DISCLAIMER © Copyright: 2014
DISCLAIMER: This publication is intended for EDUCATIONAL purposes only. The information contained
herein is subject to change with no notice, and while a great deal of care has been taken to provide accurate
and current information, UBC, their affiliates, authors, editors and staff (collectively, the "UBC Group") makes
no claims, representations, or warranties as to accuracy, completeness, usefulness or adequacy of any of the
information contained herein. Under no circumstances shall the UBC Group be liable for any losses or
damages whatsoever, whether in contract, tort or otherwise, from the use of, or reliance on, the information
contained herein. Further, the general principles and conclusions presented in this text are subject to local,
provincial, and federal laws and regulations, court cases, and any revisions of the same. This publication is
sold for educational purposes only and is not intended to provide, and does not constitute, legal, accounting, or
other professional advice. Professional advice should be consulted regarding every specific circumstance
before acting on the information presented in these materials.
? Copyright: 2014 by the UBC Real Estate Division, Sauder School of Business, The University of British
Columbia. Printed in Canada. ALL RIGHTS RESERVED. No part of this work covered by the copyright hereon
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LESSON 1
Finance Fundamentals I
Note: Selected readings can be found under "Lesson 1" on your course website
Assigned Reading
1. UBC Real Estate Division. 2014. CPD 151 Real Estate Finance Basics. Vancouver: UBC Real
Estate Division.
Lesson 1: Finance Fundamentals I
Recommended Reading
1. HP10BII: Introduction to the Calculator and Review of Mortgage Finance Techniques
2. HP10BII Computer Based Training. Learn how to use the HP 10BII calculator by using our new
interactive training tool. This will show you the steps on the calculator that are required to solve real
estate finance problems. Please note that this will link to the Hewlett Packard website and to view
this application, users must have Macromedia Shockwave Flash Player installed. To download this
free plug-in, visit the Macromedia website and follow the on-screen instructions.
3. Math Review Kit. An overview of math and algebra calculations. Provided with permission from
CGA Canada.
4. Excel tutorials.
?
Microsoft: Various tutorials ranging from easy to advanced for Excel 2007, 2010, 2013, and
excel for Mac 2011.
?
: Provides quite basic instructions for various versions of Excel (2002, 2007,
2010, etc.). Explains the basic with screenshots and video tutorials. Some lessons include cell
basics, creating complex formulas, formatting, and creating tables.
excel?search=excel
Learning Objectives
After completing this lesson, the student should be able to:
1. explain the difference between simple and compound interest;
2. define and differentiate between a variety of interest rate types, including nominal, periodic,
effective, and equivalent rates of interest;
3. discuss the underlying mathematics for financial analysis and apply this in structuring solutions to
problems using both a financial calculator and spreadsheet software;
4. solve for the specific calculations necessary in lump sum problems, including present value (PV),
future value (FV), timeframe (N), or interest rate (I/YR); and
5. convert equivalent interest rates based on different compounding frequencies.
1.1
?Copyright: 2014 by the UBC Real Estate Division
Lesson 1
Instructor's Comments
This lesson outlines the basic tools and techniques required for real estate mathematics. The basis for all
financial analysis is interest rates. Since these can be quoted and applied in many different ways, it is crucial
to be fluent in working with the varying definitions and also to be able to apply these properly in
mathematical solutions. As a result, much of this initial lesson focuses on interest rate explanations and
calculations. This includes the difference between nominal and periodic rates, plus the calculations necessary
to convert equivalent interest rates where the compounding frequencies differ.
Financial Fluency
Mathematics is often described as another form of language. Like learning a new language, this requires
understanding the grammar and then a lot a memorization and repetition until you can use it without really
thinking about it. For financial analysis, the mathematics involves the use of formulas. These are usually
pre-programmed into a financial calculator or into a spreadsheet; therefore, most financial analysts do not
work with the formulas directly. However, in all cases, the interest rate must be correctly applied, or the
calculator/spreadsheet will not operate accurately. To be successful in financial analysis, you must be fluent
in your understanding of how interest rates are stated and in how to work between the different types as
required for the financial tool you are working with.
The financial calculations in this lesson will start out with somewhat simple problems, such as interest
accrual loans and investments involving the present and future value of a single cash flow. The calculations
will advance to more complicated examples in Lessons 2 and 3. Much like the construction of a high-rise,
you need a solid foundation before you can start building the upper floors. This lesson focuses on the
foundations of financial analysis.
Math Formulas and Financial Calculators
Finance calculations involve complicated mathematical formulas. If you are comfortable with algebra, these
formulas can be solved manually and using any calculator. However, financial calculators and spreadsheets
have the formulas pre-programmed into them, making financial calculations much easier. Once you have a
programmed tool, whether a calculator or computer software, the financial problems become less about
mathematics and more about structured problem solving: in general, you need only specify the inputs for the
problem, and the calculator/computer will do the mathematics for you.
In this course we will use the Hewlett Packard (HP) 10BII/10BII+ calculator to demonstrate analytical
techniques. There is nothing particularly special about this particular calculator; it is a standard financial
calculator that is able to carry out the necessary calculations and not a lot more. There are a variety of preprogrammed financial calculators on the market, some of which perform more sophisticated calculations or
have greater programming capacity. Students in Real Estate Division courses are welcome to choose other
calculators if they prefer, but it is up to the student to ensure that the alternate calculator will perform all
necessary calculations and to determine its operations. As well, for Real Estate Division courses with
proctored final examinations, it is important to understand that only silent, cordless, hand-held calculators
that are not both alphanumeric and programmable are permitted in the examination room.
