that accountants depreciate them over a period.

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Rule 2: Only Incremental cash flows are relevant, not historical cash flows, not averages, not sunk costs!

Example 1: Consider a firm having made an investment one year in the past. The project required an initial investment of $10,000, with the expectation of $14,000 to be generated within two years. At a discount rate of 10% should the firm have made the investment?

14,000 -1 0

110,000

Of course it should have. The NPV was: NPV = 1,564

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Of course it should have, the NPV was Positive = $1,564

But now assume that things have changed. an expected new device introduced by a competitor has made the product obsolete. as a result expected cash flows has declined from $14,000 to $7,000. clearly, the investment, in retrospect did not pay off as expected and the project is now a loser.

However, suppose that for an additional investment of

$5,000, you can regain your competitive position, so that expected cash flow will increase to the original $14,000. should you make the new investment?

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14,000

-1 0 -5,000 110,000

Note that the project, looked at as a whole is still a loser:

NPV(-1) = -10,000 - 5,000 + 14,000 (1.1) (1.1)2

= - 2,975 9-10

NPV(-1) = -10,000 + 5,000 + 14,000 (1.10) (1.10)2

= -$2,975

NPV(-1) = -10,000 + 5,000 + 14,000 (1.10) (1.10)2

= -$2,975

BUT IN FACT, the additional investment should be made. The incremental cash flows looks like:

The Net Present Value from the incremental cash flow is:

And this has a NPV of:9-11

-5,000

7,000

Example 2: Assume that the original cash flow estimates were accurate. But, that you can, by making an additional investment of 1,000 generate total second period cash flow of 15,050. Should the additional investment be made?(Still Assume r= 10%)

NPV (of Additional Investment) = -1000 + 1050 = -45.45 1.1

Even though, the original project is a winner, do not make the additional investment Rule 2 says Ignore Sunk Costs, and consider only incremental cash flows.

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NPV(of additional investment) = -1,000 +1,050 = -45.45 (1.10)

NPV(of additional investment) = -1,000 +1,050 = -45.45 (1.10)

-10,000

-10,000

-1

-1 0

014,000

15,050

1

1

-1,000

Initial

With

Additional

Investment

Rule 3: Treat inflation consistently

Make sure that inflation is accounted for in a consistent manner. either:

1. State cash flows in terms of actual dollars, at the time the cash flows are received. These are nominal cash flows. Or,

2. State the cash flows in terms of current dollars, at the time the projections are made. These are real cash flows.

If cash flows are in nominal terms, then use nominal discount rates to discount the cash flows.

If cash flows are in real terms then use real discount rates to discount the cash flows.

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Example: There is 8% anticipated inflation per year. The real price of Honda Accords is expected to remain constant into the foreseeable future at $20,000. What will the nominal price be after 5 years? Nominal Price = (Real Price) (1.08)5

= $20,566

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Nominal Price = (Real Price) (1 + in)T

= (20,000) (1.08)5

= $29,386.56

Nominal Price = (Real Price) (1 + in)T

= (20,000) (1.08)5

= $29,386.56

In general terms: Converting nominal cash flows to real cash flows, and nominal

interest rates to real interest rates.

If Y(t) is the nominal cash flow in period t, in is the annual anticipated inflation rate, then the real cash flow, y(t) is:

y(t) = Y(t) and Y(t) = y(t)(1+in)t (1+in)t if R is the annual nominal interest rate, and r is the real interest rate, then:

(1+R) = (1+r)(1+in) (1+r) = (1+R)/(1+in)

Don't assume that all cash flows will be affected equally by inflation. Beware of the Approximation: R = r + in This works only if r X in is small.

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(1+R) = (1+r)(1+in)(1+r) = (1+R)/(1+in)

(1+R) = (1+r)(1+in)(1+r) = (1+R)/(1+in)

y(t) = Y(t) (1+in)t

y(t) = Y(t) (1+in)t

Y(t) = y(t)(1+in)tY(t) = y(t)(1+in)t

Rule 4: Tying up assets uses a valuable resource and must be accounted for. That is we must consider the Opportunity Cost of our assets

Example: A firm is considering installing a brick manufacturing oven. The initial investment will require $300,000 in building and equipment. The oven will be located on a vacant lot having an estimated market value of $1,000,000. The project is expected to generate net cash flow of $50,000 per year for 20 years. After 20 years, the oven will be worthless. It is anticipated that the lot could be sold for $2,000,000 at the end of 20 years. At a 10% discount rate, is this a worthwhile project? (Ignore taxes)

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• The Wrong Way Ignoring the opportunity cost of the (tied-up) land.

