lecture 10 investing in risk-free projects. a fortune magazine cover story financial markets and...

Lecture 10

Investing in Risk-Free Projects

A Fortune magazine cover story

Financial Markets and Corporate Strategy, David Hillier

“The Real Key to Creating Wealth,” discusses a technique known as Economic Value Added (or EVA™). “Managers who run their businesses according to EVA have hugely increased the value of their companies,” the article reported. Companies that have benefited from EVA include CSX, Briggs and Stratton, and Coca-Cola, all of which have witnessed dramatic increases in their stock prices since the adoption of EVA. Fortune, September 20, 1993.

A Fortune magazine cover story


•Net present value (NPV)•Discounted cash flow (DCF)

•Economic Value Added (EVA™)•The Discount rate: Yield-to-maturity of a zero-coupon bond•Using different discount rates at different maturities

Definitions:NPV: the difference between the project’s present value (PV), the value of a portfolio of financial instruments that track the project’s future cash flows, and the cost of implementing the project

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Project evaluation with the net present value rate


Arbitrage and NPV

Result 10.1 The wealth maximizing net present value criterion is that:•All projects with positive net present values should be accepted.•All projects with negative net present values should be rejected.

The Relation between Arbitrage, NPV, and DCF

Result 10.2 For a project with riskless cash flows, the NPV—that is, the market value of the project’s tracking portfolio less the cost of initiating the project—is the same as the discounted value of all present and future cash flows of the project.

Financing Versus Tracking the Real Asset’s Cash Flows

Example 10.1: The Relation between Arbitrage and NPV


Consider the cash flows below:

Explain how to finance the project so that the combined future cash flows from the project and its financing are zero. What determines whether this is a good or a bad project?Answer: The cash flows from the project at dates 1, 2, and 3 can be offset by1.issuing—that is, selling—short, zero-coupon bonds maturing at date 1 with a face value of £40 million,2.purchasing zero-coupon bonds maturing at date 2 with a face value of £10 million, and3.selling short zero-coupon bonds maturing at date 3 with a face value of £30 million.

The cash flows from this bond portfolio in combination with the project are

Cash Flows (in £ millions) at Date0 1 2 3

20 40 10 30

Cash Flows at Date

0 1 2 3V 0 0 0

Present Values and Net Present Values Have the Value Additivity Property


•Implications of Value Additivity for Project Adoption and Cancellation

•Implications of Value Additivity When Evaluating Mutually Exclusive Projects

Result 10.3 Given a set of investment projects, each with positive NPV, one should select the project with the largest positive NPV if allowed to adopt only one of the projects.

Cash Flows at Date

0 101

0 1

CC

r

Example 10.2: Mutually Exclusive Projects and NPV


The law firm of Jacob & Meyer is small and has the resources to take on only one of four cases. The cash flows for each of the four legal projects and their net present values discounted at the rate of 10 percent per period are given below.

Cash Flows (in £000s)at Date

Net Present Value0 1 2 (in £000s)

Project A 7 11 12.1 13

Project B 1 22 12.1 9

Project C 5 44 24.2 15

Project D 1 11 0 9

Example 10.2: Mutually Exclusive Projects and NPV


Answer: These cash flows are calculated as the cash flows of the firm with the project less the cash flows of the firm without any of the four projects. Clearly, project C has the highest net present value and should be adopted.

Cash Flows (in £000s)at Date

Net Present Value0 1 2 (in £000s)

Project A (less C) 2 33 36.3 2Project B (less C) 4 22 12.1 6Project C (less A) 2 33 36.3 2

Project D(less C) 4 33 24.2 6

Using NPV with capital constraints


•Probability indexThe net present value rule says that one should select projects for which

•Net profitability rate

1 - index)lity (profitabi rate) free-risk (1 rateity profitabilNet

0C if 1 and 0C if 1 00

00

C

PV

C

PV

Example 10.4: The Profitability Index


There is a capital constraint of £10,000 in the initial period. The two scalable projects available for investment are projects B and C from Example 10.2. The cash flows, NPVs at 10 percent, and profitability indexes are given below. Which is the better project?

Answer: Project B is the best because it gives the biggest “bang per buck.”

Cash Flow (in £000s)at Date Net Present

Values Profitability0 1 2 (in £000s) Index

Project B 1 22 12.1 9 10Project C 5 44 24.2 15 4

Using NPV to evaluate projects that can be repeated over time


Example 10.5: Evaluating Projects with Different Lives

Answer:

Cash Flow (in £millions)

at Date Net Present Value(in £millions)0 1 2

Machine A .8 1.1 1.21 1.2Machine B 1.9 3.30 1.1

Cash Flow (in £millions)at Date Net Present Value

0 1 2 (in £millions)Machine A .8 1.1 1.21 1.2First machine B 1.9 3.3 1.1Second machine B

1.9 3.30 1.0

Sum of the twoB machines

1.9 1.4 3.30 2.1

Economic Value Added (EVA)


1 1 00 0

2 2 1

2

1 1 2 1

1

1Discounted stream =

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+ ...1

1 1 +

1 1

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T T

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rC I I r

r

C I I r C I r

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1 2 1

0 2 1 = ...

