Question

Printing Services is considering replacing its old printer with a new one. The old printer is expected to provide year-end cash inflows of £5,000 in each of the next 3 years before it fails. The new printer costs a significant £20,000 to buy and will last for 4 years. However, it is much more efficient than the old printer and is expected to provide year-end annual cash inflows of £10,000 (i.e., in each year of its life).

1. What is the equivalent annual cost of buying the new printer and what is this cost’s interpretation?

2. What are the annual incremental cash flows of buying the new printer?

3. Assuming a discount rate of 12%, should the firm replace the old printer now?

Answer 1

Sol:

rate (r) = 12%

Period (n) = 4 years

a) Annuity factor = (1-(1/(1+r)^(n)/r

Annuity factor = (1-(1/(1+12%)^(4)/12%

Annuity factor =  (1-(1/(1.012)^(4)/0.12

Annuity factor = 3.0373

Equivalent annual cost of buying the new printer = Printer cost / Annuity factor

Equivalent annual cost of buying the new printer = £20,000/3.0373 = £6584.80

The company can compare the cost effectiveness of the new printer with old as both have different lifespan.

Therefore average annual cost of £6,584.80 is being incurred on the new printer over the 4 year period.

b) Annual incremental cash flows of buying the new printer assuming the old printer will be working alongside the new printer:

Year 1 = £10000

Year 2= £10000

Year 3= £10000

c)

	0	1	2	3	4
Initial investment	-20000
Cash flows	0	10000	10000	10000	10000
Discount factor @12%	1	0.8929	0.7972	0.7118	0.6355
PVs	-20000	8928.57	7971.94	7117.80	6355.18
NPV 10373.49

NPV of new printer is $10,373.49, therefore the company should replace the old printer.

Note - The analysis were done ignoring the the cash flows foregone on the old printer of £5,000 for 3 years. It also ignores the proceeds from the sale of the old printer if no longer needed.