Question

D Question 10 10 pts An investor is considering the purchase of a rental house for $120,000. The house generates monthly rent of $1.250 per month with no expected vacancy. and annual operating expenses are expected to be $4,800. The investor expects to hold the property for five years and then hopes to sell for $150,000. Based on these assumptions, what is the expected overall return on this investment? 9.27% 10.22% 10.69% 11.48% 12.40%

Answer 1

Solution:-

Annual cash inflow= 1,250*12 - 4,800 = $10,200

We can calculate the return of the investment by calculating the internal rate of return. IRR is calculated through trial and error method with the basic premise that the NPV of an investment is zero when IRR is used as discount rate.

Using trial and error method, we need to find the two discount rates between which the IRR falls. The idea is to get a range between which IRR exists and than use that range to calculate the exact IRR.

Let's find out the NPV using discount rate of 10%.

NPV= Present value of cash inflows - present value of cash outflows

NPV= {(Annual cash inflow*sum of PV factors at 10% for 5 years) + sale value*PV factor 5th year} - 120,000

NPV= 10,200*3.791 + 150,000*0.621 - 120,000 = $11,818.2

If NPV was zero, 10% would be the IRR. But since NPV is positive it means that IRR is higher than 10%. Let's now calculate NPV at 13%.

NPV= Present value of cash inflows - present value of cash outflows

NPV= {(Annual cash inflow*sum of PV factors at 10% for 5 years) + sale value*PV factor 5th year} - 120,000

NPV= 10,200*3.517 + 150,000*0.543 - 120,000 = -$2,676.6

Since NPV is negative at 13% and positive at 10%, it means that IRR lies between these two rates and hence calculated as below:

IRR= 10% + [11,818.2/{(11,818.2-(-2,676.6)}]*(13%-10%)

IRR= 10% + (11,818.2/14,494.8)*3%

IRR= 12.4%

Thus, the expected return on investment is 12.4% and the correct option is the fourth option.