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? Copyright: 2014 by the UBC Real Estate Division, Sauder School of Business, The University of British

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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.

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?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.

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?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)

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?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.

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?Copyright: 2014 by the UBC Real Estate Division

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