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Actsc 372 F08: Assignment 4 Solution (Total marks: 35)
Q1:
[6 marks, 2 marks each]
a.
If m is the systematic risk portion of return, then:
m =
β
GNP
Δ
GNP +
β
r
Δ
Interest rates
m = 2.04(4.8% – 3.5%) – 1.90(7.80% – 7.10%) = 1.32%
b.
The unsystematic is the return that occurs because of a firm specific factor such
as the increase in market share. If
ε
is the unsystematic risk portion of the return,
then:
ε
= 0.36(27% – 23%) =
1.44%
c.
The total return is the expected return, plus the two components of unexpected
return: the systematic risk portion of return and the unsystematic portion. So, the
total return of the stock is:
ε
+
+
=
m
R
R
R = 10.50% + 1.32% + 1.44%
= 13.26%
Q2)
[4 marks]
The discount rate for the project is equal to the expected return for the security,
R
S
, since the project has the same risk as the firm as a whole.
Apply the CAPM to
express the firm’s required return,
R
S
, in terms of the firm’s beta,
β
, the risk–free rate,
R
F
,
and the expected market return,
R
M
.
R
S
=
R
F
+
β
×
(
R
M
–
R
F
)
= 0.05 + 1.6 (0.09) = 0.194
Subtract the initial investment at year 0.
To calculate the PV of the cash inflows, apply
the annuity formula, discounted at 0.194.
NPV
= C
0
+ C
1
A
T
r
= –$1,450,000 + $510,000 A
5
0.194
=
$
277.402.65
Undertake the project since the NPV is positive.
Q3)
[4 marks]
a.
Lang Cosmetics should use its stock beta in the evaluation of the project only if
the risk of the perfume project is the same as the risk of Lang Cosmetics as a
whole.
b.
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 Winter '09
 MARYHARDY

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