Exercise: LCC Cost Model

You have been retained by a government department to help them to select a
standard, all-purpose photocopier to be used by them over the next 5 years.

Two competing models have been short-listed. Their characteristics are given in
the Table below. The department has tested both models and is prepared to accept
the capacity and MTBF (mean time between failure) information provided by the
contractor.

The expected demand is estimated at 30,000 - 60,000 copies per work station/per
year. The photocopying paper costs $12 per 1000 sheets.

The opportunity cost of time for those who are expected to use photocopiers is
estimated between $0 and $50 per hour.

Both machines use very little energy when they are idle (not in use). The cost of
energy when idle is ignored.

Also, the opportunity cost of lost production due to failure is ignored.

There is no need to consider the accessibility of photocopiers to users or queues of
users.

The required discount rate is 10 per cent.
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1. Select the copier model that the department should purchase.
2. Show details of your evaluations and explain your choice.
Capacity/speed
"MTBF"
Price basic
Price add-onsa
Cost of serviceb
- per month
- per 1000 copies
Unit of measur.
(copies/minute)
($)
($)
Model A
10
15,000
1,200
100
Model B
30
15,000
4,000
500
($/month)
($/1000 copies)
20
8
40
12
Notes:
(a)
It is assumed that all add-on equipment will be purchased.
(b)
The service comprises a per-month charge plus an additional charge based on
usage (per 1000 copies)
Evaluation
The cost of paper is irrelevant, as both photocopiers will use the same quantity of it.
There is no information about repairs and response to failure so you may ignore the
MTBF data. However, you may wish to use it later to make some assumptions about
the cost of repairs and the cost of downtime.
You need to make some assumptions about the annual rate of demand for
photocopying and the opportunity cost of user time.
Sum PV
Year 0
Year 1
Year 2
Year 3
Year 4
Year 5
Discount
factor
1
(1+ r) = 1.1
(1+ r)2 =
1.21
(1+ r)3 =
1.33
(1+ r)4 =
1.46
(1+ r)5 =
1.61
Capital
cost A
$1,300
Capital
cost B
$4,500
Annual
demand
(assume)
45,000
45,000
45,000
45,000
45,000
User opp.
cost
(assume)
$25/hr =
$0.42/
minute
$25/hr =
$0.42/
minute
$25/hr =
$0.42/
minute
$25/hr =
$0.42/
minute
$25/hr =
$0.42/
minute
Service
cost A
$20x12 +
$8x45,000/1
000=$600
$20x12 +
$8x45,000/1
000=$600
$20x12 +
$8x45,000/1
000=$600
$20x12 +
$8x45,000/1
000=$600
$20x12 +
$8x45,000/1
000=$600
Service
cost B
$40x12 +
$12x45,000/
1000=$1020
$40x12 +
$12x45,000/
1000=$1020
$40x12 +
$12x45,000/
1000=$1020
$40x12 +
$12x45,000/
1000=$1020
$40x12 +
$12x45,000/
1000=$1020
User time
cost A
45000/10x$
0.42=$1890
45000/10x$
0.42=$1890
45000/10x$
0.42=$1890
45000/10x$
0.42=$1890
45000/10x$
0.42=$1890
User time
cost B
45000/30x$
0.42=$630
45000/30x$
0.42=$630
45000/30x$
0.42=$630
45000/30x$
0.42=$630
45000/30x$
0.42=$630
Operating
cost A
$2,490
$2,490
$2,490
$2,490
$2,490
Operating
cost B
$1,650
$1,650
$1,650
$1,650
$1,650
Total disc.
cost A*
$10,745.73*
1,300
2,263.64
2,057.85
1,872.18
1,705.48
1,546.58
Total disc.
cost B*
$10,759.22
4,500
1,500.00
1,363.64
1,240.60
1,130.14
1,024.84
* Expressed in base (present) year dollars
Given our initial assumptions, photocopier A is a marginally better buy than photocopier B. You can
now engage in some sensitivity analysis. What happens when the annual rate of demand increases to
60,000 copies or decreases to 30,000? What happens if the opportunity cost of user time is $0? Or
$50/hour? Perhaps you can add some assumptions about the cost of failure.