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Chapter 8

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Economics

ECON 2560

Tahsin Mehdi

Summer

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Chapter 8 ECON 2560
Net Present Value & Other Investment Criteria
NET PRESENT VALUE
Opportunity cost of capital: Expected rate of return given up by investing in a project (also known as discount rate)
Net present value (NPV): Present value of cash flows minus initial investment
A comment on risk and present value
You can guess/predict/forecast the value of future investments but will never be certain
Most investors avoid risk when they can do so without sacrificing return
Not all projects are equally risky
Valuing long-lived projects
NPV rule works for projects of any length
PV = C 1 + C 2 + C 3
(1 + r) (1+r)2 (1+r)3
If multiple years it can be smarter to recognize the cash flows are level and you can use the annuity formula to calculate present
value
PV = cash flow x annuity factor x [(1/ discount rate) – (1/ discount rate (1 + discount rate) ^ years)]
NPV calculations are only as good as the underlying cash-flow forecast
“Pentagon law of large projects” says that anything big takes longer & costs more than you were originally led to believe
Using the NPV Rule to choose among projects
Mutually exclusive projects: 2 or more projects that can’t be pursued simultaneously
Almost all real world decisions are either-or choices = mutually exclusive
When need to choose between mutually exclusive projects, the decision rule says calculate the NPV of each project and
from those options choose the one w/ the highest positive NPV
OTHER INVESTMENT CRITERIA
A project w/ a positive NPV is worth more than it costs so it will be making its shareholders better off
Management will look at NVP but also may look at projects payback or discounted payback and its internal rate of return
Payback
Payback period: Time until cash flows recover the initial investment of the project
Payback rule states that a project should be accepted if its payback period is less than a specified cut-off period
Problems can occur as if the cut-off point prevent analyzing what inflows the next period could bring
To use payback rule a firm has to decide on an appropriate cut-off period depending on project life
The main attraction of payback criterion is simplicity but it saves you only the easy part of analysis
Payback is most commonly used when the capital investment Is small or when the merits of the project are so obvious that
more formal analysis isn’t needed
Discounted Payback
Discounted Payback period: The # of periods before the present value of prospective cash flows equals or exceeds the initial
investment
The defeats the objection that equal weight is given to all cash flows before the cut-off date BUT still doesn’t account the
cash flows after cut-off date
Easier to use then the NPV rule but better than the payback rule Internal Rate of Return
Instead of calculating a projects NPV, companies often will prefer to ask whether the project’s return is higher or lower than
the opportunity cost of capital
Rate of return = Profit = C1 – investment
Investment Investment
Two rules for whether to proceed w/ investment project…
1. The NPV Rule: Invest in any project that has a positive NPV when its cash flows are discounted at the opportunity cost of
capital
2. The Rate of Return Rule: Invest in any project offering a rate of return that’s higher than the opportunity cost of capital
*The 2 rules set the same cut-off point
NPV = C0+ C1___
(1 + r)
*If project ends w/ NPV of zero the project makes you no richer or poorer and so it is worth what it costs
Calculating the Rate of Return for Long-Lived Projects
C0= The time 0 cash flow which is the initial investment is negative
Rate of Return = Profit = C - Investment = C + C
1 1 0
Investment Investment - C0
Internal rate of return (IRR)/ Discounted cash flow (DCF): The discount rate at which a project NPV = 0
The usual agreement between the NPV & Internal rate of return rules should not come

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