2002, Prentice Hall, Inc.

Ch. 9: Capital Budgeting

DecisionCriteria

Capital Budgeting: the process of planning for purchases of long-

term assets.

• example:

Suppose our firm must decide whether to purchase a new plastic molding machine for $125,000. How do we decide?

• Will the machine be profitable?

• Will our firm earn a high rate of return on the investment?

Decision-making Criteria in Capital Budgeting

How do we decide if a capital investment

project should be accepted or

rejected?

• The Ideal Evaluation Method should:

a) include all cash flows that occur during the life of the project,

b) consider the time value of money,

c) incorporate the required rate of return on the project.

Decision-making Criteria in Capital Budgeting

Payback Period

• How long will it take for the project to generate enough cash to pay for itself?

Payback Period

• How long will it take for the project to generate enough cash to pay for itself?

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Payback Period

• How long will it take for the project to generate enough cash to pay for itself?

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 150 150 150

Payback period = 3.33 years.

• Is a 3.33 year payback period good?

• Is it acceptable?

• Firms that use this method will compare the payback calculation to some standard set by the firm.

• If our senior management had set a cut-off of 5 years for projects like ours, what would be our decision?

• Accept the project.

Payback Period

Drawbacks of Payback Period

• Firm cutoffs are subjective.

• Does not consider time value of money.

• Does not consider any required rate of return.

• Does not consider all of the project’s cash flows.

Drawbacks of Payback Period

• Does not consider all of the project’s cash flows.

• Consider this cash flow stream!

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 (300) 0 0

Drawbacks of Payback Period

• Does not consider all of the project’s cash flows.

• This project is clearly unprofitable, but we would accept it based on a 4-year payback criterion!

0 1 2 3 4 5 86 7

(500) 150 150 150 150 150 (300) 0 0

Discounted Payback

• Discounts the cash flows at the firm’s required rate of return.

• Payback period is calculated using these discounted net cash flows.

Problems:

• Cutoffs are still subjective.

• Still does not examine all cash flows.

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.37

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.37 2 years

88.33

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.37 2 years

88.33

3 250 168.74

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.37 2 years

88.33

3 250 168.74 .52 years

Discounted Payback

0 1 2 3 4 5

(500) 250 250 250 250 250

Discounted

Year Cash Flow CF (14%)

0 -500 -500.00

1 250 219.30 1 year

280.70

2 250 192.37 2 years

88.33

3 250 168.74 .52 years

The Discounted Payback

is 2.52 years

Other Methods

1) Net Present Value (NPV)

2) Profitability Index (PI)

3) Internal Rate of Return (IRR)

Each of these decision-making criteria:

• Examines all net cash flows,

• Considers the time value of money, and

• Considers the required rate of return.

Net Present Value

NPV = the total PV of the annual net cash flows - the initial outlay.

NPVNPV = - IO = - IO FCFFCFtt

(1 + k)(1 + k) tt

nn

t=1t=1

Net Present Value

Decision Rule:

If NPV is positive, accept. If NPV is negative, reject.

NPV ExampleNPV Example

• Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

NPV ExampleNPV Example

0 1 2 3 4 5

(250,000) 100,000 100,000 100,000 100,000 100,000

• Suppose we are considering a capital investment that costs $250,000 and provides annual net cash flows of $100,000 for five years. The firm’s required rate of return is 15%.

Net Present Value (NPV)

NPV is just the PV of the annual cash flows minus the initial outflow.

Using TVM:

P/Y = 1 N = 5 I = 15

PMT = 100,000

PV of cash flows = $335,216

- Initial outflow: ($250,000)

= Net PV $85,216

NPV with the HP10B:

• -250,000 CFj

• 100,000 CFj

• 5 shift Nj

• 15 I/YR

• shift NPV

• You should get NPV = 85,215.51.

NPV with the HP17BII:

• Select CFLO mode.• FLOW(0)=? -250,000 INPUT• FLOW(1)=? 100,000 INPUT• #TIMES(1)=1 5 INPUT

EXIT• CALC 15 I% NPV• You should get NPV = 85,215.51

NPV with the TI BAII Plus:

• Select CF mode.

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

• C01=? 100,000 ENTER

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

• C01=? 100,000 ENTER

• F01= 1 5 ENTER

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

• C01=? 100,000 ENTER

• F01= 1 5 ENTER

• NPV I= 15 ENTER

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

• C01=? 100,000 ENTER

• F01= 1 5 ENTER

• NPV I= 15 ENTER CPT

NPV with the TI BAII Plus:

• Select CF mode.

