Question

The XYZ Company has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $14 million but realizes after-tax inflows of $6 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $17 million and realizes after-tax inflows of $4.5 million per year for 8 years, after which it must be replaced. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. If the cost of capital is 12 percent, which machine should the company use? Show all work.

ANSWER ASAP please

Answer 1

When two projects have unequal lives, we use the Equivalent Annual Annuity approach to compare the two projects.

First, we will compute the Net present value of both the machines.

	MACHINE A				MACHINE B
Year	Cash Flows (a)	Present value factor @12% (b)	Present Value (a*b)	Year	Cash Flows	Present value factor @12%	Present value
0	(14,000,000)	1	(14,000,000)	0	(17,000,000)	1	(17,000,000)
1	6,000,000	0.893	5,358,000	1	4,500,000	0.893	4,018,500
2	6,000,000	0.797	4,782,000	2	4,500,000	0.797	3,586,500
3	6,000,000	0.712	4,272,000	3	4,500,000	0.712	3,204,000
4	6,000,000	0.636	3,816,000	4	4,500,000	0.636	2,862,000
				5	4,500,000	0.567	2,551,500
				6	4,500,000	0.507	2,281,500
				7	4,500,000	0.452	2,034,000

				8	4,500,000	0.404	1,818,000
		NPV	4,228,000			NPV	5,356,000

Here, the NPV of machine A comes out to be $4,228,000 and the NPV of Machine B comes out to be $5,356,000.

We will now calculate the EAA of both the machines to compare between the two.

where,

EAA = Equivalent Annual Annuity

r = cost of capital

NPV = Net present value

n= Porject life

This implies that,

EAA OF MACHINE A = 12% * 4228000 / [1 -{(1.12)^ -4}]

= 12%* 4228000/ 1-0.6355

= 12% * 4228000/ 0.3645

=507360/0.3645

= $1,391,934.15

EAA OF MACHINE B = 12% * 5356000/ [1- {(1.12)^ -8}]

=12% * 5356000/ 1-0.4038

= 12% * 5356000/ 0.5962

= 642720/ 0.5962

= $1,078,027.5

Therefore, it can be observed that though Machine B has a greater NPV than Machine A, EAA of Machine A comes out to be more than that of Machine B. EAA tells about the average cash flows each machine will generate.

Therefore, we recommend company XYZ to invest in Machine A.