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**Unformatted text preview: **ve years. The firm’s
$100,000
required rate of return is 15%.
15%
(250,000) 100,000 100,000 100,000 100,000 100,000 0 1 2 3 4 5 Net Present Value
Net
NPV is just the PV of the annual cash
NPV
flows minus the initial outflow.
flows
Using TVM: P/Y = 1 N = 5
P/Y
PMT = 100,000
PMT I = 15 PV of cash flows = $335,216
PV
$335,216
- Initial outflow: ($250,000)
Initial
($250,000)
= Net PV
$85,216
Net
$85,216 Rationale for the NPV method
Rationale
NPV = PV of inflows – Cost
= Net gain in wealth If projects are independent, accept if the
If
project NPV > 0.
project If projects are mutually exclusive, accept
If
projects with the highest positive NPV, those
highest
those
that add the most value.
that Profitability Index Profitability Index
n NPV = Σ t=1 FCFt
t
(1 + k) - IO Profitability Index
n NPV = Σ t=1
n PI = Σ t=1 FCFt
t
(1 + k) - IO FCFt
(1 + k) t IO Profitability Index
• Decision Rule:
• If PI is greater than or equal
to 1, accept.
• If PI is less than 1, reject. Internal Rate of Return: IRR
Internal
0 1 2 3 CF0
Cost CF1 CF2
Inflows CF3 IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0. Internal Rate of Return (IRR)
Internal IRR: The return on the firm’s
invested capital. IRR is simply the
rate of return that the firm earns on
rate
its capital budgeting projects.
its Internal Rate of Return (IRR)
Internal Internal Rate of Return (IRR)
Internal
n NPV = Σ t=1 FCFt
(1 + k) t - IO Internal Rate of Return (IRR)
Internal
n NPV = Σ t=1 n IRR: Σ t=1 FCFt
(1 + k) t FCFt
t
(1 + IRR) - IO = IO Internal Rate of Return (IRR)
Internal
n IRR: Σ FCFt
t
(1 + IRR) = IO t=1 IRR is the rate of return that makes the PV
IRR
rate
of the cash flows equal to the initial outlay.
of
equal
initial This looks very similar to our Yield to
This
Maturity formula for bonds. In fact, YTM
is the IRR of a bond.
is How is a project’s IRR similar to a bond’s
YTM?
YTM? They are the same thing. Think of a bond as a project. The YTM
Think
on the bond would be the IRR of the
“bond” project.
“bond” EXAMPLE: Suppose a 10-year bond
EXAMPLE:
with a 9% annual coupon sells for
$1,134.20.
$1,134.20. Solve for IRR = YTM = 7.08%, the annual
Solve
return for this project/bond.
return Calculating IRR
Calculating Looking again at our problem: The IRR is the discount rate that
The
makes the PV of the projected cash
flows equal to the initial outlay.
equal
(250,000) 100,000 100,000 100,000 100,000 100,000 0 1 2 3 4 5 IRR
IRR
Decision Rule: • If IRR is greater than or equal to
If
the required rate of return (or
WACC), accept.
WACC) accept
• If IRR is less than the required
If
rate of ret...

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