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Making Investment Decisions Lecture 2 Fall 2009

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Making Investment Decisions Lecture 2 Fall 2009

Advanced Corporate Finance

FINA 7330

Ronald F. Singer

1. Net Present Value is the "Discounted value of incremental 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

(c) consider the impact of the project on cash flows from other projects

(d) exclude fixed or sunk costs

(e) exclude allocated overhead unless it will change as a result of the project.

4.Treat inflation consistently:

Discount real cash flow by real discount rates

Discount nominal cash flows by nominal discount rates

Note: Revenues and costs will not necessarily react uniformly to inflation.

5. All Cash Flow should be on an After-Tax basis.

Use actual tax changes when paid!

Don't forget to allow for the tax on capital gains Use future marginal tax rates applied to future taxable income

6. Include the opportunity cost of the project, even if there is no explicit cash flow realized

Account for assets sold and not sold as a result of adoption of a project.

7. Account for changes in working capital and only changes in working capital. Recognize that working capital will in general be re-couped at the end of the project.

8. Ignore financing including the tax shield on interest

9. Include Asset's Entire Life

10.Include the depreciation tax shield, but not depreciation itself.

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

- For now we are going to assume that the appropriate discount rate is known.
- The problem we want to tackle is to forecast the relevant cash flows.

What is and is not Cash Flow

-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.

- 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-----------------1

10,000

14,000

-1---------------0-----------------1

10,000

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

- NOW THINGS CHANGE. A NEW DEVICE INTRODUCED BY A COMPETITOR MAKES THE PRODUCT OBSOLETE. THUS EXPECTED CASH FLOWS DECLINE TO $7,000. THAT IS THE INVESTMENT, DID NOT PAY OFF AS EXPECTED AND THE PROJECT IS NOW A LOSER.
- SUPPOSE THAT FOR AN ADDITIONAL INVESTMENT OF $5,000, YOU CAN REGAIN YOUR COMPETITIVE POSITION, SO THAT EXPECTED CASH FLOW INCREASES TO THE ORIGINAL $14,000. SHOULD YOU MAKE THE NEW INVESTMENT?

14,000

-1---------------0-----------------1

-10,000 -5,000

- 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

14,000

-1---------------0-----------------1

-10,000 -5,000

- 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

BUT the additional investment should be made.

- Determine the incremental cash flows.
- Determine Net Present Value of the incremental cash flows
Incremental Cash Flow: -5,000 + 7,000/(1.1) = 1,363.65

- 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%)

14,000

-1---------------------0-----------------------1 initial

-10,000 -5,000

1,050

-1---------------------0-----------------------1 Incremental

-1,000

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

1.1

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

- Make sure that inflation is accounted for in a consistent manner. Either:
- State cash flows in terms of actual dollars, at the time the cash flows are received. These are nominal cash flows
Or

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

- State cash flows in terms of actual dollars, at the time the cash flows are received. These are nominal cash flows
- If cash flows are in nominal terms, use nominal discount rates to discount the cash flows.
- If cash flows are in real terms use real discount rates to discount the cash flows.

- Suppose you are buying a machine that you believe will produce 10,000 widgets per year at a unit cost of $3.00. The machine will last for 10 years.
- You can sell the widgets for $5.00 per unit.
- The risk of widget production is about average, relative to the economy as a whole. (i.e. has a Beta of 1).
- Your CFO thinks the return on the market will average 10% per year, over the next 10 years.
- What is the NPV of this project if the machine costs $130,000?

- Annuity is $20,000 per year for 10 years
- Discount rate is 10%
- NPV = 122,891 – 130,000 = -7109
- Reject

- Example: There is 3% 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) (1.03)5

= $23,185.48

- 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 times in is small.

- The problem is what is convenient and conventional is typically inconsistent with this rule:
- How do you project CF over time?
- How do you determine the appropriate discount rate?

