Question

X Company must replace one of its current machines with either Machine A or Machine B. The useful life of both machines is seven years. Machine A costs $51,000, and Machine B costs $59,000. Estimated annual cash flows with the two machines are as follows:

Year	Machine A	Machine B
1	$-6,000	$-7,000
2	-8,000	-4,000
3	-8,000	-3,000
4	-8,000	-3,000
5	-6,000	-3,000
6	-5,000	-2,000
7	-4,000	-2,000

If X Company buys Machine B instead of Machine A, what is the payback period (in years)?

Present Value of $1.00

Period	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%
1	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	0.901	0.893
2	0.943	0.925	0.907	0.890	0.873	0.857	0.842	0.826	0.812	0.797
3	0.915	0.889	0.864	0.840	0.816	0.794	0.772	0.751	0.731	0.712
4	0.888	0.855	0.823	0.792	0.763	0.735	0.708	0.683	0.659	0.636
5	0.863	0.822	0.784	0.747	0.713	0.681	0.650	0.621	0.593	0.567
6	0.837	0.790	0.746	0.705	0.666	0.630	0.596	0.564	0.535	0.507
7	0.813	0.760	0.711	0.665	0.623	0.583	0.547	0.513	0.482	0.452
8	0.789	0.731	0.677	0.627	0.582	0.540	0.502	0.467	0.434	0.404

Present Value of an Annuity of $1.00

Period	3%	4%	5%	6%	7%	8%	9%	10%	11%	12%
1	0.971	0.962	0.952	0.943	0.935	0.926	0.917	0.909	0.901	0.893
2	1.913	1.886	1.859	1.833	1.808	1.783	1.759	1.736	1.713	1.690
3	2.829	2.775	2.723	2.673	2.624	2.577	2.531	2.487	2.444	2.402
4	3.717	3.630	3.546	3.465	3.387	3.312	3.240	3.170	3.102	3.037
5	4.580	4.452	4.329	4.212	4.100	3.993	3.890	3.791	3.696	3.605
6	5.417	5.242	5.076	4.917	4.767	4.623	4.486	4.355	4.231	4.111
7	6.230	6.002	5.786	5.582	5.389	5.206	5.033	4.868	4.712	4.564
8	7.020	6.733	6.463	6.210	5.971	5.747	5.535	5.335	5.146	4.968

Answer 1

Extra cost of machine B =	$59000-$51000
	$8000
Year	Incremental cash flow	Cumulative Cash flow
0	($8000)	($8000)
1	($1000)	($9000)
2	$4000	($5000)
3	$5000	$0
4	$5000	$5000
5	$3000	$8000
6	$3000	$11000
7	$2000	$13000
Payback period is 3 years