This preview shows page 1. Sign up to view the full content.
Unformatted text preview: ve years. The firm’s
required rate of return is 15%.
(250,000) 100,000 100,000 100,000 100,000 100,000 0 1 2 3 4 5 Net Present Value
NPV is just the PV of the annual cash
flows minus the initial outflow.
Using TVM: P/Y = 1 N = 5
PMT = 100,000
PMT I = 15 PV of cash flows = $335,216
- Initial outflow: ($250,000)
= Net PV
$85,216 Rationale for the NPV method
NPV = PV of inflows – Cost
= Net gain in wealth If projects are independent, accept if the
project NPV > 0.
project If projects are mutually exclusive, accept
projects with the highest positive NPV, those
that add the most value.
that Profitability Index Profitability Index
n NPV = Σ t=1 FCFt
(1 + k) - IO Profitability Index
n NPV = Σ t=1
n PI = Σ t=1 FCFt
(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
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
its capital budgeting projects.
its Internal Rate of Return (IRR)
Internal Internal Rate of Return (IRR)
n NPV = Σ t=1 FCFt
(1 + k) t - IO Internal Rate of Return (IRR)
n NPV = Σ t=1 n IRR: Σ t=1 FCFt
(1 + k) t FCFt
(1 + IRR) - IO = IO Internal Rate of Return (IRR)
n IRR: Σ FCFt
(1 + IRR) = IO t=1 IRR is the rate of return that makes the PV
of the cash flows equal to the initial outlay.
initial This looks very similar to our Yield to
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? They are the same thing. Think of a bond as a project. The YTM
on the bond would be the IRR of the
“bond” EXAMPLE: Suppose a 10-year bond
with a 9% annual coupon sells for
$1,134.20. Solve for IRR = YTM = 7.08%, the annual
return for this project/bond.
return Calculating IRR
Calculating Looking again at our problem: The IRR is the discount rate that
makes the PV of the projected cash
flows equal to the initial outlay.
(250,000) 100,000 100,000 100,000 100,000 100,000 0 1 2 3 4 5 IRR
Decision Rule: • If IRR is greater than or equal to
the required rate of return (or
• If IRR is less than the required
rate of ret...
View Full Document
This document was uploaded on 02/03/2014.
- Spring '14
- Internal Rate Of Return (IRR)