The document outlines tools and techniques for financial decision-making, focusing on a systematic six-step approach: creating a constructive environment, generating alternatives, exploring and choosing the best alternative, checking the decision, and communicating it. Additionally, it explains financial statement analysis, which involves analyzing reported financial information to assess risk and profitability, using techniques like ratio analysis, funds flow analysis, and cash flow analysis. The document serves as a comprehensive guide for effective decision-making and financial evaluation.

1. EDUCATION HOLEPRESENTS
2013
FINANCIAL MANAGEMENT – 1
Tools for financial decision making Module-II
By:-Management Department
WWW.EDHOLE.COM

2. Table of Contents BBA 302 Module -II
Systematic Approach to Decision Making..........................................................................3
Step 1: Create a constructive environment................................................................................................3
Step 2: Generate Good Alternatives...........................................................................................................4
Generating Ideas......................................................................................................................4
Considering Different Perspectives ...........................................................................................4
Step 3 : Explore the Alternatives...............................................................................................4
Step 4: Choose the Best Alternative ...........................................................................................................5
Step 5: Check Your Decision...........................................................................................................................5
Step 6: Communicate Your Decision, and Move to Action............................................................................6
Financial statement analysis.............................................................................................6
Financial statement analysis consists of ........................................................................................................6
Interpretation of funds flow statement.............................................................................8
a. Sources..............................................................................................................................8
Long term sources..........................................................................................................................................8
Short term sources.........................................................................................................................................8
Long term applications ..................................................................................................................................8
Short term applications .................................................................................................................................9
Cash flow statement.................................................................................................................9
Financial Ratio........................................................................................................................10
1. Debt-to-Equity Ratio ................................................................................................................................10
2. Current Ratio............................................................................................................................................10
3. Quick Ratio...............................................................................................................................................10
4. Return on Equity (ROE) ............................................................................................................................11
5. Net Profit Margin .....................................................................................................................................11
Common Size Financial Statement Analysis..................................................................... 11
Comparative Financial Statement Analysis...................................................................... 11
Comparative statement.................................................................................................. 12
Trend analysis ................................................................................................................ 12
Other analysis techniques............................................................................................... 13
Formula of calculating trends ......................................................................................... 13
Time Value of Money...................................................................................................... 13
Compounding and discounting........................................................................................ 13
Compounding...............................................................................................................................................14
Discounting ..................................................................................................................................................14
Formula and Definition................................................................................................... 14
Future Value of an Annuity..........................................................................................................................15

3. Example of Future Value of an Annuity Formula.........................................................................................15
Present Value of a Single Amount ...............................................................................................................16
Present Value of Annuities .....................................................................................................16
Present Value of an Ordinary Annuity .........................................................................................................16
Systematic Approach to Decision Making
A logical and systematic decision-making process helps you address the critical elements that
result in a good decision. By taking an organized approach, you're less likely to miss
important factors, and you can build on the approach to make your decisions better and
better.
There are six steps to making an effective decision:
1. Create a constructive environment.
2. Generate good alternatives.
3. Explore these alternatives.
4. Choose the best alternative.
5. Check your decision.
6. Communicate your decision, and take action.
Here are the steps in detail:
Step 1: Create a constructive environment
To create a constructive environment for successful decision making, make sure you do the
following:
• Establish the objective - Define what you want to achieve.
• Agree on the process - Know how the final decision will be made, including whether
it will be an individual or a team-based decision. The Vroom-Yet ton-Jogo Model is
a great tool for determining the most appropriate way of making the decision.
• Involve the right people - Stakeholder Analysis is important in making an effective
decision, and you'll want to ensure that you've consulted stakeholders appropriately
even if you're making an individual decision. Where a group process is appropriate,
the decision-making group - typically a team of five to seven people - should have a
good representation of stakeholders.
• Allow opinions to be heard - Encourage participants to contribute to the discussions,
debates, and analysis without any fear of rejection from the group. This is one of the
best ways to avoid groupthink. The Stepladder Technique is a useful method for
gradually introducing more and more people to the group discussion, and making sure
everyone is heard. Also, recognize that the objective is to make the best decision
under the circumstances: it's not a game in which people are competing to have their
own preferred alternatives adopted.
• Make sure you're asking the right question - Ask yourself whether this is really the
true issue. The 5 Whys technique is a classic tool that helps you identify the real
underlying problem that you face.
• Use creativity tools from the start - The basis of creativity is thinking from a
different perspective. Do this when you first set out the problem, and then continue it
while generating alternatives. Our article Generating New Ideas will help you create
new connections in your mind, break old thought patterns, and consider new
perspectives.

