P17.6
A.
Permian Basin #1
E(CF
1
)
=
$1,000,000
σ
1
=
$200,000
CV
1
=
0.2
Permian Basin #2
E(CF
2
)
=
$900,000
σ
2
=
$360,000
CV
2
=
0.4
Notice that CV2 = 2*CV1 (Factor of 2 will be used to calculate RADR for Project #2.)
B.
Permian Basin #1
NPV
1
= (PVIFA, N = 10, i = 8% + 12% = 20%)
× E(CF
1
) - Cost
= (4.1925)($1,000,000) - $3,000,000
= $1,192,500
Permian Basin #2
NPV
2
= (PVIFA, N = 10, i = 8% + 2(12%) = 32%)
× E(CF
2
) - Cost
= (2.9304)($900,000) - $3,000,000
= -$362,640 (A loss)
Therefore, the less risky Permian Basin #1 has a positive
NPV
1
and should be
undertaken, whereas the more risky Permian Basin #2 project has an
NPV
2
< 0 and
should be rejected.
(
Note
:
V
2
= 2V
1
so the appropriate risk premium for Permian Basin #2 is 24%
= 2 × 12%.)
C.
Permian Basin #1
:
PI
1
=
4,192,500 / 3,000,000 = 1.398
Permian Basin #2
PI
2
=
2,637,360 / 3,000,000 = 0.879
Because the
PI
1
> PI
2
, the Permian Basin #1 project is ranked ahead of the Permian
Basin #2 project.
Moreover, because
PI
2
< 1, this latter project should not be
pursued in any event.