Thus,
NPV
= $600,000 for project A, $450,000 for project B, and $300,000 for project C.
With capital rationing, the firm can undertake either project A only or projects B and C.
Ranking projects according to their
NPV
, the firm would undertake projects B and C with
total NPV of $750,000
(
b
) Since the firm faces capital rationing, however, it should use the profitability index
(
PI
) as its investment criterion. The
PI
of each project is given by the ratio of the
PVNCF
to the
C
0 of each project
For project A,
PI
= $3,000,000/$2,400,000 = 1.25.
For project B,
PI
= $1,750,000/$1,300,000 = 1.35.
For project C,
PI
= $1,400,000/$1,100,000 = 1.27.
Using the
PI
investment criterion indicates that the firm should undertake projects B
and C. The reason for this is that projects B and C provide a higher rate of return
per dollar invested than project A. Note that the sum of the
NPV
of projects B and C
exceeds the
NPV
for project A.
10. The cost of equity capital for this firm (
ke
) can be calculated with the dividend
valuation
model, as follows
ke
= (
D/P)
+
g
where
D
is the amount of the yearly dividend paid per share of the common stock of the
firm,
P
is the price of a share of the common stock of the firm, and
g
is the expected
annual growth rate of dividend payments.
Since the company pays half of its expected $200 million in net after-tax earnings in
dividends and there are 100 million shares of common stock of the firm, the dividend per
share is $1. With a share of the common stock of the firm selling for eight times current
earnings, the price of a share of the common stock of the firm is $8.
With the expected annual growth of earnings and dividends of the firm of 7.5 percent, the
cost of equity capital for this firm is
ke
= ($1/$8) + 0.075 = 0.125 + 0.075 = 0.20 or 20%