by Russell Burdt

The interactive application below implements the real estate investment strategy described in The Book on Rental Property Investing: How to Create Wealth and Passive Income Through Intelligent Buy & Hold Real Estate Investing! by Brandon Turner. The app can be used to assess the current and future value of a real estate investment.

This model of a real estate investment relies on three categories of investment parameters. **Transactions and mortgage** parameters are all associated with the initial purchase and loan. **Monthly rent and expenses** represent all recurring costs and income on a monthly basis. And then **appreciation and sale** are all parameters associated with the final sale.

The application automatically calculates investment metrics from investement parameters. Categories of investment metrics include **initial investment metrics** representing metrics relevant at the initial purchase, **monthly investment metrics** representing monthly cash flow calculations, and then **final investment metrics** that include the total annual return and other metrics determined at the time of sale.

Modify the investment parameters below to update the investment metrics and assess the current and future value of a real estate investment. Go to the *Investment Charts* tab to view the dependence of any metric on any parameter (all else being equal). The case study below the application is a full explanation of the calculations behind the application.

This case study reflects default investment parameters in the interactive application. The case study describes an assessment of a rental investment property. A similar use of the interactive application could apply to a single family home, e.g. by setting the monthly rent and vacancy costs to zero.

The **initial investment metrics** are determined at the time of the initial purchase. The principal initial investment metric will be the total invested capital, which represents all capital required to close the deal.

- The calculation of down payment is straightforward —

\(\text{Down Payment} = \text{Down Payment Percentage} \times \text{Purchase Price} = 0.20 \times $688,000 = $137,600\) - The calculation of loan amount is also straightforward —

\(\text{Loan Amount} = \text{Purchase Price} - \text{Down Payment} = $688,000 - $137,600 = $550,400\) - The total invested capital, representing all capital needed to close the deal, is then —

\(\text{Total Invested Capital} = \text{DownPayment} + \text{Purchase Closing Costs} + \text{Initial Repairs} + \text{Pre-Rent Holding Cost} = $137,600 + $2,000 + $6,000 + \text{Pre-Rent Holding Cost}\) - The purchase closing costs may be zero or may include legal fees or some other costs and are estimated as $2,000 for the case study. The cost of initial repairs is estimated to be $6,000 for the case study.
- The pre-rent holding cost requires knowledge of monthly expenses in order to be calculated —

\(\text{Pre-Rent Holding Cost} = \frac{\text{Pre-Rent Holding Days}}{30} \times \left(\text{Monthly Expenses} - \text{Vacancy Cost} - \text{Property Management}\right) = \frac{15}{30} \times \left($3,614 - $117 - $100\right) = $1,699\) - Vacancy cost associated with monthly expenses is explained in the next section, and it is not the same thing as the cost associated with vacancy immediately after the purchase and before rent is first received. Also the property management monthly expense is typically not incurred before rent is first received. For these reasons those expenses are removed from the total monthly expenses when calculating the pre-rent holding cost, as seen in the above equation.
- Total invested capital for the case study can then be calculated as $147,299.

The **monthly investment metrics** apply every month between the initial purchase and the final sale. It is critical to understand the full monthly cash flow equation and not to leave out any term that could impact monthly expenses.

- The principal monthly cash flow equation is —

\(\text{Monthly Cash Flow} = \text{Monthly Rent} - \text{Monthly Expenses} = $4,200 - \text{Monthly Expenses}\) - The monthly rent is an estimate of the amount received from renters, $4,200 in the case study. Monthly rent is a single number to estimate. Monthly expenses on the other hand is the sum of several components, all of which must be individually calculated or estimated and not omitted —

\(\text{Monthly Expenses} = \text{Mortgage Payment} + \text{Taxes} + \text{Insurance} + \text{Capex} + \text{HOA} + \text{Property Management} + \text{Vacancy Cost}\) - The monthly mortgage payment can be calculated directly, however it is not straightforward to do so. Typically some sort of web-based calculator would be used or a lender would provide the numbers. This being a tech blog with an emphasis on programming, here is a Python function to do it. The function returns a monthly mortgage payment of $2,433 for the numbers in the case study.

```
def get_monthly_mortgage_payment(amount, interest, term):
"""
return a monthly mortgage payment from the loan amount, interest rate, and term in years
"""
# get the modified interest rate and term in month units
interest = interest / 100 / 12
term = term * 12
# calculate and return the mortgage monthly payment
sum = 0
for i in range(int(term)):
sum += (1 + interest) ** i
return (amount / sum) + (interest * amount)
```

