Internal rate of return:

A c autionary tale

Temp ted b y a p ro ject w ith a h ig h in tern al rate

o f return ? B etter ch eck th o se in terim cash

fl o w s ag ain .

M ay b e fi nanc e m anag ers just en jo y liv in g

o n th e ed g e. W h at else w o uld ex p lain th eir

w eak n ess fo r usin g th e in tern al rate o f

return (IR R ) to assess cap ital p ro jects? F o r

d ecad es, fin an ce tex tb o o k s an d acad emics

h av e w arn ed th at ty p ical IR R calculatio n s

b uild in rein v estmen t assump tio n s th at

mak e b ad p ro jects lo o k b etter an d g o o d

o n es lo o k g reat. Y et as recen tly as 19 9 9 ,

acad emic research fo un d th at th ree-q uarters

o f C F O s alw ay s o r almo st alw ay s use IR R

w h en ev aluatin g cap ital p ro jects.1

O ur o w n research un d erlin ed th is p ro cliv ity

to risk y b eh av io r. In an in fo rmal surv ey o f

3 0 ex ecutiv es at co rp o ratio n s, h ed g e fun d s,

an d v en ture cap ital firms, w e fo un d o n ly 6

w h o w ere fully aw are o f IR R ’s mo st critical

d eficien cies. O ur n ex t surp rise came w h en

w e rean aly z ed so me tw o d o z en actual

in v estmen ts th at o n e co mp an y mad e o n th e

b asis o f attractiv e in tern al rates o f return .

If th e IR R calculated to justif y th ese

in v estmen t d ecisio n s h ad b een co rrected fo r

th e measure’s n atural flaw s, man ag emen t’s

p rio ritiz atio n o f its p ro jects, as w ell as its

v iew o f th eir o v erall attractiv en ess, w o uld

h av e ch an g ed co n sid erab ly .

S o w h y d o fin an ce p ro s co n tin ue to d o

w h at th ey k n o w th ey sh o uld n ’t? IR R d o es

h av e its allure, o fferin g w h at seems to b e a

straig h tfo rw ard co mp ariso n o f, say , th e

3 0 p ercen t an n ual return o f a sp ecific

p ro ject w ith th e 8 o r 18 p ercen t rate th at

mo st p eo p le p ay o n th eir car lo an s o r

cred it card s. Th at ease o f co mp ariso n

seems to o utw eig h w h at mo st man ag ers

v iew as larg ely tech n ical d eficien cies th at

create immaterial d isto rtio n s in relativ ely

iso lated circumstan ces.

Ad mitted ly , so me o f th e measure’s

d eficien cies are tech n ical, ev en arcan e,2 b ut

th e mo st d an g ero us p ro b lems w ith IR R are

n eith er iso lated n o r immaterial, an d th ey can

h av e serio us imp licatio n s fo r cap ital b ud g et

man ag ers. W h en man ag ers d ecid e to fin an ce

o n ly th e p ro jects w ith th e h ig h est IR R s, th ey

may b e lo o k in g at th e mo st d isto rted

calculatio n s— an d th ereb y d estro y in g

sh areh o ld er v alue b y selectin g th e w ro n g

p ro jects alto g eth er. C o mp an ies also risk

creatin g un realistic ex p ectatio n s fo r

th emselv es an d fo r sh areh o ld ers, p o ten tially

co n fusin g in v esto r co mmun icatio n s an d

in flatin g man ag erial rew ard s.

W e b eliev e th at man ag ers must eith er av o id

usin g IR R en tirely o r at least mak e

ad justmen ts fo r th e measure’s mo st

d an g ero us assump tio n : th at in terim cash

flo w s w ill b e rein v ested at th e same h ig h

rates o f return .

T h e troub le w ith IR R

P ractitio n ers o f ten in terp ret in tern al rate o f

return as th e an n ual eq uiv alen t return o n a

g iv en in v estmen t; th is easy an alo g y is th e

so urce o f its in tuitiv e ap p eal. B ut in fact,

IR R is a true in d icatio n o f a p ro ject’s

an n ual return o n in v estmen t o n ly w h en th e

p ro ject g en erates n o in terim cash flo w s— o r

1 6 | M c K ins ey on F inanc e | S u m m e r 2 0 0 4

John C. Kelleher

a nd Ju s tin J.

M a c Corm a c k

when those interim cash flows really can be

invested at the actual IRR.

