Question

Hotaling Corporation is analyzing a capital expenditure that will involve a cash outlay of $146,040. Estimated cash flows are expected to be $30,000 annually for seven years. The present value factors for an annuity of $1 for 7 years at interest of 6%, 8%, 10%, and 12% are 5.582, 5.206, 4.868, and 4.564, respectively. The internal rate of return for this investment is:

Answer 1

Answer:

The solution shows that a rate of return of 10% which provides an annuity factor of 4.868 generates an NPV which is equal to zero. Thus, our IRR or internal rate of return is 10%.

Explanation:

The IRR or internal rate of return is the rate at which NPV or Net Present Value of the investment becomes zero. We are provided with the initial outlay for the project and the annual cash inflows along with time period. Using the annuity factors given below, we need to find out the factor which makes the NPV zero. The NPV is calculated as follows,

NPV = Present Value of Cash Inflows - Initial Outlay

We can try out each annuity factor and see what NPV is generates.

1. 6% rate (Annuity factor = 5.582)

NPV = (30000 * 5.582)  -  146040

NPV = $21420

2. 8% rate (Annuity factor = 5.206)

NPV = (30000 * 5.206)  -  146040

NPV = $10140

3. 10% rate (Annuity factor = 4.868)

NPV = (30000 * 4.868)  -  146040

NPV = $0

So, from the above solution we can see that a rate of return of 10% which provides an annuity factor of 4.868 generates an NPV which is equal to zero. Thus, our IRR or internal rate of return is 10%