Question

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?

Answer 1

IRR is within range (17.48%, 22.99%)

Step-by-step explanation:

`NPV = -5,000,000+(1,000,000)/((1+IRR)^(1) )+(1,500,000)/((1+IRR)^(2) )+(2,000,000)/((1+IRR)^(3) )+(2,000,000)/((1+IRR)^(4) )+(2,000,000)/((1+IRR)^(5) )`

Approximation by defect:

Be

`CF = 1,000,000 + 1,500,000 + 2,000,000 + 2,000,000 + 2,000,000 = 8,500,000`

`INV = 5,000,000`

`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`

`IRR = ((CF)/(INV))^{(CF)/(XCF) } -1`

`IRR = ((8,500,000)/(5,000,000))^{(8,500,000)/(28,000,000) }-1`

`IRR = (1.7)^(0.30357 )-1= 1.17478-1 = 0.17478`

IRR = 17.48%

Approximation by excess:

Be

`CF = 1,000,000 + 1,500,000 + 2,000,000 + 2,000,000 + 2,000,000 = 8,500,000`

`INV = 5,000,000`

`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`

`IRR = ((CF)/(INV))^{(YFC)/(CF) } -1`

`IRR = ((8,500,000)/(5,000,000))^{(3,316,667)/(8,500,000) } -1`

`IRR = (1.7)^(0.39) -1=1.2299-1=0.2299`

IRR = 22.99%

Then,

17.48%<IRR<22.99%

Hope this helps!