Question

Consider the investment projects given in the table below. Assume that MARR 13% in the following questions. Click the icon to view the net cash flows for the projects. Click the icon to view the interest factors for discrete compounding when MARR = 13% per year. (a) Computo for each investment. If the problem has more than one / , identify all of them Compute i for Project 1. Select the correct choice below and 0 More Info O A. Project 1 has a unique positive i of % (Round to B. Project 1 has two positive / values: % and 0% Net Cash Flow OC. Project 1 has no positive /' value. n Project 1 Project 2 - $1,100 - $1,100 2,400 1,980 - 760 1,000 Project 3 - $1,100 1,500 - 200 Print Done

Answer 1

Project 1

NPV of project=-1100+2400/(1+i)-760/(1+i)²

AT r=irr, NPV=0

-1100+2400/(1+i)-760/(1+i)²=0

-1100*(1+i)²+2400*(1+i)-760=0

1100*(1+i)²-2400*(1+i)+760=0

Let 1+i=x

1100x²-2400*x+760=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$x=\frac{2400\pm \sqrt{(-2400)^{2}-4*1100*760}}{2*1100}$

$x=\frac{2400\pm 1554.3487 }{2*1100}$

x=0.384387 or x=1.797431

(1+i)=0.384387 or (1+i)=1.797431

i=-0.615613 or i=0.797431

Project 1 has unique positive IRR i.e.79.74%

Project 2

NPV of project=-1100+1980/(1+i)+1000/(1+i)²

AT r=irr, NPV=0

-1100+1980/(1+i)+1000/(1+i)²=0

-1100*(1+i)²+1980*(1+i)+1000=0

1100*(1+i)²-1980*(1+i)-1000=0

Let 1+i=x

1100x²-1980*x-1000=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$x=\frac{1980\pm \sqrt{(-1980)^{2}-4*1100*(-1000)}}{2*1100}$

$x=\frac{1980\pm 2884.5104 }{2*1100}$

x=-0.411141 or x=2.211141

1+i=-0.411141 or x=2.211141

r=-1.411141 or r=1.211141

Project 2 has unique positive IRR i.e.121.11%

Project 3

NPV of project=-1100+1500/(1+i)-200/(1+i)²

AT r=irr, NPV=0

-1100+1500/(1+i)-200/(1+i)²=0

-1100*(1+i)²+1500*(1+i)-200=0

1100*(1+i)²-1500*(1+i)+200=0

Let 1+i=x

1100x²-1500*x+200=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}$

$x=\frac{1500\pm \sqrt{(-1500)^{2}-4*1100*200}}{2*1100}$

$x=\frac{1500\pm 1170.4700 }{2*1100}$

x=1.213850 or x=0.149786

1+i=1.213850 or 1+i=0.149786

i=0.213850 or i=-0.850214

Project 3 has unique positive IRR i.e. 21.38%