Internal Rate of Return Example
Initial investment is $303,280.
Useful life is five years.
Net cash inflows is $80,000 per year.
What is the IRR of this project?
$303,280 ÷ $80,000 = 3.791 (PV annuity factor)
10% (from the table, five-period line)
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Comparison of NPV and IRR
The NPV method has the advantage that the end result of the computations is expressed in dollars and not in a percentage.
Individual projects can be added.
It can be used in situations where the required rate of return varies over the life of the project.
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Comparison of NPV and IRR
The IRR of individual projects cannot be added or averaged to derive the IRR of a combination of projects.
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Learning Objective 4
Use and evaluate the payback method.
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Payback Method
Payback measures the time it will take to recoup, in the form of expected future cash flows, the initial investment in a project.
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Payback Method Example
Assisted Living is considering buying Machine 1.
Initial investment is $210,000.
Useful life is eleven years.
Estimated residual value is zero.
Net cash inflows is $35,000 per year.
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Payback Method Example
How long would it take to recover the investment?
$210,000 ÷ $35,000 = 6 years
Six years is the payback period.
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Payback Method Example
Suppose that as an alternative to the $210,000 piece of equipment, there is another one
(Machine 2) that also costs $210,000 but will save $42,000 per year during its five-year life .
What is the payback period?
$210,000 ÷ $42,000 = 5 years
Which piece of equipment is preferable?
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Payback Method Example
Assisted Living is considering buying Machine 3.
Initial investment is $250,000.
Useful life is eleven years.
Cash savings are $160,000, $180,000, and $110,000 over its life.
What is the payback period?
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Payback Method Example
Year 1 brings in $160,000.
Recovery of the amount invested occurs in Year 2.
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Payback Method Example
=
=
+
÷
Payback = 1 year
$ 90,000 needed to complete recovery
180,000 net cash inflow in Year 2
1 year + 0.5 year
1.5 years or 1 year and 6 months
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Learning Objective 5
Use and evaluate the accrual accounting rate-of-return
(AARR) method.
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Accrual Accounting
Rate-of-Return Method
The accrual accounting rate-of-return (AARR) method divides an accounting measure of income by an accounting measure of investment.
AARR =
Increase in expected average annual operating income
÷
Initial required investment
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Accrual Accounting
Rate-of-Return Method Example
Initial investment is $303,280.
Useful life is five years.
Net cash inflows is $80,000 per year.
IRR is 10%.
What is the average operating income?
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Accrual Accounting
Rate-of-Return Method Example
Straight-line depreciation is $60,656 per year.
Average operating income is
$80,000 – $60,656 = $19,344.
What is the AARR?
AARR
= ($80,000 – $60,656) ÷ $303,280
= .638, or 6.4%
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Learning Objective 6
Identify and reduce conflicts from using DCF for capital budgeting decisions and accrual accounting for performance evaluation.
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Performance Evaluation
A manager who uses DCF methods to make capital budgeting decisions can face goal congruence problems if AARR is used for performance evaluation.
Suppose top management uses the AARR to judge performance if the minimum desired rate of return is 10%.
A machine with an AARR of 6.4% will be rejected.
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Performance Evaluation
The conflict between using AARR and
DCF methods to evaluate performance can be reduced by evaluating managers on a project-by-project basis.
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End of Chapter 21
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