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CHAPTER 10

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The Basics of Capital Budgeting

Omar Al Nasser, Ph.D.

FIN 6352

- Net Present Value
- The Payback Rule
- The Internal Rate of Return
- The Profitability Index

CF2

CF1

CFN

NPV = + + ··· + − Initial cost

(1 + r )1

(1 + r)2

(1 + r)N

The Big Picture:

The Net Present Value of a Project

Project’s Cash Flows (CFt)

Project’s

debt/equity capacity

Market

interest rates

Project’s risk-adjusted

cost of capital

(r)

Project’s

business risk

Market

risk aversion

Analysis of potential projects.

Long-term decisions; involve large expenditures.

Very important to firm’s future.

- The difference between the market value of a project and its cost
- How much value is created from undertaking an investment?
- The first step is to estimate the expected future cash flows.
- The second step is to estimate the required return for projects of this risk level.
- The third step is to find the present value of the cash flows and subtract the initial investment.

- If the NPV is positive, accept the project
- A positive NPV means that the project is expected to add value to the firm and will therefore increase the wealth of the owners.
- Since our goal is to increase owner wealth, NPV is a direct measure of how well this project will meet our goal.

n

CFt

.

∑

NPV =

(1 + r)t

t = 0

n

CFt

.

∑

- CF0 .

NPV =

(1 + r)t

t = 1

- NPV equal to the PV of future net cash flows, discounted at the cost of capital.

Cost often is CF0 and is negative.

- You are looking at a new project and you have estimated the following cash flows:
- Year 0:CF = -165,000
- Year 1:CF = 63,120;
- Year 2:CF = 70,800;
- Year 3:CF = 91,080;

- Your required return for assets of this risk is 12%.

- Using the formulas:
- NPV = 63,120/(1.12) + 70,800/(1.12)2 + 91,080/(1.12)3 – 165,000 = $12,627.41

- Using the calculator:
- CF0 = -165,000; C01 = 63,120; F01 = 1; C02 = 70,800; F02 = 1; C03 = 91,080; F03 = 1; NPV; I = 12; CPT NPV = 12,627.41

- Do we accept or reject the project?

0

0

1

1

2

2

3

3

10%

10%

S’s CFs:

L’s CFs:

-100.00

-100.00

70

10

60

50

20

80

0

1

2

3

10%

L’s CFs:

-100.00

10

60

80

9.09

49.59

60.11

18.79 = NPVL

NPVS = $19.98.

-100

10

60

80

10

CF0

CF1

CF2

CF3

I

NPV

= 18.78 = NPVL

Projects are:

independent, if the cash flows of one are unaffected by the acceptance of the other.

mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

If Franchises S and L are mutually exclusive, accept S because NPVs > NPVL.

If S & L are independent, accept both; NPV > 0.

NPV is dependent on cost of capital.

- The number of years required for an investment to recover its cost, or how long does it take to get the business’s money back?
- Computation
- Estimate the cash flows
- Subtract the future cash flows from the initial cost until the initial investment has been recovered

- Decision Rule – Accept if the payback period is less than some preset limit

2.4

0

1

2

3

CFt

-100

10

60

80

-30

Cumulative

-100

-90

0

50

2+30/80 = 2.375 years

PaybackL

=

1.6

0

1

2

3

CFt

-100

70

50

20

Cumulative

-100

20

40

-30

0

1 + 30/50 = 1.6 years

PaybackS

=

Strengths:

Provides an indication of a project’s risk and liquidity.

Easy to calculate and understand.

Weaknesses:

Ignores CFs occurring after the payback period.

Unlike the NPV, which tells us by how much the project should increase shareholder wealth, the payback tells us when we get our investment back.

No specification of acceptable payback.

- This is the most important alternative to NPV
- It is based entirely on the estimated cash flows and is independent of interest rates found elsewhere.
- IRR is the discount rate that forces a project’s NPV to equal zero.
- Decision Rule: Accept the project if the IRR is greater than the required return

n

CFt

∑

= NPV

.

(1 + r)t

t = 0

n

CFt

∑

= 0

.

(1 + IRR)t

t = 0

IRR: Enter NPV = 0, solve for IRR.

0

1

2

3

IRR = ?

-100.00

10

60

80

PV1

PV2

PV3

Enter CFs in CFLO, then press IRR: IRRL = 18.13%. IRRS = 23.56%.

