The Tool Box needs to purchase a new machine costing $1.46 million. Management is estimating the machine will generate cash inflows of $223,000 the first year and $600,000 for the following three years. If management requires a minimum 12 percent rate of return, should the firm purchase this particular machine based on its IRR? Why or why not?

Yes, because the IRR is 10.75 percent
Yes, because the IRR is 12.74 percent
No, because the IRR is 10.75 percent
No, because the IRR is 12.74 percent
The answer cannot be determined as there are multiple IRRs

Question

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Respuesta :

DeniceSandidge DeniceSandidge · Answer 1 · 2019-12-16T16:38:36+01:00

Answer:

yes, because the IRR is 12.74 percent

Explanation:

given data

present value = $1.46 million

first year cash inflows c1 = $223,000

next three years cash inflows c2,c3,c4 = $600,000

rate of return minimum = 12 %

to find out

firm purchase this particular machine based on its IRR

solution

we consider here IRR is = r

we apply here present value formula that is express as

present value = [tex]\frac{c1}{(1+r)} +\frac{c2}{(1+r)^2} +\frac{c3}{(1+r)^3} +\frac{c4}{(1+r)^4}[/tex] .......1

put here value

$1.46 million = [tex]\frac{223000}{(1+r)} +\frac{600000}{(1+r)^2} +\frac{600000}{(1+r)^3} +\frac{600000}{(1+r)^4}[/tex]

solve it we get

r = 12.74%

so here IRR = 12.74% is higher than the rate of return minimum = 12%

so it will create a positive net present value of cash inflows

and project will accepted and firm purchase the machine

so we can say yes, because the IRR is 12.74 percent