1 1 1 1T T

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Economic Value Added is simply a way of accounting for the cost of using capital in computing profit. EVA attempts to account for the cash flow impact of capital.

Let It=the date t book value, adjusted for economic depreciation, of the project’s capital assets

Example 10.6: Computing EVAs


Assume that NASA is allowed to select one of three commercial projects for the next space shuttle mission. Each of these projects has industrial spin-offs that will generate cash for NASA over the next two periods. The cash flows and NPVs of the projects are described below.

Answer: The EVAs of the three projects occur only at dates 1 and 2. The following table gives the six EVAs and their present values for each project.

Cash Flow(in $millions) at Date NPV at 2%

0 1 2 (in $millions)Project A 17.0 12 9 3.42Project B 16.8 10 11 3.58Project C 16.9 11 10 3.50

at 2% (in $millions)

Project A 11.660 12 17.0(.02)

8.34 9 17.0(.02) 17.0

3.42

Project B 9.664 = 10 16.8(.02)

6.14 11 16.8(.02) 16.8

3.58

Project C 10.662 11 16.9(.02)

7.24 10 16.9(.02) 16.9

3.50

1PV EVA

2PV EVA

1 $EVA in millions 2 $EVA in millions

Using NPV for Other Corporate Decisions


Example 10.7: Laying Off Workers as an Investment Decision

Ace Farm Equipment is currently suffering from a slowdown in sales and temporary overstaffing. The company can save €600,000 at the end of each of the next three years if it cuts its workforce by 25 individuals. In four years, however, it expects that its market will improve and that it will have to hire replacements for the 25 individuals who were laid off. Ace estimates that the cost of hiring and training workers is €100,000 per employee, or €2.5 million for the 25 employees. If the discount rate is 10 percent per year, should Ace temporarily cut its workforce?

Answer: The incremental cash flows associated with the layoffs are as follows:

2 3 4

€.6 million €.6 million €.6 million €2.5 million€.215 million =

1.1 1.1 1.1 1.1NPV

Cash Flow (in €millions)

at End of Year1 2 3 4

0.6 0.6 0.6 2.5

Using NPV for Other Corporate Decisions


Example 10.8: Cutting Product Price as an Investment Decision

Assume that Local Beers Ltd, currently sells about 10,000 cases of beer per month in the UK, which is 15 percent of the beer market. Management at Local Beers is considering a temporary price cut to attract a larger share of the market. If management chooses to lower beer prices from £4.00 to £3.80 a case, Local Beers will expand its market by 50 percent. Dr. Kaka, the CFO, estimates that the beer costs £3.50 per case, so that the company would be making £5,000 per month with the higher price but only £4,500 per month with the lower price. However, the company plans to stick with the lower price for two years and then raise the price to £3.90 per case. Management believes that at this higher price they still will be able to keep their new customers for the subsequent two years, allowing Local Beers to generate a monthly cash flow of £6,000 per month in years 3 and 4. If the discount rate is 1 percent per month, should prices be lowered?

Answer: The incremental cash flows are as follows:

Cash Flow at the End of Month 1 2 ... 24 25 26 … 48

£500 £500 … £500 £1,000 £1,000 … £1,000

Evaluating Real Investments with the Internal Rate of Return


The internal rate of return (IRR) for a cash flow stream

at dates 0, 1, . . . , T, respectively, is the interest rate y that makes the net present value of a project equal zero; that is, the y that solves

(10.3)

•Intuition for the IRR Method

•Numerical Iteration of the IRR

1 2

0 20 ...

1 1 1T

T

C C CC

y y y

,C . . . ,C ,C T10

Example 10.9: An IRR Calculation and a Comparison with NPV


Clacher’s Snooker Emporium is considering whether to recover its snooker tables, which will generate additional business. The project’s cash flows, which occur at dates 0, 1, 2, and 3, are assumed to be riskless and are described by the following table.