0 = NPV

-100

10

60

80

CF0

CF1

CF2

CF3

IRR

= 18.13% = IRRL

- If IRR > the required return , then the project’s rate of return is greater than its cost– the project expected to earn more than the cost of capital need to finance the project.
- Example:
the required return = 10%, IRR = 15%.

- So this project adds extra return to shareholders.

If S and L are independent, accept both: IRRS > r and IRRL > r.

If S and L are mutually exclusive, accept S because IRRS > IRRL.

- NPV and IRR will generally give us the same decision
- Despite a strong academic preference for NPV, surveys indicate that executives prefer IRR over NPV because managers find it more appealing to evaluate investments in terms of percentage rates of return than dollars of NPV.
- However, you should always use NPV as your decision criteria because it selects the project that adds the most to shareholder’s wealth.
- Whenever there is a conflict between NPV and another decision rule, you should always use NPV

- MIRR is the discount rate which causes the PV of a project’s terminal value (TV) to equal the PV of costs.
- TV is found as the sum of the future values of the cash inflows compounded at the firm’s cost of capital.
- MIRR assumes that all cash flows are reinvested at the firm's cost of capital. Therefore, MIRR more accurately reflects the profitability of a project.

0

1

2

3

10%

L’s CFs:

-100.00

10

60

80

Project L:

0

1

2

3

10%

10

60

80

9.09

49.59

60.11

118.79

First, enter cash inflows in CFLO register:

CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80

Second, enter I/YR = 10.

Third, find PV of inflows:

Press NPV = 118.78

Enter PV = -118.78, N = 3, I/YR = 10, PMT = 0.

Press FV = 158.10 = FV of inflows.

For this problem, there is only one outflow, CF0 = -100, so the PV of outflows is -100.

Enter FV = 158.10, PV = -100, PMT = 0, N = 3.

Press I/YR = 16.50% = MIRR.

- First, enter cash inflows in CFLO register:
- CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
- Second, enter I = 10.
- Third, find PV of inflows:
- Press NPV = 118.78
Then:

- Enter PV = -118.78, N = 3, I = 10, PMT = 0.
- Press FV = 158.10 = FV of inflows.
Then:

- Enter FV = 158.10, PV = -100, PMT = 0, N = 3.
- Press I = 16.50% = MIRR.

- The profitability index (PI) is the present value of future cash flows divided by the initial cost.
- Profitability index is a good tool for ranking projects because it allows you to clearly identify the amount of value created per unit of investment.
- If PI > 1 then accept the project if PI < 1 then reject the project.
- The higher the PI, the higher the project’s ranking.

Project L:

0

1

2

3

10%

10

60

80

9.09

49.59

60.11

118.79

$118.79

PV future CF

PIL =

=

Initial Cost

$100

PIL = 1.1879

PIS = 1.1998

- So project L is expected to produce $1.1879 for each $1 of investment. A profitability index of 1.1879 implies that for every $1 of investment, we receive $ 1.1879 worth of benefits, so we create an additional $0.1879 in value
- Both projects should be accepted by PI, but project S will be ranked ahead of L because it has a higher PI .

- An investment project has the following cash flows: CF0 = -1,000,000; C01 – C08 = 200,000 each
- If the required rate of return is 12%, what decision should be made using NPV?
- What decision should be made using IRR?

- You are looking at a new project and you have estimated the following cash flows:
- Year 0:CF = -165,000
- Year 1:CF = 63,120;
- Year 2:CF = 70,800;
- Year 3:CF = 91,080;

- Your required return for assets of this risk is 12%.

- Spreadsheets are an excellent way to compute NPVs, especially when you have to compute the cash flows as well.
- Using the NPV function
- The first component is the required return entered as a decimal
- The second component is the range of cash flows beginning with year 1
- Subtract the initial investment after computing the NPV
- Check your calculations with a hand held calculator to ensure that the formulae have been correctly set up.

- You start with the cash flows the same as you did for the NPV
- You use the IRR function
- You first enter your range of cash flows, beginning with the initial cash flow
- You can enter a guess, but it is not necessary
- The default format is a whole percent – you will normally want to increase the decimal places to at least two

- The profitability index (PI) is the present value of future cash flows divided by the initial cost.
- You start with the calculating the PV of future cash flows, then divided by the initial cost.

PV future CF

PI =

Initial Cost

- Modified Internal Rate of Return – the cash flow cell range is the same as in the IRR, but both the required rate of return, and the re-investment rate, are entered into the formula.