Question

The Explorer 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 $15 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 $20 million and realizes after-tax inflows of $5 million per year for 7 years, after which it must be replaced. The cost of capital is 9%. What is the equivalent annual annuity for each machine? Which machine should the Explorer Company choose and why?

Answer 1

Calculation of Equivalent Annual Annuity of the Each Machine
Year	Machine A	Machine B
Cash Flows	Discount Factor @9%	Discounted Cash Flows	Cash Flows	Discount Factor @9%	Discounted Cash Flows
A	B	C = 1/(1+9%)^n	D = B*C	E	F = 1/(1+9%)^n	G = E*F
0	-15000000	1	-15000000	-20000000	1	-20000000
1	6000000	0.917431193	5504587.156	5000000	0.917431193	4587155.96
2	6000000	0.841679993	5050079.96	5000000	0.841679993	4208399.97
3	6000000	0.77218348	4633100.88	5000000	0.77218348	3860917.4
4	6000000	0.708425211	4250551.266	5000000	0.708425211	3542126.06
5		0.649931386	0	5000000	0.649931386	3249656.93
6		0.596267327	0	5000000	0.596267327	2981336.63
7		0.547034245	0	5000000	0.547034245	2735171.22
NPV			4438319.262			5164764.18
Equivilant Annual Annuity of Machine B = [r * NPV] / [1 - (1+r)^-n]
		= [9% * $4438319.262] / [1 - (1+9%)^-4]
		= $399,448.7336 / 0.291574789
		= $1,369,970.069
		= $1,369,970.07
Equivilant Annual Annuity of Machine B = [r * NPV] / [1 - (1+r)^-n]
		= [9% * $5,164,764.18] / [1 - (1+9%)^-7]
		= $464,828.776 / 0.45296576
		= $1,026,189.66
EAA of Machine A is higher than Machine B
Therefore, Machine A should be selected