If the yields of riskless zero-coupon bonds maturing at years 1, 2, and 3 are 8 percent, 5 percent, and 6 percent per period, respectively, find the net present value and the internal rate of return of the cash flows.Answer: The NPV, obtained by discounting the cash flows at the zero-coupon yields, is

The IRR is approximately 16.6 percent per period; that is

Cash Flows (in £000s) at Date

0 1 2 3

9 4 5 3

758,1£06.1

000,3£

05.1

000,5£

08.1

000,4£000,9£

32

0£166.1

000,3£

166.1

000,5£

166.1

000,4£000,9£

32

Example 10.10: NPV and IRR with Irregular Periods


A contractor is considering whether to take on a renovation project that will take two and a half years to complete. Under the proposed deal, the contractor has to initially spend more money to pay workers and acquire material than he receives from the customer to start the project. After the initial phase is completed, there is a partial payment for the renovation. A second phase then begins. When the company completes the second phase, the customer makes the final payment. The cash flows of the project are described by the following table:

The respective annualized zero-coupon rates are

Answer: The NPV of the project is:

This is a negative number. The IRR is approximately 6.10 percent per year.

Years from Now: 0 5 1.25 2.5

Cash flows (in €000s): 10 5 15 18

Years to Maturity: .5 1.25 2.5Yield (% year): 6% 6% 8%

.5 1.25 2.5

€5,000 €15,000 €18,000€10,000 €4,240

1.06 1.06 1.08

Example 10.11: Multiple Internal Rates of Return


Strip Mine, Inc., is considering a project with cash flows described in the following table

Compute the IRR of this project.

Answer:

This project has two internal rates of return, 213.19 percent and 0 percent, determined by making different initial guesses in the IRR program of a financial calculator or spreadsheet.

Cash Flows (in $millions) at Date

0 1 2 3

10 41 30 1

Exhibit 10.1 Net Present Value for Cash Flows in Example 10.11 as a Function of Discount Rates


Exhibit 10.2 Net Present Value for Cash Flows in Example 10.12 as a Function of Discount Rates


Result 10.5


The appropriate hurdle rate for comparison with the IRR is that which makes the sum of the discounted future cash flows of the project equal to the selling price of the tracking portfolio of the future cash flows.

Cash flow sign patterns and the number of internal rates of return


•Later cash flow streams•Early cash flow streams •The correct hurdle rate with multiple hurdle rates

Date 0-5 Time Line

Cash Flow Sign at Date

0 1 2 3 4 5

Example 10.14: Implementing the IRR Rule for Investing


Refer to the Clacher’s Snooker Emporium project in Example 10.9, where the stream of cash flows (in £000s) at dates 0, 1, 2, and 3 was respectively, with associated zero-coupon yields of 8 percent, 5 percent, and 6 percent at maturity dates 1, 2, and 3, respectively. How does the IRR compare with the hurdle rate for the project?

Answer:

The yield to maturity (or IRR), y, of the bond portfolio that tracks the future cash flows of the project satisfies the equation

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000,3£

)1(

000,5£

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000,4£

06.1

000,3£

05.1

000,5£

08.1

000,4£

yyy

Example 10.15: Implementing the IRR Rule for Borrowing Needs


Consider the cancellation of the project in Example 10.14, immediately after Clacher’s Snooker Emporium made the adoption decision. In other words, the decision was made not to recover the snooker tables following the earlier decision to recover them. What are the cash flows from canceling the project? How does the IRR compare with the hurdle rate in this case?

Answer: The relevant incremental cash flows for the cancellation decision (a project in its own right) are found by subtracting the cash flow position of the snooker emporium when it adopted the table recovering project from its cash flow position without the project. These cash flows are simply the negatives of the cash flows in Example 10.3: £9,000 at t 0, £4,000 at t 1, £5,000 at t 2, and £3,000 at t 3. The net present value calculation is

758,1£06.1

000,3£

05.1

000,5£

08.1

000,4£000,9£

32

Result 10.6 -The appropriate internal rate of return rule


In the absence of constraints, a project with a later cash flow stream should be adopted only if its internal rate of return exceeds the hurdle rate(s). A project with an early cash flow stream should only be adopted if the hurdle rate(s) exceed the internal rate of return of the project.

Mutually Exclusive Projects and the Internal Rate of Return


•Do Not Select the Project with the Largest IRR

•How Multiple Internal Rates of Return Arise from Mutually Exclusive Projects

Result 10.7

The project with the largest IRR is generally not the project with the highest NPV and thus is not the best among a set of mutually exclusive projects.

Example 10.17: Mutually Exclusive Projects and the IRR


Consider a firm with two projects, each with a discount rate of 2 percent per period. The following table describes their cash flows, net present values, and internal rates of return.

Given that the firm must select only one project, should it choose A or B?

Answer: The net present value of project A, about €3.149 million, is higher than the net present value of B, about €2.534 million. Thus, project A is better than project B, even though it has a lower internal rate of return.

Cash Flows at Date

NPV at 2%0 1 2 (in €millions) IRR

Project A 10 16 30 €3.149 10.79%Project B 10 2 11 €2.534 15.36%

Popular but incorrect procedures for evaluating real investments


•The payback method

•The accounting rate of return

criterion

•Return on assets

Thank You

lecture 10 investing in risk-free projects. a fortune magazine cover story financial markets and...

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