Net present value calculation

-300,000 + PMT(50,000, 10%, 20) -300,000 + 425,693.05 = 125,693.05

Accept Project

The problem with this is that you ignore the fact that you lose the use of $1,000,000 that you could have had if you had not adopted the project and sold the land (or used it in an alternative project).

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-300,000 + PVA(10%,20,$50,000)-300,000 + 425,693.05 = 125,693.05

-300,000 + PVA(10%,20,$50,000)-300,000 + 425,693.05 = 125,693.05

The Right Way

Present Value Calculation

NPV = -1,000,000 -300,000 + PV of the Annuity(50,000, 10%, 20)

+ PV of the Lump Sum($2,000,000,10%,20) = - 1,300,000 + 425,693.05 + 297,287.96 = - 577019 Reject Project

Notice how the tied up land is treated!

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NPV = -$1,000,000 – 300,000 +PVA(10%,20,$50,000) +PV(10%,20,$2,000,000)

= -$1,300,000 + 425,693.05 + 297,287.96 = - $577,019 < 0

NPV = -$1,000,000 – 300,000 +PVA(10%,20,$50,000) +PV(10%,20,$2,000,000)

= -$1,300,000 + 425,693.05 + 297,287.96 = - $577,019 < 0

Other Incremental Costs AreIncreases in overhead costs as a result of project. Increases in working capital as a result of project.

Notice the reduction in working capital is a positive cash inflow at the time of the cash flow.

Do not use allocated overhead, or allocated working capital. Example: Suppose, due to the adoption of the project, the

firm is required to increase working capital from $100,000 to $110,000 per annum for the life of the project. How do you account for the working capital?

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Rule 5: Remember taxes and the effect of non-cash expenses

1. Calculate all cash flows after taxes 2. Include non-cash expenses (depreciation) for its effect on

taxes, but not as a cash flow in and of itself. • How to handle the Depreciation Tax Shield we want the project's After Tax Cash FlowEquals:

Before Tax Cash Flow Less Corporate Taxes

Taxes = tc [Cash revenue - Cash Expenses - Depreciation]

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Taxes = tc (cash revenue – cash expense – depreciation)Taxes = tc (cash revenue – cash expense – depreciation)

Therefore, for each year: After Tax Cash Flow = (Cash Revue - Cash Expenses)(1 - tc)+ tc Depreciation

Where: tc x Depreciation is the Depreciation Tax Shield

3. Tax on gains/losses from sale of assets is an additional cash flow

Tax on Gains/Losses=tcx(Market Value – Adjusted Basis) On sale If Market Value > Book Value, then tax on gain is cash outflow. If Market Value < Book Value, then we have a loss on sale, tax is

negative, and there is a cash inflow. Example:

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Tax on Gaines/Losses = tc X (Market Value - Basis) on Sale

After Tax Cash Flow = (Cash Revenue –Cash expenses)(1- tc ) + tc Depreciation

Rule 6: Ignore the means of financing both as a direct cash flow and as its effect on taxes.

Interest payment is not a cash flow. Discounting already takes the value of time into account. To deduct interest would be double counting.

Example: Suppose that you borrow $500, and put in $500 of your money into the following project. (Bank charges 8% on loan)

0 1 Cash Flow -1000 1125 Interest -40 Net -1000 1085To say that we reject the project since NPV (of net cash flow) is negative at

10% (NPV = -13) is double counting. We penalize the project twice, one by deducting interest, second by discounting.

The NPV of this project is: - 1,000 + (1,125) X (0.909) = 23

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-1000 +PV(8%, 1 ,1,125) = 23

-1000 +PV(8%, 1 ,1,125) = 23

Project Analysis

• Cash Flow Analysis Sales Less: Cost of Goods Sold Other Costs

Tax on Operations Cash Flow from Operations Less: Change in Working Capital

Gross Change in Capital (Capital Investment less Disposal)

Net Cash Flow 9-23

Project Analysis

• Real, versus Nominal Cash Flows: Suppose the nominal rate is 20% and anticipated inflation is 10%, then: Net Present Value from Initial Projections Discounted at the real rate of: r = (1 + 0.20)/(1 + 0.10) - 1 = 9.09% Net Cash Flows• Real cash flows• Nominal cash flows• Percentage difference, nominal against real

Net Present Value at the Real Rate Net Present Value at the Nominal Rate Why are they different? Which one is correct?

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