Question

The NPV of a series of cash flows is the following:

At a 5% required rate of return, the NPV is $41,728

At a 10% required rate of return, the NPV is $24,708

At a 15% required rate of return, the NPV is $9,940

At a 20% required rate of return, the NPV is -$2,968 (note the negative sign)

The IRR for the series of cash flows is in which range:

Multiple Choice

0% to 5%

Between 5% and 10%

Between 10% and 15%

Between 15% and 20%

Answer 1

The correct answer is option (d). Between 15% and 20%

INTERNAL RATE OF RETURN (IRR) means the rate at which NPV is zero . It means the rate at which present values of total cash inflows is equal to present value of total cash outflows.

We know that as discount rate increases the Net present value of series of cash flows decreases.

EXPLANATION

We can observe that in the given case as required rate increased from 5% to 20% the NPV of series of cash flows has decreased from $41,728 to -$2,968.

So, we need to find the required rate at which the net present value (NPV) is zero.

From the given case we can observe that the NPV is near to zero when the required rate is 20% (-$2,968).

And as the rate has decreased to 15% the NPV has increased and became positive ($9,940). It means the required discount rate at which NPV is zero is present in between the required rates of 15% and 20%.

I have concluded that NPV is zero when required rate is between 15% and 20% because, we know that a number changes its sign from negative to positive or positive to negative at Zero (0). In the given case the NPV has changed from $9,940 (positive) to -$2,968 (negative) when in between 15% and 20%. So, I have concluded that the NPV is zero when the rate is in between 15% and 20%.

Internal rate of return means the rate at which NPV is zero. From our discussion NPV is zero between 15% and 20%.

So, IRR (Internal rate of return) is present in between the required rate of 15% and 20%.

​​​​​​Hope you understood the solution. If you have any doubt please leave your doubt in the comment section so that I can clarify your doubt.

Thank you.