Download - Capital budgeting
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Capital Budgeting
DecisionCriteria
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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?
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Decision-making Criteria in Capital Budgeting
How do we decide if a capital investment
project should be accepted or
rejected?
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• 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
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Payback Period
• How long will it take for the project to generate enough cash to pay for itself?
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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
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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.
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• 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
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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.
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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.
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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
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Net Present Value
Decision Rule:
If NPV is positive, accept. If NPV is negative, reject.
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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%.
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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%.
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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
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Profitability Index
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Profitability Index
NPV = - IO FCFt
(1 + k) t
n
t=1
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Profitability Index
PI = IO FCFt
(1 + k)
n
t=1 t
NPV = - IO FCFt
(1 + k) t
n
t=1
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Decision Rule:
If PI is greater than or equal to 1, accept.
If PI is less than 1, reject.
Profitability Index
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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.
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Internal Rate of Return (IRR)
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Internal Rate of Return (IRR)
NPV = - IO FCFt
(1 + k) t
n
t=1
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Internal Rate of Return (IRR)
NPV = - IO FCFt
(1 + k) t
n
t=1
n
t=1IRR: = IO
FCFt
(1 + IRR) t
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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
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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
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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%!
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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.
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• 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. (- + + - + +)
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• 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
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• 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
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• 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
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• 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
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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
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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
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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.
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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
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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
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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%.
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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%.