As a capital budgeting director for ABC company, you are evaluating the construction of a new plant. The plant has a net cost of $5 million in year 0, and it will provide net cash inflows of $1 million in year 1, $1.5 million in year 2, and $2 million ib years 3 through 5. As a first approximation, you may assume that all cash flows occur at year-end. Within what range is the plant’s IRR?

[tex]NPV = -5,000,000+\frac{1,000,000}{(1+IRR)^{1} }+\frac{1,500,000}{(1+IRR)^{2} }+\frac{2,000,000}{(1+IRR)^{3} }+\frac{2,000,000}{(1+IRR)^{4} }+\frac{2,000,000}{(1+IRR)^{5} }[/tex]

Approximation by defect:

Be

[tex]CF = 1,000,000 + 1,500,000 + 2,000,000 + 2,000,000 + 2,000,000 = 8,500,000[/tex]

[tex]INV = 5,000,000[/tex]

[tex]XCF = 1x1,000,000+2x1,500,000+3x2,000,000+4x2,000,000+5x2,000,000=1,000,000 + 3,000,000+6,000,000+8,000,000+10,000,000=28,000,000[/tex]

[tex]IRR = (\frac{CF}{INV})^{\frac{CF}{XCF} } -1[/tex]

[tex]IRR = (\frac{8,500,000}{5,000,000})^{\frac{8,500,000}{28,000,000} }-1[/tex]

[tex]IRR = (1.7)^{0.30357 }-1= 1.17478-1 = 0.17478[/tex]

IRR = 17.48%

Approximation by excess:

Be

[tex]CF = 1,000,000 + 1,500,000 + 2,000,000 + 2,000,000 + 2,000,000 = 8,500,000[/tex]

[tex]INV = 5,000,000[/tex]

[tex]YCF = 1,000,000/1+1,500,000/2+2,000,000/3+2,000,000/4+2,000,000/5=1,000,000+750,000+666,667+500,000+400,000=3,316,667[/tex]

[tex]IRR = (\frac{CF}{INV})^{\frac{YFC}{CF} } -1[/tex]

[tex]IRR = (\frac{8,500,000}{5,000,000})^{\frac{3,316,667}{8,500,000} } -1[/tex]

[tex]IRR = (1.7)^{0.39} -1=1.2299-1=0.2299[/tex]

IRR = 22.99%

Then,

17.48%<IRR<22.99%

Hope this helps!