4. Step 2: Generate Good Alternatives
This step is still critical to making an effective decision. The more good options you consider,
the more comprehensive your final decision will be.
When you generate alternatives, you force yourself to dig deeper, and look at the problem
from different angles. If you use the mindset ‘there must be other solutions out there,' you're
more likely to make the best decision possible If you don't have reasonable alternatives, then
there's really not much of a decision to make! Here's a summary of some of the key tools and
techniques to help you and your team develop good alternatives.
Generating Ideas
• Brainstorming is probably the most popular method of generating ideas.
• Another approach, Reverse Brainstorming, works similarly. However, it
starts by asking people to brainstorm how to achieve the opposite outcome
from the one wanted, and then reversing these actions.
• The Charente Procedure is a systematic process for gathering and
developing ideas from very many stakeholders.
• Use the Crawford Slip Writing Technique to generate ideas from a large
number of people. This is an extremely effective way to make sure that
everyone's ideas are heard and given equal weight, irrespective of the person's
position or power within the organization.
Considering Different Perspectives
• The Reframing Matrix uses 4 Ps (product, planning, potential, and people)
as the basis for gathering different perspectives. You can also ask outsiders to
join the discussion, or ask existing participants to adopt different functional
perspectives (for example, has a marketing person speak from the viewpoint
of a financial manager).
• If you have very few options, or an unsatisfactory alternative, use aConcept
Fan to take a step back from the problem, and approach it from a wider
perspective. This often helps when the people involved in the decision are too
close to the problem.
• Appreciative Inquiry forces you to look at the problem based on what's
‘going right,' rather than what's ‘going wrong.'
• Organizing Ideas
This is especially helpful when you have a large number of ideas. Sometimes separate
ideas can be combined into one comprehensive alternative.
• Use Affinity Diagrams to organize ideas into common themes and
groupings.
Step 3 : Explore the Alternatives

5. When you're satisfied that you have a good selection of realistic alternatives, then you'll need
to evaluate the feasibility, risks, and implications of each choice. Here, we discuss some of
the most popular and effective analytical tools.
Risk Analysis helps you look at risks objectively. It uses a structured approach for assessing
threats, and for evaluating the probability of events occurring - and what they might cost to
manage.
• Implications
Another way to look at your options is by considering the potential consequences of
each.
• Six Thinking Hats helps you evaluate the consequences of a decision by
looking at the alternatives from six different perspectives.
• Impact Analysis is a useful technique for brainstorming the ‘unexpected'
consequences that may arise from a decision.
• Validation
Determine if resources are adequate, if the solution matches your objectives, and if
the decision is likely to work in the long term.
• Star bursting helps you think about the questions you should ask to evaluate
an alternative properly.
• To assess pros and cons of each option, use Force Field Analysis, or use
the Plus-Minus-Interesting approach.
• Cost-Benefit Analysis looks at the financial feasibility of an alternative.
• Our Bite-Sized Training session on Project Evaluation and Financial
Forecasting helps you evaluate each alternative using the most popular
financial evaluation techniques.
Step 4: Choose the Best Alternative
After you have evaluated the alternatives, the next step is to choose between them. The
choice may be obvious. However, if it isn't, these tools will help:
• Grid Analysis, also known as a decision matrix, is a key tool for this type of
evaluation. It's invaluable because it helps you bring disparate factors into your
decision-making process in a reliable and rigorous way.
• Use Paired Comparison Analysis to determine the relative importance of various
factors. This helps you compare unlike factors, and decide which ones should carry
the most weight in your decision.
• Decision Trees are also useful in choosing between options. These help you lay out
the different options open to you, and bring the likelihood of project success or failure
into the decision making process.
Step 5: Check Your Decision
With all of the effort and hard work that goes into evaluating alternatives, and deciding the
best way forward, it's easy to forget to ‘sense check' your decisions. This is where you look at
the decision you're about to make dispassionately, to make sure that your process has been
thorough, and to ensure that common errors haven't crept into the decision-making process.

