16
'"'The
IRR
overstates the expected return for accepted projects because
cash
fiows cannot generally be reinvested
at the
IRR.
Therefore, the average
IRR
for accepted projects
is
greater than the true expected rate
of
return.
This
imparts
an
upward
bias
on corporate projections
based
on
IRRs.
15
Excel's
MIRR
function allows you to enter a different reinvestment rate from the
WACC
for the
cash
infiows.
However, we assume reinvestment at the
WACC,
so
the
WACC
is
entered twice
in
the
Excel
MIRR
function, shown
in
Figure
11.4.
16
Equation
112a
summarizes these
steps.
N
N
L::
c1F
,
(1
+
rt
'
""'
COF
,
t=O
fa (
1
+r)'
=
''(1
+MIRR,)
N
..
PV
costs=
TV
(1
+
MIRR)N
~
112a
COF,
is
the
cash
outfiow at
timet,
and
CIF
,
is
the
cash
infiow at time
t.
The left term
is
the
PV
of
the investment
outlays when discounted at the cost
of
capital; the numerator
of
the second term
is
the compounded value
of
the infiows, assuming the infiows
are
reinvested at the cost
of
capital. The
MIRR
is
the discount rate that
forces the
PV
of
the
TV
to
equal the
PV
of
the
costs.
Also note that there
are
alternative definitions for the
MIRR.
One difference relates
to
whether negative
cash
fiows, after the positive
cash
fiows begin, should be compounded and treated
as
part
of
the
TV
or
discounted and treated
as
a cost. A related
issue
is
whether negative and positive flows
in
a given year should
be
netted or treated separately.
For
a complete discussion,
see
William
R.
McDaniel, Daniel
E.
McCarty, and Kenneth
A
Jessell,
"Discounted
Cash
Flow with Explicit Reinvestment
Rates:
Tutorial and Extension,"
The
Financial
Review,
vol.
23,
no. 3 (August
1988),
pp. 369385; and David
M.
Shull, "Interpreting
Rates
of
Return: A Modified
Rate
of
Return Approach,"
Financial
Practice
and
Education,
vol.
10
(Fall
1993),
pp. 6771.
Modified
IRR
(MIRR)
The
discount rate
at
which
the present value
of
a
project's cost
is
equal to
the present value
of
its
terminal value, where the
terminal value
is
found
as
the sum
of
the future val
ues
of
the
cash
inflows,
compounded
at
the firm's
cost
of
capital.
382
Part 4
Investing in LongTerm Assets: Capital Budgeting
FIGURE
11.4
Finding
the
MIRR
for
Project
5,
WACC
=
10
%
r22
71
1
72
1
73

~
2.2._
.1.§_
.12.
2§._
.1.2...
*
A
I
B
I
c
I
D
I
E
I
F
I
G
WACC
=
10%
r=lO%
0
1
2
3
4
Project 5
I
$5
1
00
sd
oo
$3
1
00
$100.00
$1,000.00
I
I
I
: $330.00
$484.00
$665.50
$1,000.00
Terminal Value
(TV)=
$1
,579.50
Calculator:
N =
4,
PV
= 1000,
PMT
=
0,
FV
= 1579.5.
Press
1/YR
to
solve for
MIRR
12.11%
Excel,
RATE
function:
=
RATE
(F72,0,B73,F77)
Rate=
MIRR
12.11
o/o
Excel
,
MIRR
function
:
=
MIRR
(B73:F73,B70,B70)
12.11%
The MIRR has two significant
advantages
over the regular IRR. First, whereas
the regular IRR assumes that the cash flows from each project are reinvested
at
the
IRR, the MIRR assumes that cash flows are reinvested
at
the cost of capital
(or some
other
explicit rate). Since reinvestment
at
the IRR is generally
not
correct,
the MIRR is generally a better indicator of a project's true profitability. Second, the
MIRR eliminates the multiple IRR
problemthere
can
never
be
more
than
one MIRR,
and
it can
be
compared
with
the cost of capital
when
deciding to accept
or
reject projects.