EPJ3760 Construction Investments
Lecture 6: October 2013
6.1 Internal Rate of Return
6.1 Internal Rate of Return
Internal Rate of Return (IRR)
(The discount rate which equates the present
value of the future net cash flows with the initial
investment.)
That is:
• the discount rate which makes NPV = 0
• the maximum interest rate at which you would
borrow to finance the project
Decision Rules
• Accept projects with IRR ≥ MARR (minimum
acceptable rate of return)
• Reject projects with IRR < MARR
Calculation
n
where
1
Initial cash outlay
(time 0)
Solve for IRR by:
• Trial and error
• Other calculators (e.g. Excel function, financial tables)
2
• Considers the time value of money
• Consistent with shareholder wealth maximisation
• Intuitive appeal (rate feels better than absolute number
because it is readily comparable with other rates)
• Doesn’t require advance specification of the discount
rate
Discounted
cumulative
cash flow
(discount rate =
21,86% = IRR)
-10000
-10000
-10000
Year 1
4000
-6363,6
-6717,61
Year 2
4000
-3057,9
-4024,08
Year 3
4000
-52,6
Year 4
4000
2679,5
-1813,77
0
Disadvantages
3
6.2 Modified IRR
Modified Internal Rate of Return (MIRR)
(The discount rate which equates the present
value of the cash outflows (calculated on the basis of the
finance rate or MARR) with the present value of the
project’s terminal value. Where the terminal
value is the sum of the future values of the
project’s cash inflows compounded to the
project’s termination (at the reinvestment rate or MARR). )
Decision Rules
• Accept projects with MIRR ≥ MARR
• Reject projects with MIRR < MARR
• Where two projects are mutually exclusive, do
not rank on MIRR values, accept the one with
the higher NPV.
Emlyn Witt
IO = the initial cash investment
ACFt = Annual net cash flow in time period t
IRR = the internal rate of return
t = the projects expected life
6.1 Internal Rate of Return
For example, if an initial investment of 10000 produces
net cash flows of 4000 for 4 years, the IRR of this
investment is:
Discounted
cumulative
cash flow
(discount rate =
10%)
ACFt
(1 + IRR)t
Benefits of using IRR
Calculation
Net cash flows
Σ
t=1
6.1 Internal Rate of Return
Time
=
IO
• Reinvestment rate assumption (i.e. cash inflows are
reinvested at the IRR) may be unreasonable
• Multiple IRRs possible where sign reversals occur in
cash flow
• Requires detailed cash flow predictions over the entire
life of the project.
• Only as accurate as the cash flow predictions.
• When scale differences exist, there can be a ranking
conflict with the NPV method.
4
6.2 Modified IRR
Calculation
PVoutflows = PVinflows
n
n
Σ
t=0
ACOFt
(1 + k)t
where
5
=
Σ
ACIFt
(1 + k)n-t
t=0
(1 +
MIRR)n
TV
=
(1 + MIRR)n
ACIFt = Annual net cash inflow in time period t
ACOFt = Annual net cash outflow in time period t
TV = the Terminal Value of all the cash inflows
compounded at the discount rate
k = the appropriate discount rate
MIRR = the Modified Internal Rate of Return
n = the project’s expected life
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EPJ3760 Construction Investments
Lecture 6: October 2013
6.2 Modified IRR
6.2 Modified IRR
Calculation
Calculation
For example, if an initial investment of 10000 produces
net cash flows of 4000 for 4 years and the discount rate
is taken as 10%, the MIRR of this investment is:
Time
Net cash flows
Initial cash outlay
(time 0)
PVoutflows
-10000
Step 1 (previous slide): calculate PVoutflows
TV
(of inflows)
Step 2 (previous slide): calculate TV of inflows
(Step 1) 10000
Year 1
4000
5324
Year 2
4000
4840
Year 3
4000
4400
Year 4
4000
4000
Total
Step 3: PVoutflows =
TV
(1 + MIRR)n
18564
10000 =
(1 + MIRR)4
(Step 2) 18564
7
MIRR = 16,7%
8
6.2 Modified IRR
Benefits of using MIRR
• Considers the time value of money
• Consistent with shareholder wealth maximisation
• Intuitive appeal (rate feels better than absolute number
because it is readily comparable with other rates)
• Overcomes the reinvestment rate problem of IRR by
allowing the reinvestment rate to be specified.
Disadvantages
• Requires detailed cash flow predictions over the entire
life of the project.
• Only as accurate as the cash flow and reinvestment rate
predictions.
• When scale differences exist, there can still be a ranking
conflict with the NPV method.
• Multiple MIRRs possible where sign reversals occur in
cash flow.
Emlyn Witt
9
2