Fundamentals of Financial Management (Concise 6th Edition)

350 Part 4 Investing in Long-Term Assets: Capital Budgeting

Now consider Figure 11-6, which shows two NPV pro! les—one for Project S

and one for L—and note the following points:

• The IRRs are! xed, and S has the higher IRR regardless of the cost of capital.


• However, the NPVs vary depending on the actual cost of capital.


• The two NPV pro! le lines cross at a cost of capital of 11.975%, which is called
  the crossover rate. The crossover rate can be found by calculating the IRR of
  the differences in the projects’ cash " ows, as demonstrated:

0 1 2 3 4

Project S "$1,000 $500 $400 $300 $100

" Project L "$1,000 $100 $300 $400 $675

# CFs " CFL $ 0 $400 $100 "$100 "$575

IRR #! 11.975%! Crossover Rate

• Project L has the higher NPV if the cost of capital is less than the crossover rate,
  but S has the higher NPV if the cost of capital is greater than that rate.
  Notice that Project L has the steeper slope, indicating that a given increase in
  the cost of capital causes a larger decline in NPVL than in NPVS. To see why this is
  so, recall that L’s cash " ows come in later than those of S. Therefore, L is a long-
  term project and S is a short-term project. Next, recall the equation for the NPV:

NPV! CF 0 "

CF 1

_______

(1 " r)^1

"

CF 2

_______

(1 " r)^2

"... "

CFN

_______

(1 " r)N

Crossover Rate

The cost of capital at

which the NPV profiles of

two projects cross and,

thus, at which the projects’

NPVs are equal.

Crossover Rate

The cost of capital at

which the NPV profiles of

two projects cross and,

thus, at which the projects’

NPVs are equal.

NPV Pro" le for Project S

F I G U R E 1 1! 5

NPV

($)

5 10 15 20

0

300

200

100

–100

NPV = 0, so

IRRs = 14.489%

IRR > r = 10%,

so accept

At r = 10%,

NPV > 0,

so accept

Cost of Capital (%)

Cost of Capital NPVs

0% $300.00

5 180.00

10 78.82

IRRs! 14.489 0.00

15 "8.33

20 "83.72