6. After all, we can all now see the catastrophic consequences that over-confidence, groupthink,
and other decision-making errors have wrought on the world economy.
The first part of this is an intuitive step, which involves quietly and methodically testing the
assumptions and the decisions you've made against your own experience, and thoroughly
reviewing and exploring any doubts you might have.
A second part involves using a technique like Blinds pot Analysis to review whether
common decision-making problems like over-confidence, escalating commitment,
or groupthink may have undermined the decision-making process. A third part involves
using a technique like the Ladder of Inference to check through the logical structure of the
decision with a view to ensuring that a well-founded and consistent decision emerges at the
end of the decision-making process.
Step 6: Communicate Your Decision, and Move to Action
Once you've made your decision, it's important to explain it to those affected by it, and
involved in implementing it. Talk about why you chose the alternative you did. The more
information you provide about risks and projected benefits, the more likely people are to
support the decision.
And with respect to implementation of your decision, our articles on Project
Management and Change Management will help you get this implementation off to a good
start!
Financial statement analysis
Financial statement analysis (or financial analysis) the process of understanding the risk
and profitability of a firm (business, sub-business or project) through analysis of reported
financial information, by using different accounting tools and techniques
Financial statement analysis consists of
1) Reformulating reported financial statements
2) Analysis and adjustments of measurement errors
3) Financial ratio analysis on the basis of reformulated and adjusted financial statements. The
first two steps are often dropped in practice, meaning that financial ratios are just calculated
on the basis of the reported numbers, perhaps with some adjustments. Financial statement
analysis is the foundation for evaluating and pricing credit risk and for doing fundamental
company valuation.
4) Financial statement analysis typically starts with reformulating the reported financial
information. In relation to the income statement, one common reformulation is to divide
reported items into recurring or normal items and non-recurring or special items. In this way,
earnings could be separated in to normal or core earnings and transitory earnings. The idea is

7. that normal earnings are more permanent and hence more relevant for prediction and
valuation. Normal earnings are also separated into net operational profit after taxes (NOPAT)
and net financial costs. The balance sheet is grouped, for example, in net operating assets
(NOA), net financial debt and equity.
5) Analysis and adjustment of measurement errors question the quality of the reported
accounting numbers. The reported numbers can for example be a bad or noisy representation
of invested capital, for example in terms of NOA, which means that the return on net
operating assets (RNOA) will be a noisy measure of the underlying profitability (the internal
rate of return, IRR). Expensing of R&D is an example when such investment expenditures
are expected to yield future economic benefits, suggesting that R&D creates assets which
should have been capitalized in the balance sheet. An example of an adjustment for
measurement errors is when the analyst removes the R&D expenses from the income
statement and put them in the balance sheet. The R&D expenditures are then replaced by
amortization of the R&D capital in the balance sheet. Another example is to adjust the
reported numbers when the analyst suspects earnings management.
6) Financial ratio analysis should be based on regrouped and adjusted financial statements.
Two types of ratio analysis are performed: 3.1) Analysis of risk and 3.2) analysis of
profitability:
7) Analysis of risk typically aims at detecting the underlying credit risk of the firm. Risk
analysis consists of liquidity and solvency analysis. Liquidity analysis aims at analyzing
whether the firm has enough liquidity to meet its obligations when they should be paid. A
usual technique to analyze illiquidity risk is to focus on ratios such as the current ratio and
interest coverage. Cash flow analysis is also useful. Solvency analysis aims at analyzing
whether the firm is financed so that it is able to recover from a loss or a period of losses. A
usual technique to analyze insolvency risk is to focus on ratios such as the equity in
percentage of total capital and other ratios of capital structure. Based on the risk analysis the
analyzed firm could be rated, i.e. given a grade on the riskiness, a process called synthetic
rating. Ratios of risk such as the current ratio, the interest coverage and the equity percentage
have no theoretical benchmarks. It is therefore common to compare them with the industry
average over time. If a firm has a higher equity ratio than the industry, this is considered less
risky than if it is above the average. Similarly, if the equity ratio increases over time, it is a
good sign in relation to insolvency risk.
8) Analysis of profitability refers to the analysis of return on capital, for example return on
equity, ROE, defined as earnings divided by average equity. Return on equity, ROE, could be
decomposed: ROE = RNOA + (RNOA - NFIR) * NFD/E, where RNOA is return on net
operating assets, NFIR is the net financial interest rate, NFD is net financial debt and E is
equity. In this way, the sources of ROE could be clarified. Unlike other ratios, return on
capital has a theoretical benchmark, the cost of capital - also called the required return on
capital. For example, the return on equity, ROE, could be compared with the required return
on equity, kE, as estimated, for example, by the capital asset pricing model. If ROE < kE (or
RNOA > WACC, where WACC is the weighted average cost of capital), then the firm is

