Compound Interest and Real Estate Investment Valuation

Real estate investment is a cornerstone in many investors’ portfolios. A comprehensive understanding of the tools and methods used in evaluating real estate projects is necessary for sound investment decisions. Central to these tools are the concepts of compound interest and their applications in estimating the present and future value❓ of investments. This chapter, “Compound Interest and Methods of Real Estate Investment Evaluation,” is part of the “Fundamentals of Financial and Real Estate Calculations” course. It aims to provide participants with the theoretical knowledge and practical skills necessary to analyze and evaluate investment opportunities in the real estate sector efficiently and effectively.

Compound interest is a fundamental concept in finance and investment. It reflects the ability of capital to grow rapidly over time, where interest is calculated not only on the principal amount invested but also on the accumulated interest from previous periods. Understanding the mechanisms of compound interest is necessary to estimate the real return❓ on investment, compare different investment alternatives, and make appropriate decisions that align with the investor’s financial goals.

In the context of real estate investment, compound interest plays a crucial role in evaluating long-term projects, such as property❓❓❓ development or investment in leased properties. By using tools such as present value and future value, and using appropriate discount rates, investors can estimate the real value of the property and determine whether the investment is economically viable. Understanding capital recovery methods, such as the hoskold method❓ or the sinking fund method, and the Inwood method, helps in analyzing expected cash flows and determining the return on investment accurately.

The educational objectives of this chapter are:

1. Understanding the concept of compound interest and how to calculate it periodically (annually, quarterly, monthly, etc.).
2. Applying compound interest in calculating future value and present value.
3. Exploring methods of real estate investment evaluation, with a focus on the applications of compound interest in these methods.
4. Analyzing capital recovery methods such as the Hoskold method and the Inwood method.
5. Developing financial analysis skills.
6. Awareness of unethical practices in valuation, such as “valuation at a predetermined value.”
7. Understanding measures of central tendency (arithmetic mean, median, mode, and range) and their uses in real estate data analysis.

A. Simple and Compound Interest: Overview

Simple Interest: Calculated only on the principal amount. No interest is earned on accumulated interest.

Compound Interest: Calculated on the principal amount plus accumulated interest from previous periods. Interest earns interest, leading to faster investment growth over time.

B. How Compound Interest Works

Compound interest relies on reinvesting earned interest, allowing it to generate more interest in subsequent periods. The compounding period is a crucial factor in calculating compound interest.

Compounding Period: The time period in which interest is calculated and added to the principal amount. It can be annual, semi-annual, quarterly, monthly, or even daily.

Example:
A savings account with $1000, an annual interest rate of 5%, compounded annually.
Year 1: Interest = $1000 * 0.05 = $50. Total amount at year-end = $1050.
Year 2: Interest = $1050 * 0.05 = $52.5. Total amount at year-end = $1102.5.

Example: Quarterly Compounding:
If the annual interest rate is 10%, compounded quarterly, the quarterly interest rate is 2.5% (10% / 4 = 2.5%).

1st Quarter:
$100.00 * 0.025 = $2.50 (Interest)
$100.00 + $2.50 = $102.50 (Balance after 1st Quarter)

2nd Quarter:
$102.50 * 0.025 = $2.56 (Interest)
$102.50 + $2.56 = $105.06 (Balance after 2nd Quarter)

3rd Quarter:
$105.06 * 0.025 = $2.63 (Interest)
$105.06 + $2.63 = $107.69 (Balance after 3rd Quarter)

4th Quarter:
$107.69 * 0.025 = $2.69 (Interest)
$107.69 + $2.69 = $110.38 (Balance after 4th Quarter - End of Year)

With quarterly compounding at a 10% annual interest rate, the future value of $100 after one year is $110.38.

C. Calculating Future Value and Present Value

The relationship between present value and future value is fundamental in financial analysis. Future Value (FV) is the value of an investment at a specific future date, while Present Value (PV) is the value of a future amount today.

Formulas:

Future Value (FV):
FV = PV * (1 + r/n)^(n*t)
Where:
PV: Present Value
r: Annual interest rate (decimal)
n: Number of times interest is compounded per year
t: Number of years

Present Value (PV):
PV = FV / (1 + r/n)^(n*t)
Where:
FV: Future Value
r: Annual interest rate (decimal)
n: Number of times interest is compounded per year
t: Number of years

Importance:
These formulas help determine if an investment is worthwhile. By calculating the present value of expected future cash flows from a real estate investment, an investor can compare it to the current cost of the investment to make an informed decision.

D. Methods for Evaluating Real Estate Investment

Several methods exist for evaluating real estate investment, each with strengths and weaknesses. Key methods include:

1. Income Approach: Estimates property value based on the expected income it will generate.

   • Gross Rent Multiplier (GRM): Compares the property price to the total annual rent.

     • GRM = Property Price / Total Annual Rent

     • GRM is used to compare similar properties in the same area.

       • Net Operating Income (NOI): Represents the income generated by the property after deducting operating expenses (such as taxes, insurance, and maintenance) but before deducting debt payments and income taxes.

     • NOI = Total Income - Operating Expenses

       • Capitalization Rate (Cap Rate): Used to convert NOI into property value.

     • Cap Rate = NOI / Property Price

     • Property Price = NOI / Cap Rate
     • A higher cap rate indicates a potentially higher return, but also higher risk.
       2. Cost Approach: Estimates the cost of building a similar new property, then deducts depreciation.

   • Property Value = New Construction Cost - Accumulated Depreciation + Land Value

   • This method is typically used to evaluate unique properties or those without an active market.
     3. Sales Comparison Approach: Compares the property being evaluated to similar properties that have recently been sold in the same area.

   • Adjustments are made to the prices of comparable properties to reflect differences between them and the property being evaluated (such as location, size, and condition).

   • This is the most common method for evaluating residential properties.

E. Other methods for evaluating real estate cash flows: Hoskold and Inwood

1. Hoskold Method: Mainly used for evaluating depleted assets such as mines and quarries. This method assumes that a portion of the annual income will be placed in a sinking fund to restore invested capital. Rarely used today because investors are looking for a higher rate of return.
2. Inwood Method: This method assumes that the present value of an investment depends on the discount rate. Inwood assumes that the annual redemption amount is capable of generating compound interest and is amortized like a loan.

F. Measures of Central Tendency

Measures of central tendency are important statistical tools that help in understanding and summarizing a set of data. In the context of real estate, they can be used to analyze property values in a specific area, rental rates, or gross rent multipliers. The main measures of central tendency are:

• Mean: The sum of the values divided by the number of values. Often used to refer to the “average” area or price.

  • Mean = (Sum of Values) / (Number of Values)
  • Median: The middle value in an ordered set of data. It is often used to refer to the average price of housing.
  • Mode: The most frequently occurring value in a data set. It is important to appraisers in developing comparisons.
  • Range: The difference between the highest and lowest value in the data set.

G. Standard Deviation

Standard deviation is a statistical measure that shows the extent to which data is dispersed around the mean. In the context of real estate, it can be used to assess the volatility of property prices❓ in a particular area. A small standard deviation means that most prices are close together, while a large standard deviation means that prices are more varied.