N
AME
:
H
AAS
S
CHOOL
OF
B
USINESS
U
NIVERSITY
OF
C
ALIFORNIA
AT
B
ERKELEY
UGBA 103 S
UMMER
2008
S
OLUTION
TO
T
AKE
H
OME
M
ID

TERM
E
XAMINATION
J
UNE
13, 2008
TO
J
UNE
18, 2008
D
UE
IN
MY
MAILBOX
IN
R
OOM
F578
AT
3.30
PM
S
HOW
WORK
FOR
PARTIAL
CREDIT
.
1. Suppose we are given that an equipment costs $144,000 to buy at t=0, and the operating and maintenance (O&M) costs at
t
=1,2,…8
are $10,000, $15,000, $20,000, $25,000, $35,000, $50,000, $70,000, and $95,000 respectively. The equipment is needed on an
ongoing basis, and the firm has to decide how often it should replace one unit with another in order to minimize the total costs (sum of
replacement and O&M costs). In other words, the firm needs to work out the economic life of the equipment. Assume that the
discount rate is 4.5%, and work out how often it is that the firm should replace the equipment so as to minimize the total costs (sum of
20 points
The table below gives the costs at various points in time:
t
DF
t
Cost(t) (in $K)
PV
0
(Costs)
NPV
t
AF(4.5%, t)
EAC
t
0
1
144
144
1
0.9569
10
9.5694
153.5694
0.9569
160.48
2
0.9157
15
13.7359
167.3054
1.8727
89.3406
3
0.8763
20
17.5259
184.8313
2.7490
67.2367
4
0.8386
25
20.9640
205.7953
3.5875
57.3641
5
0.8025
35
28.08579
233.8811
4.3900
53.2762
6
0.7679
50
38.3948
272.2759
5.1579
52.7884
7
0.7348
70
51.4380
323.7139
5.8927
54.9347
8
0.7032
95
66.8026
390.5164
6.5959
59.2061
The economic life is 6 years.
2. ABC Fitness Club has exercise equipment that costs $234,000. They replace it every 20 quarters with an identical unit [the same
make and model], and sell the old unit for $54,000. The technology and the prices are expected to remain unchanged in perpetuity.
Therefore, as a going concern, ABC Fitness Club can be reasonably expected to follow this replacement policy for ever. They bought
the current equipment 5 quarters ago. Therefore, given the replacement policy and normal use, it will be replaced in exactly 15
quarters from now.
XYZ Health Club, a sister facility in the neighborhood, closed down temporarily, and asked ABC Fitness Club to let its members use
ABC’s facilities until it reopens. Taking into account the membership of the two clubs, it is estimated that ABC Club will have to
replace their current equipment in 12 quarters if they still want to sell the old unit for $54,000. In other words, the life of the current
unit will be shortened by 3 quarters on account of its use by members of XYZ Health Club. Assuming the discount rate to be 3.15%
per quarter, what payment from XYZ Health Club would compensate ABC Fitness Club for the fact that their current equipment will
need replacement 3 quarters earlier?
20 points