8. economically profitable at any given time over the period of ratio analysis. The firm creates
values for its owners. Insights from financial statement analysis could be used to make
forecasts and to evaluate credit risk and value the firm's equity. For example, if financial
statement analysis detects increasing superior performance ROE - kE > 0 over the period of
financial statement analysis, then this trend could be extrapolated into the future. But as
economic theory suggests, sooner or later the competitive forces will work - and ROE will be
driven toward kE. Only if the firm has a sustainable competitive advantage, ROE - kE > 0 in
"steady state".
Interpretation of funds flow statement
For the correct interpretation of the funds flow statement, the sources
and application of funds can be categorized as below.
a. Sources
Long term sources
Following types of sources may be treated as short term sources.
1. Issue of shares/debentures.
2. Long term borrowing of funds
3. Operating
4. Sale of fixed assets
Short term sources
Following types of sources may be treated as short term sources.
1. Short term borrowing of funds.
2. Increase in current liabilities.
3. Decrease in current assets.
b. Applications
Long term applications
Following types of applications may be treated as long term applications.
1. Purchases of fixed assets.
2. Redemption of preferences shares/debentures.
3. Repayment of long borrowings.

9. Short term applications
Following types of application may be treated as short term applications.
1. Increase in current assets.
2. Decrease in current liabilities.
3. Repayment of short term loans/deposits
4. Dividends/taxes
The techniques
used for the analysis and interpretation of financial statements are:
• Ratio Analysis is a systematic technique of analysis and interpretation of financial
statements 𝑖. 𝑒 Profitability statement and Balance sheet with the help of various
ratios so that the strengths and weakness and the financial position of the firm can be
determined. This technique is not a creative technique as the information already
given in the financial statements is used.
• Funds Flow Analysis: is the analysis in which Funds flow statement is prepared in
order to determine the sources and application of funds. Fund flow statement is
commonly used in business plans and proposals to show investors about the flowing
of their funds through the organization. This is not used in annual reports. It is used
by bankers who want to know how borrowed funds will flow through company
operations. It is used to show the management how the cash is flowing through the
company operations.
• Cash Flow Analysis is the analysis in which Cash Flow Statement is prepared which
shows changes in inflow & outflow of cash during the period. Cash flow statement is
an analysis tool used by large and medium scale companies for Inflow and Outflow
of money during a particular period of time.
Cash flow statement
In financial accounting, a cash flow statement, also known as statement of cash flows, is
a financial statement that shows how changes in balance sheet accounts and income
affect cash and cash equivalents, and breaks the analysis down to operating, investing, and
financing activities. Essentially, the cash flow statement is concerned with the flow of cash in
and out of the business. The statement captures both the current operating results and the
accompanying changes in the balance sheet.[1]
As an analytical tool, the statement of cash
flows is useful in determining the short-term viability of a company, particularly its ability to

