Question

The Petersik family is considering purchasing a second home to use for short term rentals near the beach. If it purchases the house, they will place a down payment of $62,000 on the house. They estimate they will get an annual net rental profit of $7,500 after their mortgage and expenses are paid. After 18 years, they plan to pass the rental home along to their children, so assume the home has negligible salvage value. What would be the ERR if the Petersik family decides to invest in a rental home, assuming they keep the home for 18 years? Assume their MARR is 14%.

Answer 1

Given: Initial Outlay = 62000 , Net Annual Income = 7500, Period = 18 years , MARR = 14%

Compute ERR.

ERR is the economic rate of return of the investment. It is the rate at which present value of cash inflows is equal to initial outlay. It is the IRR of the project.

You need to go with hit and trial method And then interpolation.

In hit and trial method you need to guess the rate at which the present value of monthly payments is equal to the Loan amount. You need to continue guess till you get the two rate. At one rate your Pv is less than loan amount and at other Pv is more than loan amount and then Do interpolation to find the rate.

While guessing you need to think smart as to reduce the work because for exact and/or Close approximation answer the difference between the two rate should be minimal.

Calculate the PV of Net Annual income at rate = 10%

PV = Net annual income x Cumulative discounting factor @ 10% for 18 periods

[ For Cumulative discount/pv factor refer the table or can calculate as it is sum of (100/110) + (100/110)² ...............(100/110)¹⁸ ]

= 7500 x 8.20141

= 61510.575

Pv is lower than 62000 so decrease the rate little bit to get higher amount

Calculate the PV of Net Annual income at rate = 9%

PV = Net annual income x Cumulative discounting factor @ 9% for 18 periods

[ For Cumulative discount/pv factor refer the table or can calculate as it is sum of (100/109) + (100/109)² ...............(100/109)¹⁸ ]

= 7500 x 8.75563

= 65667.225

Now you have two rates. Do interpolation to get the IRR at which PV is 63000.

=

= 9 + (3667.225 / 4156.65 ]

= 9 + 0.88225

= 9.88225

ERR = 9.88 % Approx

Since ERR is Lower than MRR. SO do not Invest in that property.