capital budgeting net present value (npv) internal rate of return (irr) npv and irr compared payback...
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Capital Budgeting
• Net Present Value (NPV)
• Internal Rate of Return (IRR)
• NPV and IRR compared
• Payback Method
• Accounting Rate of Return
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Net Present Value
k = the discount rate (cost of capital)
n = life of the project
NPVn
i = 1
Annual net
Cash Inflows (1+k)i
= Net Investment-
What is the project worth, in today’s dollars?
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Net Present Value
k = the discount rate (cost of capital)
n = life of the project
NPVn
i = 1
1 _ (1+k)i
= Net Investment
-
What is the project worth in today’s dollars? Now assume annual cash inflows are constant for the life of the project.
Annual
net cash
Inflows
x
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Net Present Value
Table 1Number
of Periods 8% 10% 12%
1 .926 .909 .893
2 .857 .826 .797
3 .794 .751 .712
4 .735 .683 .636
5 .681 .621 .567
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Net Present Value
Advantages:
For choosing among projects, this is probably the best method.
Disadvantages:
No significant disadvantages, although NPV assumes cashflows can be reinvested for a return of k.
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Net Present Value
Example
Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital.
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Net Present Value
Table 1Number
of Periods 8% 10% 12% 10%
1 .926 .909 .893 0.909
2 .857 .826 .797 1.736
3 .794 .751 .712 2.487
2.486
Table 2
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Net Present ValueAcme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 3 years. The cost of the investment is $15,000. What is the net present value of the investment using a 10% cost of capital.
$8,000 x 2.487 = 19,896
$19,896 - $15,000 = $4,896
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Internal Rate of Return
IRR is the interest rate computed such that the NPV of the project is zero.
Annual net
Cash Inflows (1+k)i
Net Investment-
n
i = 1
0 =
Let:
And solve for k. This is the IRR.
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Internal Rate of Return
Advantages:
IRR is a measure of profitability that is independent of the size of the project.
Disadvantages:
Can motivate managers to forego positive net present value projects.
Assumes cash flows can be reinvested at the same internal rate of return.
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Internal Rate of Return
Example
Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment.
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Internal Rate of Return
Example
Acme Mining Company is considering an investment that will yield an annual cash flow of $8,000 per year for 4 years. The cost of the investment is $25,920. What is the internal rate of return on the investment.
$25,920 ÷ $8,000 = 3.24
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Net Present Value
Table 2Number
of Periods 8% 10% 12%
1 .926 .909 .893
2 1.78 1.74 1.69
3 2.58 2.49 2.40
4 3.31 3.17 3.04
5 4.00 3.79 3.61
So interpolating, the IRR is approximately 9%
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IRR and NPV Compared
If the IRR is less than the discount rate, NPV is negative.
If NPV > 0, IRR is greater than the discount rate.
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IRR and NPV ComparedCalculate the NPV and IRR of each project.
EXAMPLE
Year-end
Project Initial Cost Cash Flow
A $1,000 $1,200
B $ 50 $ 100
The project life for both projects is 1 year. Let K = 10%
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IRR and NPV Compared
EXAMPLE
Project Initial Cost Cash flow IRR NPV
A $1,000 $1,200 20% $91
B $ 50 $ 100 100% $41
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Payback
PAYBACK = NET INVESTMENT AVERAGE EXPECTED CASH FLOWAdvantages:
Easy to Calculate.
Disadvantages:
Fails to account for the time value of money.
Ignores returns after the payback period.
How long will it take to recover the investment?
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Accounting Rate of Return
Disadvantage: Ignores the time value of money.
Accounting rate of return =
Average book investmentAverage annual net income
In the simplest scenario, the numerator, net income, is cash flow less depreciation expense; and the denominator, book investment, is the cost of the project, net of accumulated depreciation.
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Accounting Rate of ReturnAccounting rate of return =
Average book investmentAverage annual net income
Example: A machine costs $100,000, and has a useful life of 2 years. The machine will generate revenues net of operating expenses of $70,000 per year. The tax rate is 40%. The company uses straight-line depreciation.
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Accounting Rate of ReturnA machine costs $100K and has a useful life of 2 years. It will generate annual revenues net of operating expenses of $70K. The tax rate is 40%.
Depreciation expense is $50,000 per year ($100,000/2).
The average book investment is also $50,000.
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Accounting Rate of Return
The average of any straight line is the midpoint:
0 21
$100 K
$ 0
$ 50 K
Year 1 Year 2
Zero because the machine has zero salvage value.
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Accounting Rate of ReturnAccounting rate of return =
Average book investmentAverage annual net income
Numerator:
Revenues less operating exp.s $70,000
Depreciation expense 50,000
Income before taxes 20,000
Tax Expense (40% of $20K) 8,000
Net Income 12,000
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Accounting Rate of ReturnAccounting rate of return =
Average book investmentAverage annual net income
$12,000$50,000
= 24%