Question

Nioorman Ltd is considering buying a new machine and has two options, Machine X and Machine Y. Each machine costs $120,000 and will have a five year life with no residual value at the end of that time. The net annual cash inflows for each machine are as follows:

Machine X Machine Y

$ $

Year 1 40,000 25,000

2 40,000 50,000

3 40,000 40,000

4 40,000 45,000

5 40,000 50,000

Norman’s cost of capital is 12%.

Required:

(a) Calculate the payback period for Machine X and Machine Y.

(b) Calculate the Net Present Value of Machine X and Machine Y using the present value table given below.

Answer 1

Ans.

(a) Calculate the payback period for Machine X and Machine Y

Machine X

Payback Period = Initial Investment / Annual Payback

= $ 120,000 / $ 40,000 = 3 Years

Machine Y

Year	Cash Flows	Cumulative
0	$ (120,000.00)	$ (120,000.00)
1	$       25,000.00	$    (95,000.00)
2	$       50,000.00	$    (45,000.00)
3	$       40,000.00	$      (5,000.00)
4	$       45,000.00	$      40,000.00
5	$       50,000.00	$      90,000.00

So by the table we get that within 3 years $ 115,000 is recovered and $ 5,000 is recovered in 4th Years so ( $ 5,000 / $ 45,000 = 0.1111years) .

So total Payback Period is 3 + 0.11 = 3.11 Years

(b) Calculate the Net Present Value of Machine X and Machine Y

Net Present Value is calculated as Present Value of Cash Inflows - Present Value of Cash Outflows

Machine X

Year	Cash Flows	Present Value Factor @ 12%	Present Value
0	$ (120,000.00)	1	$ (120,000.00)
1	$       40,000.00	0.892857143	$      35,714.29
2	$       40,000.00	0.797193878	$      31,887.76
3	$       40,000.00	0.711780248	$      28,471.21
4	$       40,000.00	0.635518078	$      25,420.72
5	$       40,000.00	0.567426856	$      22,697.07
		NPV	$      24,191.05

Machine Y

Year	Cash Flows	Present Value Factor @ 12%	Present Value
0	$ (120,000.00)	1	$ (120,000.00)
1	$       25,000.00	0.892857143	$      22,321.43
2	$       50,000.00	0.797193878	$      39,859.69
3	$       40,000.00	0.711780248	$      28,471.21
4	$       45,000.00	0.635518078	$      28,598.31
5	$       50,000.00	0.567426856	$      28,371.34
		NPV	$      27,621.99