Question

Question 1. A company is planning to purchase a new machine to expand its production. There are two brand available A and B in the market. Both the machines are costing OMR 10000. The following cash inflows are expected to come for both the machines.

Years	Machine A	Machine B
1	2400	1200
2	3600	3000
3	5800	4800
4	6000	7600
5	6500	9200

Calculate Pay back period and Discounted Payback period for Machine A and Machine B and comment on which machine is better using the two techniques. The discount rate is 3.05%.

Solution: Payback period

Years	Machine A		Years	Machine B
Outflow			Outflow
1			1
2			2
3			3
4			4
5			5

Solution: Discounted Payback period

Years	Machine A			Years	Machine B
Outflow				Outflow
1				1
2				2
3				3
4				4
5				5

Answer 1

Payback period is the amount of time taken to breakeven or in other words the time taken to cover the initial cash outflow

Discounted payback uses the same terminology but uses the discounted cash flows to get the discounted payback period

The initial outflow or costing is 10000 for both the machines

From the cash flows it can be seen that Machine A requires less than 3 but more than 2 years to cover the 10000 while machine B requires less than 4 but more than 3 years to cover the 10000

Machine A covers 6000 in first 2 years and hence the remaining 4000 will be covered in 3rd year and the time taken will be (4000/5800) = 0.689

Hence payback period for Machine A = 2 + 0.689 = 2.689

Similarly for Machine B the 9000 gets covered in first 3 years and the remaining 1000 will be in 4th year and time taken can be calculated as (1000/7600) = 0.131

Hence payback period for Machine B = 3 + 0.131 = 3.131

Now the discounted cash flows can be given as

Years	Machine A	Machine A Discounted Cash Flows	Machine B	Machine B Discounted Cash Flows
1	2400	2328.967	1200	1164.483
2	3600	3390.053	3000	2825.044
3	5800	5300.099	4800	4386.289
4	6000	5320.584	7600	6739.406
5	6500	5593.368	9200	7916.767

Now using the same method but using the discounted cash flows we can calculate the discounted payback period

Discounted Payback period for Machine A

= 2.807

Discounted Payback period for Machine AB

= 3.241

As we can see that Machine A has shorter Payback and discounted payback period and is covering the initial cost quickly as compare to Machine B

Hence Machine A should be used