Fundamentals of Financial Management (Concise 6th Edition)

Chapter 11 The Basics of Capital Budgeting 351

Now recognize that the impact of an increase in the cost of capital is much greater
on distant than near-term cash " ows, as we demonstrate here:

Effect of doubling r on a Year 1 cash " ow:

PV of $100 due in 1 year @ r! 5%: __$100
(1.05)^1
! $95.24

PV of $100 due in 1 year @ r! 10%: __$100
(1.10)^1
! $90.91

Percentage decline due to higher r! $95.24 ___# $90.91
$95.24
! 4.5%

Effect of doubling r on a Year 20 cash " ow:

PV of $100 due in 20 years @ r! 5%: ___$100
(1.05)^20
! $37.69

PV of $100 due in 20 years @ r! 10%: ___$100
(1.10)^20
! $14.86

Percentage decline due to higher r! $37.69 ___# $14.86
$37.69
! 60.6%

NPV Pro" les for Projects S and L

F I G U R E 1 1! 6

NPV

($)

At r = 10%,

NPVL > NPVs, but

IRRs > IRRL, so

there is a con#ict

Cost of Capital (%)

5 10

15

IRRs

IRRL

20

0

500

400

300

200

100

–100

Crossover rate;

con!ict if r is to

the left, no con!ict

if r is to the right

L

S

Cost of Capital NPVs NPVL

0% $300.00 $475.00

5 180.42 268.21

10 78.82 100.40

Crossover! 11.975 42.84 42.84

IRRL! 13.549 15.64 0.00

IRRS! 14.489 0.00 "24.37

15 "8.33 "37.26

20 "83.72 "151.33