Question

X Company is considering replacing one of its machines in order to save operating costs. Operating costs with the current machine are $65,000 per year; operating costs with the new machine are expected to be $33,530 per year. The new machine will cost $154,000 and will last for five years, at which time it can be sold for $3,000. The current machine will also last for five more years but will not be worth anything at that time. It cost $40,000 four years ago, but its current disposal value is only $4,000.

9. Assuming a discount rate of 7%, what is the incremental net present value of replacing the current machine?

10. Assume the following two changes: 1) both machines will last for six more years, 2) the salvage value of the new machine after six years will be zero. If X Company replaces the current equipment, what is the approximate internal rate of return?

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

	Years	0	1 - 5	5
	Cost of new machine	-154000
	Sale of old machine	4000
	Savings in operating cost(65000-33530)		31470
	Salvage of new machine			3000
	NCF	-150000	31470	3000
	PV Factor @ 7%	1	4.100	0.7130
	PV of NCF	-150000	129033	2139
	Incremental NPV =		-18828
	IRR is the rate at which the NPV =0
	New cashflows
	Years	0	1 - 6
	Cost of new machine	-154000
	Sale of old machine	4000
	Savings in operating cost(65000-33530)		31470
	NCF	-150000	31470
	PV of Inflow = PV of outflow
	PVAF(r,6) x 31470 =	150000
	PVAF(r,6) =	150000/31470
		4.766
	From annuity table -
	PVAF(r,6) =	4.766
	r =	7%
	(Check in annuity table annuity factor for 6 years )