Question

(10000, -6000, -5500)

(10000, -3200, -8960)

(10000, -6800, -4320)

a. What is the interest rate for each of the cash flows?

Answer 1

a)

i)

Let r be interest rate

(10000, -6000, -5500)

NPV=10000-6000/(1+r)-5500/(1+r)^2

Put NPV=0

0=10000-6000/(1+r)-5500/(1+r)^2

10000*(1+r)^2-6000*(1+r)-5500=0

Let 1+r=x

10000x^2-6000x-5500=0

100x^2-60x-55=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}=\frac{60\pm \sqrt{(-60)^{2}-4*100*(-55)}}{2*100}$

$x=\frac{60\pm 160}{2*100}=1.1 \; and\; -0.50$

We know that 1+r=x

for x=1.1, r=0.1 or 10%

for x=-0.50, r=-1.50 or -150%

We ignore negative value of r,

So, interest rate=10%

ii)

Let r be interest rate

(10000, -3200, -8960)

NPV=10000-3200/(1+r)-8960/(1+r)^2

Put NPV=0

0=10000-3200/(1+r)-8960/(1+r)^2

10000*(1+r)^2-3200*(1+r)-8960=0

Let 1+r=x

10000x^2-3200x-8960=0

1000x^2-320x-896=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}=\frac{320\pm \sqrt{(-320)^{2}-4*1000*(-896)}}{2*1000}$

$x=\frac{320\pm 1920}{2*1000}=1.12 \; and\; -0.80$

We know that 1+r=x

for x=1.12, r=0.12 or 12%

for x=-0.80, r=-1.80 or -180%

We ignore negative value of r,

So, interest rate=12%

iii)

Let r be interest rate

(10000, -6800, -4320)

NPV=10000-6800/(1+r)-4320/(1+r)^2

Put NPV=0

0=10000-6800/(1+r)-4320/(1+r)^2

10000*(1+r)^2-6800*(1+r)-4320=0

Let 1+r=x

10000x^2-6800x-4320=0

1000x^2-680x-432=0

$x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}=\frac{680\pm \sqrt{(-680-)^{2}-4*1000*(-432)}}{2*1000}$

$x=\frac{680\pm 1480}{2*1000}=1.08 \; and\; -0.40$

We know that 1+r=x

for x=1.08, r=0.08 or 8%

for x=-0.40, r=-1.40 or -140%

We ignore negative value of r,

So, interest rate=8%