 BUSI 121 - Foundations of Real Estate Mathematics

Real Estate Division. 2017. Foundations of Real Estate Mathematics. Vancouver, BC: UBC Real Estate Division.

• Chapter 1: The Basis of Financial Analysis
Mathematics of Finance: Time Value of Money
Math Formulas and Financial Calculators
Financial Analysis of Real Estate: Asset Rental
Simple and Compound Interest
Compound Interest Calculations
Future Value and Present Value of Lump Sums
Other Lump Sum Calculations: Interest Rate and Holding Period
Summary
Appendix 1.1: Financial Algebra and Exponents
Appendix 1.2: Six Functions of a Dollar

• Chapter 2: Equivalent Interest Rates
The Importance of Compounding Frequency
Framework for Interest Rate Conversions
Interest Rate Conversions Using Mathematical Formulas
Interest Rate Conversions Using Financial Functions
Interest Rate Conversions in Practice: Interest Adjustments
Appendix 2.1: Calculator Steps for Examples

• Chapter 3: Present Value Analysis
Irregular Patterns of Costs and Benefits
Present Value of Irregular Cash Flows
Regular Payments and Irregular Intervals
Present Value of Regular Cash Flows
Mathematics of Annuities
Types of Annuities
Annuities Due
Perpetual Annuities
Present Value of Perpetual Annuities Due
Deferred Annuities
Summary
Appendix 3.1: Calculator Steps for Examples
Appendix 3.2: Proof for Present Value of an Annuity Relationship
Appendix 3.3: Verification of Alternative Methods for Annuity Due
Appendix 3.4: Proof of a Perpetual Annuity Formula
Appendix 3.5: Proof of Perpetual Annuities Due

• Chapter 4: Future Value Analysis
Future Values of Irregular Cash Flows
Future Value of Regular Cash Flows
Sinking Funds
Future Value Analysis and Ordinary General Annuities
Future Values and Deferred Annuities
Summary
Appendix 4.1: Calculator Steps for Examples
Appendix 4.2: Proof for Future Value of an Annuity Relationship
Appendix 4.3: Interest Only Loans

• Chapter 5: Mortgage Loan Analysis
Features of Constant Payment Mortgages
Calculation of Mortgage Loan Amount (Present Value)
Calculation of Payments to Amortize a Loan
Calculation of Interest Rates
Calculation of Amortization Periods
Calculation of Outstanding Balance
Calculation of Principal and Interest Components of Payments
Calculation of Final Payments on Fully Amortized Loans
Innovative Options for Constant Payment Mortgages
Summary
Appendix 5.1: Calculator Steps for Examples

• Chapter 6: Mortgage Finance Applications: Vendor Financing and Assumable Loans
Impact of Financing on Real Estate Transactions
Vendor-Supplied (Take-Back) Mortgage
Mortgage Assumption
Summary
Appendix 6.1: Calculator Steps for Examples
Appendix 6.2: Calculator Steps for Illustration 6.6

• Chapter 7: Mortgage Finance Applications: Cost of Borrowing and Investment Yields
Impact of Brokerage and Other Fees
Yield to the Lender
Investment Yield
Summary
Appendix 7.1: Calculator Steps for Examples

• Chapter 8: Real Estate Investment Analysis
Introduction to Investment Analysis
Time Value of Money
Present Value of Irregular Cash Flows
Net Present Value (NPV)
Present Value Ratios
Profitability Index
Internal Rate of Return (IRR)
Reinvestment Assumptions and Investment Measures
Comparison of Investment Alternatives
Summary
Appendix 8.1: Calculator Steps for Examples

• Chapter 9: Mathematics of Graphing and Surveying
Introduction to Graphing and Surveying
Part One: Graphing
Part Two: Surveyor’s Mathematics
Summary
Appendix 9.1: Examples of Living Area and Calculations

• Chapter 10: Foundations of Statistics
What is Statistics?
Working with Data
Simple Data Description: Absolute and Relative Frequencies
Pictorial Data Description
Simple Descriptive Statistics
Summary
Appendix 10.1: Calculator Steps for Examples

• Chapter 11: Exploring Statistical Relationships
Scatter Plots
Crosstabulation Analysis
Linear Correlation Coefficients
Simple Linear Regression Analysis
Summary
Appendix 11.1: Calculator Steps for Examples

• Chapter 12: Multiple Regression and Real Estate
Multivariate Regression Analysis
Evaluating Multiple Regression Results
Multiple Regression Analysis and Mass Appraisal
Summary
Appendix 12.1: Calculator Steps for Illustration

• Chapter 13: Further Topics in Statistics: Sampling and Time Series Analysis
Part 1: Sampling Theory
Sampling Methods
Sample Bias
Statistical Reliability
Part 2: Analysis of Time Series Data
Components of Time Series Data
Techniques to Determine the Components of Time Series Data
Moving Averages
Index Numbers
Summary
Appendix 13.1: Calculator Steps for Examples

• Index