When the calculated IRR is higher than the

true reinvestment rate for interim cash flows,

the measure will overestimate—sometimes

very significantly—the annual equivalent

return from the project. The formula

assumes that the company has additional

projects, with equally attractive prospects, in

which to invest the interim cash flows. In this

case, the calculation implicitly takes credit

for these additional projects. Calculations of

net present value (N PV ), by contrast,

generally assume only that a company can

earn its cost of capital on interim cash flows,

leaving any future incremental project value

with those future projects.

IRR’s assumptions about reinvestment can

lead to major capital budget distortions.

Consider a hypothetical assessment of two

different, mutually exclusive projects, A and

B, with identical cash flows, risk levels, and

durations—as well as identical IRR values

of 4 1 percent. U sing IRR as the decision

yardstick, an executive would feel

confidence in being indifferent toward

choosing between the two projects.

H owever, it would be a mistake to select

either project without examining the

relevant reinvestment rate for interim cash

flows. Suppose that Project B’s interim cash

flows could be redeployed only at a typical

8 percent cost of capital, while Project A’s

cash flows could be invested in an attractive

follow-on project expected to generate a

4 1 percent annual return. In that case,

Project A is unambiguously preferable.

E ven if the interim cash flows really could

be reinvested at the IRR, very few

e x h i b i t 1

Identical IRRs, but very different annual returns

1Compound annual growth rate.

Key assumption: reinvestment rate = IRR Key assumption: reinvestment rate = cost of capital

True return is nearly 5 0 % less b ecause of low er reinvestment rate

Year

C as h flo w s , $ m illio n

IRR

Year

C as h flo w s , $ m illio n

2

5

3

5

4

5

0

– 10

1

5

5

5

$ 5 6million

$ 2 9million

4 1 %

. . . h ow ever, interim cash flow s are reinvested at d ifferent rates

Internal- rate-of- return (IRR) values are id entical for 2 projects . . .

V alu e o f c as h flo w s at y ear 5 if rein v es ted at 41%

Year

C A G R1

C A G R1

2 3 40 1

5

5

41%

41%

41%

41%

4 1 %

5

7

10

14

20

5

5

5

P roject A IRR

2

5

3

5

4

5

0

– 10

1

5

5

5 4 1 %

P roject B

P roject A

V alu e o f c as h flo w s at y ear 5 if rein v es ted at 8 %

Year

C A G R1

C A G R1

2 3 40 1

5

5

8 %

8 %

8 %

8 %

2 4 %

5

5

6

6

7

5

5

5

P roject B

Y ear 5 value of $ 1 0 million investment = Y ear 5 value of $ 1 0 million investment =

Internal rate of return: A cautionary tale | 17

18 | McKinsey on Finance | Summer 2004

practitioners would argue that the value of

future investments should be commingled

with the value of the project being

evaluated. M ost practitioners would agree

that a company’s cost of capital—by

definition, the return available elsewhere to

its shareholders on a similarly risky

investment—is a clearer and more logical

rate to assume for reinvestments of interim

project cash flows (Exhibit 1).

When the cost of capital is used, a project’s

true annual equivalent yield can fall

significantly—again, especially so with

projects that posted high initial IRRs. Of

course, when executives review projects

with IRRs that are close to a company’s

cost of capital, the IRR is less distorted by

the reinvestment-rate assumption. But when

they evaluate projects that claim IRRs of

10 percent or more above their company’s

cost of capital, these may well be

significantly distorted. Ironically, unadjusted

IRRs are particularly treacherous because

the reinvestment-rate distortion is most

egregious precisely when managers tend to

think their projects are most attractive. And

since this amplification is not felt evenly

across all projects,3 managers can’t simply

correct for it by adjusting every IRR by a

standard amount.

How large is the potential impact of a

flawed reinvestment-rate assumption?

M anagers at one large industrial company

approved 23 major capital projects over five

years on the basis of IRRs that averaged

7 7 percent. Recently, however, when we

conducted an analysis with the reinvestment

rate adjusted to the company’s cost of

capital, the true average return fell to just

16 percent. The order of the most attractive

projects also changed considerably. The top-

ranked project based on IRR dropped to

the tenth-most-attractive project. M ost

striking, the company’s highest-rated

projects—showing IRRs of 800, 15 0, and

130 percent—dropped to just 15 , 23, and

22 percent, respectively, once a realistic

reinvestment rate was considered (Exhibit 2).

Unfortunately, these investment decisions

had already been made. Of course, IRRs this

extreme are somewhat unusual. Yet even if a

project’s IRR drops from 25 percent to

15 percent, the impact is considerable.

W hat to d o?