10. pay bills. International Accounting Standard 7 (IAS 7), is the International Accounting
Standard that deals with cash flow statements.
People and groups interested in cash flow statements include:
• Accounting personnel, who need to know whether the organization will be able to cover
payroll and other immediate expenses
• Potential lenders or creditors, who want a clear picture of a company's ability to repay
• Potential investors, who need to judge whether the company is financially sound
• Potential employees or contractors, who need to know whether the company will be able
to afford compensation
• Shareholders of the business.
Financial Ratio
A financial ratio (or accounting ratio) is a relative magnitude of two selected numerical
values taken from an enterprise's financial statements. Often used in accounting, there are
many standard ratios used to try to evaluate the overall financial condition of a corporation or
other organization. Financial ratios may be used by managers within a firm, by current and
potential shareholders (owners) of a firm, and by a firm's creditors. Financial analysts use
financial ratios to compare the strengths and weaknesses in various companies. If shares in a
company are traded in a financial market, the market price of the shares is used in certain
financial ratios.
Top 5 Financial Ratios
The most cost commonly and top five ratios used in the financial field include:
1. Debt-to-Equity Ratio
The debt-to-equity ratio, is a quantification of a firm’s financial leverage estimated by
dividing the total liabilities by stockholders’ equity. This ratio indicates the proportion of
equity and debt used by the company to finance its assets.
The formula used to compute this ratio is
Total Liabilities / Shareholders Equity
2. Current Ratio
The current ratio is a liquidity ratio which estimates the ability of a company to pay back
short-term obligations. This ratio is also known as cash asset ratio, cash ratio, and liquidity
ratio. A higher current ratio indicates the higher capability of a company to pay back its
debts. The formula used for computing current ratio is:
Current Assets / Current Liabilities
3. Quick Ratio

11. The quick ratio, also referred as the “acid test ratio” or the “quick assets ratio”, this ratio is a
gauge of the short term liquidity of a firm. The quick ratio is helpful in measuring a
company’s short term debts with its most liquid assets.
The formula used for computing quick ratio is:
(Current Assets – Inventories)/ Current Liabilities
A higher quick ratio indicates the better position of a company.
4. Return on Equity (ROE)
The return on equity is the amount of net income returned as a percentage of shareholders
equity. Moreover, the return on equity estimates the profitability of a corporation by
revealing the amount of profit generated by a company with the money invested by the
shareholders. Also, the return on equity ratio is expressed as a percentage and is computed as:
Net Income/Shareholder's Equity
The return on equity ratio is also referred as “return on net worth” (RONW).
5. Net Profit Margin
The net profit margin is a number which indicates the efficiency of a company at its cost
control. A higher net profit margin shows more efficiency of the company at converting its
revenue into actual profit. This ratio is a good way of making comparisons between
companies in the same industry, for such companies are often subject to similar business
conditions.
The formula for computing the Net Profit Margin is:
Common Size Financial Statement Analysis
Common Size Statement involves representing the income statement figures as a percentage
of sales and representing the balance sheet figures as a percentage of total assets. Financial
statements represent absolute figures and a comparison of absolute figures can be misleading.
For example, the cost of goods sold might have increased but as a percentage of sales it might
have decreased. So, to have a perfect understanding about these increases and decreases, the
figures reported are converted into percentages to some common base. In Income Statement,
Sales figure is assumed to be 100% and all other figures are expressed as a percentage of
sales. In Balance Sheet, the total of assets is taken as 100% and all other figures are expressed
as a percentage of total assets. This type of Statement so prepared is called as the Common
Size Statement and the analysis performed on the Common Size Statement is called as the
Common Size Financial Statement Analysis or otherwise called as Vertical Analysis.
Comparative Financial Statement Analysis
Comparative Financial Statement analysis provides information to assess the direction of
change in the business. Financial statements are presented as on a particular date for a