- Suppose you are buying a machine that you believe will produce 10,000 widgets per year at a unit cost of $3.00. The machine will last for 10 years.
- You can sell the widgets for $5.00 per unit.
- The widget industry has an asset Beta which is similar to the Beta of the S&P 500
- Your CFO thinks the return on the market will average 10% per year, over the next 10 years.
- What is the NPV of this project if the machine costs $130,000?

- Annuity is $20,000 per year for 10 years
- Discount rate is 10%
- NPV = 122,891 – 130,000 = -7109
- Reject

- Assume that inflation is anticipated to be 3% per year:
- Now we have a growing annuity:
- CF(1) = 20,600
- CF(2) = 21,218
- ……….

- We had made the classic error of mixing real CF with nominal discount rates.
- Use Real CF and Real interest rates:
- Real rate = (1.10/1.03) -1 = 6.80%
- Then NPV = $141,780 – 130,000 = 11,780
- Accept Project

- Example: A firm is considering installing a brick manufacturing kiln. The initial investment will require $300,000 in building and equipment. The kiln 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 kiln will be worthless. It is anticipated that the lot could be sold for $2,653,000 at the end of 20 years. At a 10% discount rate, is this a good investment? (Ignore taxes)

- ALTERNATIVE ONE
Ignoring the opportunity cost of the (tied-up) land.

NET PRESENT VALUE CALCULATION:

NPV=-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).

- ALTERNATIVE TWO
Explicitly consider the land as part of the inputs: You estimate that the land will be worth $2,653,000 in 20 years.

PRESENT VALUE CALCULATION:

NPV = -1,000,000 -300,000 + PMT(50,000, 10%, 20)

+ PV($2,653,000, 10%,20)

= - 1,300,000 + 425,678 + 394,352

= - 479,970

REJECT PROJECT

- NOTICE HOW THE TIED UP LAND IS TREATED!

- ALTERNATIVE THREE
Consider this as two projects:

- Consider land as priced correctly in the market (In fact the return to the land is (and should be 5%)
- So NPV of investment in land is 0
- What is the right way to do this?

- Other Incremental Costs Are
Increases in overhead costs as a result of project.

Increases in working capital as a result of project.

- Notice the reduction in working capital would be a cash inflow at that time.
- 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?

So you see that this is simply a timing problem

1. Calculate all cash flows after taxes

2. Include non-cash expenses (depreciation) for its effect on taxes, but not as a cash flow itself.

- HOW TO HANDLE THE DEPRECIATION TAX SHIELD
We want the project's AFTER TAX CASH FLOW

Equals: Before Tax Cash Flow Less Corporate Taxes

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

Therefore, for each year:

After Tax Cash Flow =(Cash Revue - Cash Expenses)(1 - tc)+ tc Depr

Where: tc x Depr is the Depreciation Tax Shield)

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

Tax on

Gains/Losses = tc x (Market Value - Book Value)

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:
- XYZ Corp. has a project which is going to last 5 years. P & E for this project of $1,000,000 can assume a scrap value of 300,000 at the end of 5 years. On a straight line basis, that means the firm depreciates the assets @ $140,000 per year, leaving 300,000 when the project ends.

- However, you expect that you can sell the asset for $500,000 at the end of 5 years. Thus there is a taxable capital gain of: (MV-BV) = $200,000.
- At a 35% Corporate Capital Gain Tax rate, that means that after tax cash flow from the disposal of P&E is
0.35 * $200,000 = $70,000

Thus the Cash flow from selling the asset is:

$500,000 -70,000 = $430,000

(Remember to add back Book Value)

- 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 1085

- To 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

1. MAKE INITIAL PROJECTIONS

Made by operations manager

Generally in form of income statement

Clarify assumptions

2. ADJUST FOR INFLATION IF APPROPRIATE

3. REARRANGE IN CASH FLOW FORM

4. PERFORM NET PRESENT VALUE CALCULATIONS

5. PERFORM "WHAT IF" CALCULATIONS