Fundamentals of Financial Management (Concise 6th Edition)

Appendix A Solutions to Self-Test Questions and Problems A-13

PaybackX! 2 #

$500

______

$3,000

! 2.17 years

PaybackY! 2 #

$3,000

______

$3,500

! 2.86 years

Discounted payback:
To determine the discounted payback, construct the cumulative discounted
cash " ows at the! rm’s WACC of 12% for each project:

Project X

Years

Cash Flow

Discounted Cash Flow

Cumulative Discounted Cash Flow

!10,000

!10,000

6,500

5,803.57

!10,000 !4,196.43

3,000

2,391.58

!1,804.85

3,000

2,135.34

"330.49

1,000

635.52

"966.01

0 1 2 3 4

Discounted PaybackX! 2 # $1,804.85/$2,135.34! 2.85 years

Project Y

Years

Cash Flow

Discounted Cash Flow

Cumulative Discounted Cash Flow

!10,000

!10,000

3,500

3,125.00

!10,000 !6,875.00

3,500

2,790.18

!4,084.82

3,500

2,491.23

!1,593.59

3,500

2,224.31

"630.72

0 1 2 3 4

Discounted PaybackY! 3 # $1,593.59/$2,224.31! 3.72 years

b. The following table summarizes the project rankings by each method:

Project That Ranks Higher

NPV X

IRR X

MIRR X

Payback X

Discounted payback X

Note that all methods rank Project X over Project Y. In addition, both projects
are acceptable under the NPV, IRR, and MIRR criteria. Thus, both projects
should be accepted if they are independent.
c. In this case, we would choose the project with the higher NPV at r! 12%, or
Project X.
d. To determine the effects of changing the cost of capital, plot the NPV pro! les
of each project. The crossover rate occurs at about 6% to 7% (6.2%). See the
graph on the next page.
If the! rm’s cost of capital is less than 6.2%, a con" ict exists because
NPVY % NPVX, but IRRX % IRR Y. Therefore, if r is 5%, a con" ict exists.
Note, however, that when r! 5.0%, MIRRX! 10.64% and MIRRY!
10.83%; hence, the modi! ed IRR ranks the projects correctly even if r is to
the left of the crossover point.
e. The basic cause of the con" ict is differing reinvestment rate assumptions be-
tween NPV and IRR. NPV assumes that cash " ows can be reinvested at the
cost of capital, while IRR assumes reinvestment at the (generally) higher IRR.
The high reinvestment rate assumption under IRR makes early cash " ows es-
pecially valuable; hence, short-term projects look better under IRR.