• CFo=? -250,000 ENTER

• C01=? 100,000 ENTER

• F01= 1 5 ENTER

• NPV I= 15 ENTER CPT

• You should get NPV = 85,215.51

Profitability Index

Profitability Index

NPV = - IO FCFt

(1 + k) t

n

t=1

Profitability Index

PI = IO FCFt

(1 + k)

n

t=1 t

NPV = - IO FCFt

(1 + k) t

n

t=1

Decision Rule:

If PI is greater than or equal to 1, accept.

If PI is less than 1, reject.

Profitability Index

PI with the HP10B:

• -250,000 CFj• 100,000 CFj• 5 shift Nj • 15 I/YR • shift NPV• Add back IO:+ 250,000• Divide by IO: / 250,000 =• You should get PI = 1.34

Internal Rate of Return (IRR)

• IRR: the return on the firm’s invested capital. IRR is simply the rate of return that the firm earns on its capital budgeting projects.

Internal Rate of Return (IRR)

Internal Rate of Return (IRR)

NPV = - IO FCFt

(1 + k) t

n

t=1

Internal Rate of Return (IRR)

NPV = - IO FCFt

(1 + k) t

n

t=1

n

t=1IRR: = IO

FCFt

(1 + IRR) t

Internal Rate of Return (IRR)

• IRR is the rate of return that makes the PV of the cash flows equal to the initial outlay.

• This looks very similar to our Yield to Maturity formula for bonds. In fact, YTM is the IRR of a bond.

n

t=1IRR: = IO

FCFt

(1 + IRR) t

Calculating IRR

• Looking again at our problem:

• The IRR is the discount rate that makes the PV of the projected cash flows equal to the initial outlay.

0 1 2 3 4 5

(250,000) 100,000 100,000 100,000 100,000 100,000

IRR with your Calculator

• IRR is easy to find with your financial calculator.

• Just enter the cash flows as you did with the NPV problem and solve for IRR.

• You should get IRR = 28.65%!

IRR

Decision Rule:

If IRR is greater than or equal to the required rate of return, accept.

If IRR is less than the required rate of return, reject.

• IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +)

• Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

• IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +)

• Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

• IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +)

• Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 1

• IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +)

• Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2

• IRR is a good decision-making tool as long as cash flows are conventional. (- + + + + +)

• Problem: If there are multiple sign changes in the cash flow stream, we could get multiple IRRs. (- + + - + +)

0 1 2 3 4 5

(500) 200 100 (200) 400 300

1 2 3

Summary Problem

• Enter the cash flows only once.

• Find the IRR.

• Using a discount rate of 15%, find NPV.

• Add back IO and divide by IO to get PI.

0 1 2 3 4 5

(900) 300 400 400 500 600

Summary Problem

• IRR = 34.37%.

• Using a discount rate of 15%,

NPV = $510.52.

• PI = 1.57.

0 1 2 3 4 5

(900) 300 400 400 500 600

Modified Internal Rate of Return(MIRR)

• IRR assumes that all cash flows are reinvested at the IRR.

• MIRR provides a rate of return measure that assumes cash flows are reinvested at the required rate of return.

MIRR Steps:

• Calculate the PV of the cash outflows.– Using the required rate of return.

• Calculate the FV of the cash inflows at the last year of the project’s time line. This is called the terminal value (TV).– Using the required rate of return.

• MIRR: the discount rate that equates the PV of the cash outflows with the PV of the terminal value, ie, that makes:

• PVoutflows = PVinflows

MIRR• Using our time line and a 15% rate:

• PV outflows = (900)

• FV inflows (at the end of year 5) = 2,837.

• MIRR: FV = 2837, PV = (900), N = 5

• solve: I = 25.81%.

0 1 2 3 4 5

(900) 300 400 400 500 600

MIRR• Using our time line and a 15% rate:

• PV outflows = (900)

• FV inflows (at the end of year 5) = 2,837.

• MIRR: FV = 2837, PV = (900), N = 5

• solve: I = 25.81%.

• Conclusion: The project’s IRR of 34.37%, assumes that cash flows are reinvested at 34.37%.

MIRR• Using our time line and a 15% rate:

• PV outflows = (900)

• FV inflows (at the end of year 5) = 2,837.

• MIRR: FV = 2837, PV = (900), N = 5

• solve: I = 25.81%.

• Conclusion: The project’s IRR of 34.37%, assumes that cash flows are reinvested at 34.37%.

• Assuming a reinvestment rate of 15%, the project’s MIRR is 25.81%.