The problems covered in this course will initially provide both mathematical formulas and calculator steps.
In subsequent problems, this will be abbreviated to provide calculator steps only. As well, the use of
computer spreadsheets is becoming increasingly important in financial analysis, more or less a mandatory
tool in contemporary business. In recognition of this, the lessons will also provide the formulas and steps for
the equivalent analysis in Microsoft Excel at key points.
1.2
?Copyright: 2014 by the UBC Real Estate Division
Real Estate Finance Basics
The HP10BII/10BII+ has some unique features, so some basic orientation will help avoid difficulties.
1.
Setting Up Your Calculator
The HP 10BII+ has two O (shift) keys. One is orange (for financial functions); the other is blue (for
statistical functions). To access the financial functions on the calculator, students should always
use the ORANGE O (shift) key. All functions that are activated by the ORANGE O (shift) key are
located on the lower half of each of the calculator keys, and are also labeled in ORANGE. We do
not use the BLUE O (shift) key in this course.
Decimal Places: The HP10BII/II+ allows you to set the number of decimal places displayed using
the ORANGE O then DISP key. It is best to display more decimal places than you need, so you are
working with the most accurate numbers possible. O DISP 9 will display 9 digits for all problems
(and in fact, shows 9 zeros, even if not significant, such as 0.000000000). You may also use what
is known as "floating decimals", or SHIFT DISP. However, it also displays small and large numbers
in scientific notation or exponential functions, e.g., 4/19 = 2.10526316E-2. This same value set to 9
decimal places changes the display to 0.210526316. The use of floating decimal places gives
slightly more accuracy, but you have to be comfortable working with the exponents (E-n). This is
your personal preference, as the final decimal place does not significantly affect calculations. Note
that the calculator uses its full accuracy of up to 15 decimal places regardless of the level of display
chosen.
For ease of presentation, in each of the examples presented in this course, the calculator is
programmed to display a "fixed decimal point" set to six decimal places. This is accomplished by
turning the calculator ON, pressing the ORANGE O then DISP and then the 6 key. You will see
0.000000 on your display screen. However, note that on the display portion of calculator steps in
the lessons, we will not show the display with zeros when they do not impact the result (and are
mathematically insignificant).
2.
Using Your Calculator to Solve Questions
The internal operation of the HP 10BII/10BII+ calculator requires that all financial calculations have
at least one positive and one negative cash flow. This means that at least one of the PV, FV, and
PMT keys will have to be shown and/or entered as a negative amount. Generally, cash flowing in is
positive, while cash flowing out is negative.
For example, in mortgage loan problems, the borrower receives loan funds at the beginning of the
term (cash in, so a positive amount) and pays back the loan funds either during or at the end of the
term (cash out, so negative amounts). In this type of problem, PV will be shown/entered as a
positive, while PMT and FV will be shown/entered as negatives. When entering a negative amount
the +/- key is used, not the - key.
Similarly, from an investor's perspective, the initial investment is paid out (cash out, so negative
amount) and the investor receives money in the future (cash in, so positive amount). In this type of
problem, PV will be shown/entered as a negative, while PMT and FV will be shown/entered as
positives.
Summary
Borrower's Perspective
PV +
PMT B
FV B
Investor's Perspective
PV B
PMT +
FV +
(continued on the following page)
1.3
?Copyright: 2014 by the UBC Real Estate Division
Lesson 1
(continued)
3.
Clearing Information on Your Calculator
Note that if you enter an incorrect number on the screen, it can be cleared by pushing C once or by
pressing the ? key to delete the last entered digit. If you enter an incorrect number into any of the
six financial keys, N, I/YR, PMT, PV, FV, or P/YR, it can be corrected by re-entering the desired
number into that key. You can verify what information is stored in each of the above financial keys
by pressing RCL and then the corresponding financial key you are interested in. For example, if
you obtained an incorrect solution for a financial problem, you can check what is stored in N by
pressing RCL N; I/YR by pressing RCL I/YR, etc. The HP 10BII/10BII+ calculator has a "constant
memory". This means that whatever is stored in the keys remains there until it is expressly
changed (even when the calculator is turned off), unless the ? C ALL function is used or the
batteries are removed.
4.
Troubleshooting
i.
Please be aware that the HP 10BII/10BII+ calculator has both Begin and End modes. The
Begin mode is needed for annuity due calculations, or those which require payments to be
made "in advance". For example, lease payments are generally made at the beginning of each
month, not at the end. On the other hand, interest payments are almost always calculated at
the end of each payment period, or "not in advance". These types of calculations each require
a different setting on the calculator. When your calculator is set in Begin mode, the bottom of
the display screen will show BEGIN or BEG. If BEG is not on your display screen, your
calculator must be in End mode, as there is no annunciator for this mode.
In this course, there are minimal calculations which require your calculator to be in Begin
mode, so your calculator should be in End mode at all times. You should not see the BEGIN or
BEG annunciator on your calculator's display for most of the calculations in this course. To
switch between modes, press O BEG/END.
ii.
Please be aware that if the calculator is displaying a comma (,) instead of a decimal place (.),
this can be fixed by pressing ? ./, or ? ,/..
Alert!
Students may wish to view the "Introduction to the HP10BII/10BII+ Calculator" online video tutorial found
under "Tutorial Assistance" and "Course Materials" on the Course Resources webpage. As well, students
can consult the HP 10BII/10BII+ owner's manual for more information.
1.4
?Copyright: 2014 by the UBC Real Estate Division
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