Investment Decisions -Net Present Value and others-
Capital-Budgeting
The process of decision making with respect to investments in fixed assets that is, should a proposed project be accepted or rejected.
It is easier to evaluate profitable projects than to find them.
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Source of Ideas for projects
Within the Firm: Typically, a firm has a research & development (R&D) department that searches for ways of improving existing products or finding new projects.
Other sources: Competition, Suppliers, Customers
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Capital-Budgeting Decision Criteria
1. Net Present Value
2. Internal Rate of Return
3. Payback Period
4. Profitability Index
5. Capital Rationing
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Net Present Value or NPV
NPV is equal to the present value of all future free cash flows less the investments initial outlay. It measures the net value of a project in todays dollars. NPV = FCF - Initial outlay
(1+k)n
Decision Rule:
If NPV > 0, accept If NPV < 0, reject
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NPV Example
Example: Project with an initial cash outlay of $60,000 with following free cash flows for 5 years.
Yr FCF
Initial outlay -60,000
1 25,000
2 24,000
3 13,000
4 12,000
5 11,000
The firm has a 15% required rate of return.
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NPV = - Initial outlay + FCF
(1+k)n
PV of FCF = $60,764
Subtracting the initial cash outlay of $60,000 leaves an NPV of $764.
Since NPV>0, project is feasible.
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NPV in Excel
Input cash flows for initial outlay and inflows in cells A1 to A6
In cell A7 type the following formula:
=A1+npv(.15,a2:a6)
Excel will give the NPV = $764
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NPV Trade-offs
Benefits
Considers cash flows, not profits
Considers all cash flows
Recognizes time value of money
By accepting only positive NPV projects, increases value of the firm
Drawbacks
Requires detailed long-term forecast of cash flows
NPV is considered to be the most theoretically correct criterion for evaluating capital-budgeting projects.
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Internal Rate of Return or IRR
IRR is the discount rate that equates the present value of a projects future net cash flows with the projects initial cash outlay
Decision Rule:
If IRR > Required rate of return, accept
IF IRR < Required rate of return, reject
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IRR and NPV
If NPV is positive, IRR will be greater than the required rate of return
If NPV is negative, IRR will be less than required rate of return
If NPV = 0, IRR is the required rate of return.
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IRR Example
Initial Outlay: $3,817
Cash flows:
Yr.1=$1,000, Yr. 2=$2,000, Yr. 3=$3,000
Discount rate NPV
15% $4,356
20% $3,958
22% $3,817
IRR is 22% because the NPV equals the initial cash outlay
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Payback Period
Number of years needed to recover the initial cash outlay of a capital-budgeting project
Decision Rule: Project feasible or desirable if the payback period is less than or equal to the firms maximum desired payback period.
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Payback Period Example
Example: Project with an initial cash outlay of $20,000 with following free cash flows for 5 years.
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YEAR CASH FLOW BALANCE
1 $ 8,000 ($ 12,000)
2 4,000 ( 8,000)
3 3,000 ( 5,000)
4 5,000 0
5 10,000 12,000
Payback is 4 years
Trade-offs
Benefits:
Uses cash flows rather than accounting profits
Easy to compute and understand
Useful for firms that have capital constraints
Drawbacks:
Ignores the time value of money and
Does not consider cash flows beyond the payback period.
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Profitability Index (PI)
PI is the ratio of the present value of the future free cash flows to the initial outlay. It yields the same accept/reject decision as NPV.
PI = PV FCF/ Initial outlay
Decision Rule:
PI > 1 = accept
PI < 1 = reject
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PI Example
A firm with a 10% required rate of return is considering investing in a new machine with an expected life of six years. The initial cash outlay is $50,000.
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PI Example
FCF PVF @ 10% PV
Initial Outlay
-$50,000 1.000 -$50,000
Year 1 15,000 0.909 13,636
Year 2 8,000 0.826 6,612
Year 3 10,000 0.751 7,513
Year 4 12,000 0.683 8,196
Year 5 14,000 0.621 8,693
Year 6 16,000 0.564 9,032
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PI Example
PI = ($13,636 + $6,612+$7,513 + $8,196 + $8,693+ $9,032) / $50,000
=$53,682/$50,000 = 1.0736 Project PI > 1, accept.
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NPV and PI
When the present value of a projects free cash inflows are greater than the initial cash outlay, the project NPV will be positive. PI will also be greater than 1.
NPV and PI will always yield the same decision.
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Capital Rationing
Capital Rationing
Capital rationing occurs when a limit is placed on the dollar size of the capital budget.
How to select: Select a set of projects with the highest NPVs subject to the capital constraint. Using NPV may preclude accepting the highest ranked project in terms of PI or IRR.
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Ranking Problems
Size Disparity
Time Disparity
Unequal Life
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Size Disparity This occurs when we examine mutually exclusive projects of unequal
size.
Example: Consider the following cash flows for one-year Project A and B, with required rates of return of 10%. Initial Outlay: A = $200 B = $1,500
Inflow: A = $300 B = $1,900
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Size Disparity
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Size Disparity
Which technique to use to select the better project?
Use NPV whenever there is size disparity. If there is no capital rationing, project with the largest NPV will be selected. When capital rationing exists, select set of projects with the largest NPV.
But, small companies uses in general IRR when capital rationing exists.
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Time Disparity Problem
Time Disparity problems arise because of differing reinvestment assumptions made by the NPV and IRR decision criteria.
Cash flows reinvested at:
According to NPV: Required rate of return
According to IRR: IRR
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Example: Consider two projects, A and B, with initial outlay of $1,000, cost of capital of 10%, and following cash flows in years 1, 2, and 3:
1 2 3
A: $100 $200 $2,000
B: $650 $650 $650
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Time Disparity Problem
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Time Disparity Problem
Project A Project B NPV 758.83 616.45 PI 1.759 1.616 IRR 35% 43%
Ranking Conflict: Using NPV, A is better Using IRR, B is better
Which technique to use to select the superior project?: Use NPV (especially in lease calculations)
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Unequal Lives Problem
This occurs when we are comparing two mutually exclusive projects with different life spans.
To compare projects, we compute the Equivalent Annual Annuity (EAA)
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Unequal Lives Problem
Example: If you have two projects, A and B, with equal investment of $1,000, required rate of return of 10%, and following cash flows in years 1-3 (for project A) and 1-6 (for project B)
Project A = $500 each in years 1-3
Project B = $300 each in years 1-6
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Computing EAA
1. Calculate projects NPV:
A = $243.43 and B = $306.58
2. Calculate EAA = NPV/annual annuity factor
A = $97.89 B = $70.39
3. Project A is better
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