Question

1. A college is considering the installation of a copier system. Two alternative models are available. Once selected, each model will be replaced at the end of its life by its own replica. The appropriate discount rate for the cash flows of the college is 8%. Cash flows related to the two models are as follows. All cash flows are outflows; initial purchase cost at year 0 and expenses to operate the copier system such as electricity and maintenance during its life. Model XIV has service life of 3 years and model SYC has service life of 5 years.

Model	0	1	2	3	4	5
XIV	-5,400	-500	-500	-300
SYC	-7,500	-600	-600	-600	-600	-600

1. Which model is better if each is used just one round?
2. Which model is better if each model has to be replaced at the end of its life indefinitely?

Answer 1

This question involves decision making.

A copier system has to be installed and the options given are : XIV and SYC.

The discount rate is 8%.

a) For decision about which model is better in one round i.e it will not be replaced:

Lets multiply the cashflows of different years with their respective Present Value Factors as given in the image below:

From the above image, it can be inferred that the cash flows of model SYC ($9894) are higher and hence model XIV ($6529.7) should be preferred since it has lower cash outflows.

b.) Similarly, it each model has to be replaced at the end of its period indefinitely, then following will be calculation:

Cashflows/ Rate

for model XIV: 6529.7/0.08 = $ 81621.2

for model SYC: 9894/0.08 = $123675

However, as number of years are different, each has to be divided by cumulative value of their PVF.

Model XIV: = 31671.7

Model SYC: = 30975.2

On indefinite replacement, the cash outflows of Model XIV are higher than Model SYC by $696.5. Hence, in this case , model SYC should be considered instead.