Question

Consider the following two cash flow streams:

x1=(-100, 125, 0) and x2=(-75, 0, 100)

At which of the following interest rates would an individual be indifferent between cash flow streams x1 and x2 according to the the NPV criteria? (check all that apply)

50%

150%

0%

300%

Answer 1

Let the interest rate be i

NPV of x1=-100+125/(1+i)+0/(1+i)^2=-100+125/(1+i)

NPV of x2=-75+0/(1+i)+100/(1+i)^2=-75+100/(1+i)^2

Set both NPV's equal

-100+125/(1+i)=-75+100/(1+i)^2

Set (1+i)=y

-100+125/y=-75+100/y^2

Multiply by y^2 both sides

-100y^2+125y=-75y^2+100

25y^2-125y+100=0

y^2-5y^2+4=0

y^2-4y-y+4=0

y*(y-4)-1*(y-4)=0

(y-4)*(y-1)=0

y=1 or y=4

If y=0,

1+i=1

i=0 or say 0%

If y=4

1+i=4

i=3 or say 300%

We can see that NPV is negative at i=300% for both cases. So, investor will reject both cash flows

So, correct option is

0%