The most straightforward way to avoid

problems with IRR is to avoid it altogether.

Yet given its widespread use, it is unlikely to

be replaced easily. Executives should at the

very least use a modified internal rate of

return. While not perfect, M IRR at least

allows users to set more realistic interim

reinvestment rates and therefore to calculate

a true annual equivalent yield. Even then,

we recommend that all executives who

review projects claiming an attractive IRR

should ask the following two questions.

1. What are the assumed interim-

reinvestment rates? In the vast majority of

cases, an assumption that interim flows can

be reinvested at high rates is at best

overoptimistic and at worst flat wrong.

Particularly when sponsors sell their projects

as “ unique” or “ the opportunity of a

lifetime,” another opportunity of similar

attractiveness probably does not exist; thus

interim flows won’t be reinvested at

sufficiently high rates. For this reason, the

best assumption—and one used by a proper

discounted cash-flow analysis—is that

interim flows can be reinvested at the

company’s cost of capital.

2 . A re interim c ash f lo w s b iased to w ard

the start o r the end o f the p ro jec t? Unless

e x h i b i t 2

A rude surprise

1 Disguised example of large industrial company.

%

200

18 19 20 21 22 23

0

50

100

150

800

850

1Project1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

S tandard IR R calculation M odified IR R with reinvestment at cost of cap ital

Internal rate of return: A cautionary tale | 19

the interim reinvestment rate is correct (in

other words, a true reinvestment rate rather

than the calculated IRR), the IRR distortion

will be greater when interim cash flows

occur sooner. This concept may seem

counterintuitive, since typically we would

prefer to have cash sooner rather than later.

The simple reason for the problem is that

the gap between the actual reinvestment

rate and the assumed IRR exists for a longer

period of time, so the impact of the

distortion accumulates.4

Despite flaws that can lead to poor

investment decisions, IRR will likely

continue to be used widely during capital-

budgeting discussions because of its strong

intuitive appeal. Executives should at least

cast a skeptical eye at IRR measures before

making investment decisions.

T h e a uth o rs w is h to th a n k R o b M c N is h fo r h is

a s s is ta n c e in d ev elo p in g th is a rtic le.

MoF

John Kelleher (J o h n _ K elleh er@ M c K in s ey .c o m)

and Ju s tin M a c C orm a c k (J us tin _ M a c C o rma c k @

M c K in s ey .c o m) are consultants in McKinsey’s

Toronto offi ce.

1 J o h n R o b ert G ra h a m a n d C a mp b ell R . H a rv ey , “ T h e th eo ry

a n d p ra c tic e o f c o rp o ra te fi n a n c e: E v id en c e fro m th e fi eld ,”

D uk e U n iv ers ity w o rk in g p a p er p res en ted a t th e 2001

a n n ua l meetin g o f th e A meric a n F in a n c e A s s o c ia tio n , N ew

O rlea n s (a v a ila b le a t h ttp ://s s rn .c o m/a b s tra c t= 22025 1).

2 A s a res ult o f a n a rc a n e ma th ema tic a l p ro b lem, IR R c a n

g en era te tw o v ery d ifferen t v a lues fo r th e s a me p ro jec t

w h en future c a s h fl o w s s w itc h fro m n eg a tiv e to p o s itiv e (o r

p o s itiv e to n eg a tiv e). A ls o , s in c e IR R is ex p res s ed a s a p er-

c en ta g e, it c a n ma k e s ma ll p ro jec ts a p p ea r mo re a ttra c tiv e

th a n la rg e o n es , ev en th o ug h la rg e p ro jec ts w ith lo w er IR R s

c a n b e mo re a ttra c tiv e o n a n N P V b a s is th a n s ma ller p ro j-

ec ts w ith h ig h er IR R s .

3 T h e a mp lifi c a tio n effec t g ro w s a s a p ro jec t’s fun d a men ta l

h ea lth imp ro v es , a s mea s ured b y N P V , a n d it v a ries

d ep en d in g o n th e un iq ue timin g o f a p ro jec t’s c a s h fl o w s .

4 In teres tin g ly , g iv en tw o p ro jec ts w ith id en tic a l IR R s , a

p ro jec t w ith a s in g le “ b ullet” c a s h fl o w a t th e en d o f th e

in v es tmen t p erio d w o uld b e p refera b le to a p ro jec t w ith

in terim c a s h fl o w s . T h e rea s o n : a la c k o f in terim c a s h

fl o w s c o mp letely immun iz es a p ro jec t fro m th e

rein v es tmen t- ra te ris k .