Need help calculating the IRR

Question

1. Machine A or Machine B

• Annual Production in units 40,000

• Cost of Machine A $38,000

• Cost of Machine B $32,000

• Unit Cost to Produce on Machine A $2.20

• Unit Cost to Produce on Machine B $2.22

• Useful Life 12 Years

Answer 1

Let us assume X in revenue per unit.

Equation to solve for IRR of Machine A is:

38,000 = 40,000 (X - 2.20)/(1+i(a))^1 + 40,000 (X - 2.20)/(1+i(a))^2 +....+40,000 (X - 2.20)/(1+i(a))^12

Equation to solve for IRR of Machine b is:

32,000 = 40,000 (X - 2.22)/(1+i(b))^1 + 40,000 (X - 2.22)/(1+i(b))^2 +....+40,000 (X - 2.22)/(1+i(b))^12

You have to provide a value for X to solve for IRR in either of these cases and then compare which machine provides a better IRR.

Another way to look at this is, in case of Project A for an additional $6,000 in upfront investment you have a $0.02 in cost savings per unit - which turns out to be a profit of $800 ($0.02*40,000) per year

i.e. 6,000 = 800/(1+i)^1 + 800/(1+i)^1 +...+ 800/(1+i)^12

==> i = 8.09%

In this case, rate of return on the incremental investment is 8.09%. So if the hurdle rate is less than 8.09% and capital is not constrained then you would choose Machine A.