\(\text{Monthly Cash Flow} = $4,200 - \left($2,433 + $744 + $120 + $100 + $0 + $100 + $117\right) = $586\)

The **final investment metrics** can be defined and calculated, however the exact numbers will be uncertain because annual appreciation and the number of years the property will be held can be difficult to estimate. For example, decreasing the estimate of annual appreciation in the case study from 4% to 2% (using the interactive application) removes several points from the total annual return of the investment. The *investment charts* tab of the application can be used in this case to visualize how annual appreciation (or any other investment metric) impacts the total annual return.

- The appreciation multiplier represents the total impact of annual appreciation over the duration of the investment —

\(\text{Appreciation Multiplier} = \left(1 + \text{Annual Appreciation}\right)^{\text{Holding Years}} = \left(1 + 0.04\right)^{10} = 1.48\) - The sale price is then the purchase price scaled by the appreciation multiplier —

\(\text{Sale Price} = \text{Appreciation Multiplier} \times \text{Purchase Price} = 1.48 \times $688,000 = $1,018,408\) - The agent sale fee can be a significant fraction of the sale price and 6% is common. So for the case study —

\(\text{Agent Sale Fee} = \text{Agent Sale Percentage} \times \text{Sale Price} = 0.06 \times $1,018,408 = $61,104\) - Most often the mortgage will not be fully paid when a property is sold, so there will be a mortgage balance that needs to be paid. A bank will provide the official number when the time comes, and the Python function below can be used to estimate that number. For the parameters of the case study the function returns $424,247 (the original loan amount 10 years earlier in the case study was $550,400).

```
def get_mortgage_balance(amount, interest, term, hold):
"""
return remaining mortgage balance after 'hold' years
the mortgage is defined by amount, interest, and term
"""
# get the modified interest rate, term, and hold in month units
interest = interest / 100 / 12
term = term * 12
hold = hold * 12
# calculate and return the remaining mortgage balance
sum1, sum2 = 0, 0
for i in range(int(hold)):
sum1 += (1 + interest) ** i
for i in range(int(term)):
sum2 += (1 + interest) ** i
return amount * (1 - (sum1 / sum2))
```

\(\text{Sale Expenses} = \text{Mortgage Balance} + \text{Agent Sale Fee} + \text{Closing Costs} + \text{Cleanup Costs} = $424,247 + $61,104 + $5,000 + $6,000 = $496,351\)

\(\text{Total Profit at Sale} = \text{Sale Price} - \text{Sale Expenses} = $1,018,408 - $496,351 = $522,057\)

\(\text{Total Profit} = \left(12 \times \text{Monthly Cash Flow} \times \text{Holding Years}\right) + \text{Total Profit at Sale} = \left(12 \times $585.70 \times 10\right) + $522,057 = $592,341\)

\(\text{Total Profit} = \text{Total Invested Capital} \times \left(1 + \text{Total Annual Return}\right)^{\text{Holding Years}}\)

\(\text{Total Annual Return} = \left(\frac{\text{Total Profit}}{\text{Total Invested Capital}}\right)^{1/\text{Holding Years}} - 1 = \left(\frac{$592,341}{$147,299}\right)^{1/10} - 1 = 14.9\%\)

The case study represents a positive opportunity for a real estate investment, because the equivalent total annual return of 14.9% beats the same for other average investment returns. The risk is that the real annual return will be lower because investment parameters were not estimated correctly. The interactive appliation is meant to be used to explore the impact of errors in the estimated investment parameters, to quantify the risk and ultimately to assess the current and future value of a real estate investment.

One interesting relationship to be aware of is the dependence of total annual return on the number of years the investment is held. Though it is true that profit can only increase over time (assuming only positive appreciation), it is not true that total annual return can only increase over time. For the default parameters of the case study, the *investment charts* tab was used to determine that 5 years would be the optimal holding years to maximize the total annual return (all else being equal), and that total annual return will decrease thereafter. The profit would continue to increase after 5 years however, so a decision would need to be made as to which metric is more important.

Please comment or reach out with your feedback or for more information on the interactive application.