12. particular period. The financial statement Balance Sheet indicates the financial position as at
the end of an accounting period and the financial statement Income Statement shows the
operating and non-operating results for a period. But financial managers and top management
are also interested in knowing whether the business is moving in a favourable or an
unfavourable direction. For this purpose, figures of current year have to be compared with
those of the previous years. In analyzing this way, comparative financial statements are
prepared. Comparative Financial Statement Analysis is also called as Horizontal analysis.
The Comparative Financial Statement provides information about two or more years' figures
as well as any increase or decrease from the previous year's figure and it's percentage of
increase or decrease. This kind of analysis helps in identifying the major improvements and
weaknesses. For example, if net income of a particular year has decreased from its previous
year, despite an increase in sales during the year, is a matter of serious concern. Comparative
financial statement analysis in such situations helps to find out where costs have increased
which has resulted in lower net income than the previous year.
OR
Comparative statement
Comparative statements are financial statements that cover a different time frame, but are
formatted in a manner that makes comparing line items from one period to those of a
different period an easy process. This quality means that the comparative statement is a
financial statement that lends itself well to the process of comparative analysis. Many
companies make use of standardized formats in accounting functions that make the
generation of a comparative statement quick and easy. The benefits of a comparative
statement are varied for a corporation. Because of the uniform format of the statement, it is a
simple process to compare the gross sales of a given product or all products of the company
with the gross sales generated in a previous month, quarter, or year. Comparing generated
revenue from one period to a different period can add another dimension to analyzing the
effectiveness of the sales effort, as the process makes it possible to identify trends such as a
drop in revenue in spite of an increase in units sold. Along with being an excellent way to
broaden the understanding of the success of the sales effort, a comparative statement can also
help address changes in production costs. By comparing line items that cava log the expense
for raw materials in one quarter with another quarter where the number of units produced is
similar can make it possible to spot trends in expense increases, and thus help isolate the
origin of those increases. This type of data can prove helpful to allowing the company to find
raw materials from another source before the increased price for materials cuts into the
overall profitability of the company. A comparative statement can be helpful for just about
any organization that has to deal with finances in some manner. Even non-profit
organizations can use the comparative statement method to ascertain trends in annual fund
raising efforts. By making use of the comparative statement for the most recent effort and
comparing the figures with those of the previous year’s event, it is possible to determine
where expenses increased or decreased, and provide some insight in how to plan the
following year’s event.
Trend analysis
Trend analysis is one of the tools for the analysis of the company’s monetary statements for
the investment purposes. Investors use this analysis tool a lot in order to determine the

13. financial position of the business. In a trend analysis, the financial statements of the company
are compared with each other for the several years after converting them in the percentage. In
the trend analysis, the sales of each year from the 2008 to 2011 will be converted into
percentage form in order to compare them with each other.
Other analysis techniques
Apart from trend analysis, the investors also use other techniques for the analysis purposes,
and this helps them in achieving complete data and updated view on the company’s current
financial position.
Formula of calculating trends
Formula for converting the figures:
In order to convert the figures into percentages for the comparison purposes, the percentages
are calculated in the following way:
Trend analysis percentage = (figure of the previous period – figure of the current period)/total
of both figures
The percentage can be found this way and if the current-year percentages were greater than
previous year percentage, this would mean that current-year result is better than the previous
year result.
Time Value of Money
Time Value of Money (TVM) is an important concept in financial management. It can be
used to compare investment alternatives and to solve problems involving loans, mortgages,
leases, savings, and annuities. TVM is based on the concept that a dollar that you have today
is worth more than the promise or expectation that you will receive a dollar in the future.
Money that you hold today is worth more because you can invest it and earn interest. After
all, you should receive some compensation for foregoing spending. For instance, you can
invest your dollar for one year at a 6% annual interest rate and accumulate $1.06 at the end of
the year. You can say that the future value of the dollar is $1.06 given a 6% interest
rate and a one-year period. It follows that the present value of the $1.06 you expect to
receive in one year is only $1. A key concept of TVM is that a single sum of money or a
series of equal, evenly-spaced payments or receipts promised in the future can be converted
to an equivalent value today. Conversely, you can determine the value to which a single sum
or a series of future payments will grow to at some future date
Compounding and discounting
"Compound interest - it is the greatest mathematical discovery of all time"
Albert Einstein

14. Compounding
You put money in an account today (its present value - PV) for a promised rate of return
(interest - INT) for a number of periods (NPER - usually months or years). The interest
received in reinvested at the end of each period - it compounds. The future value (FV) is the
value of the investment compounded at the end of a given number of periods. We know the
value of our initial investment and the interest rate, and can calculate the FV at the end of any
period.
Discounting
It is the reverse of compounding. We know the how
much we need on a specific date in the future (FV) and calculate how much we need to invest
today PV at an interest rate. Work from the future back to the present.
You can find Excel functions to make these calculations by searching Excel's Help File for
FV (compounding) or PV (discounting).
Future Value of a Single amount
Formula and Definition
The equation below calculates how large a single sum will become at the end of a specified
period of time. This value is referred to as the future value (FV) of a single sum.

15. Observe from the formula that the future value (FV) consists of both a present value (PV)
piece - an initial lump sum - and an accumulated interest piece. Thus, we start with a fixed
amount and calculate how large it will grow (i.e., accumulate or compound) over the
specified period of time and interest rate. The FV of a single sum formula serves as a means
of valuation. It tells us what something will be worth at a future date. This "something" can
be an asset or a liability. For example, if we borrow $1,000 today and don't make any
payments until the loan comes due two years from now, how much will we owe at that time?
Likewise, if we deposit $5,000 into a bank account today, how much will it be worth in 180
days?
Note the distinction between the FV of a single sum and the PV of a single sum. The FV of a
single sum answers the question "How much will it be worth then?" while the PV of a single
sum answers the question "What is it worth now (or before 'then')?". The PV of a single sum
is discussed separately here. Also note that the formula above gives us the FV of a single
sum; in other words, a fixed, lump sum amount. The future value of an annuity formula
gives us the FV of a series of periodic payments. The FV of an annuity is discussed
separately here.
Future Value of an Annuity
The future value of an annuity formula is used to calculate what the value at a future date
would be for a series of periodic payments.
The future value of an annuity formula assumes that
1. The rate does not change
2. The first payment is one period away
3. The periodic payment does not change
If the rate or periodic payment does change, then the sum of the future value of each
individual cash flow would need to be calculated to determine the future value of the annuity.
If the first cash flow, or payment, is made immediately, the future value of annuity due
formula would be used.
Example of Future Value of an Annuity Formula

16. An example of the future value of an annuity formula would be an individual who decides to
save by depositing $1000 into an account per year for 5 years. The first deposit would occur
at the end of the first year. If a deposit was made immediately, then the future value of
annuity due formula would be used. The effective annual rate on the account is 2%. If she
would like to determine the balance after 5 years, she would apply the future value of an
annuity formula to get the following equation
The balance after the 5th year would be $5204.04.
Present Value of a Single Amount
Present Value is an amount today that is equivalent to a future payment, or series of
payments that has been discounted by an appropriate interest rate. Since money has time
value, the present value of a promised future amount is worth less the longer you have to wait
to receive it. The difference between the two depends on the number of compounding
periods involved and the interest (discount) rate.
The relationship between the present value and future value can be expressed as:
PV = FV [ 1 / (1 + i)n
]
Where:
PV = Present Value
FV = Future Value
i = Interest Rate per Period
n = Number of Compounding Periods
Present Value of Annuities
An annuity is a series of equal payments or receipts that occur at evenly spaced intervals.
Leases and rental payments are examples. The payments or receipts occur at the end of each
period for an ordinary annuity while they occur at the beginning of each period. For
an annuity due.
Present Value of an Ordinary Annuity
The Present Value of an Ordinary Annuity(𝑃𝑉𝑜𝑎) is the value of a stream of expected or
promised future payments that have been discounted to a single equivalent value today. It is
extremely useful for comparing two separate cash flows that differ in some way. PV-𝑜𝑎 can

17. also be thought of as the amount you must invest today at a specific interest rate so that when
you withdraw an equal amount each period, the original principal and all accumulated interest
will be completely exhausted at the end of the annuity. The Present Value of an Ordinary
Annuity could be solved by calculating the present value of each payment in the series using
the present value formula and then summing the results. A more direct formula is:
𝑃𝑉𝑜𝑎 = PMT
[(1 - (1 / (1 + i)n
)) / i]
WHERE
𝑃𝑉𝑜𝑎 = Present Value of an Ordinary Annuity
PMT = Amount of each payment
i = Discount Rate per Period
n = Number of Periods