Working Capital Management and Time Value of Money
a. The Nature of Asset Growth
Any company that produces and sells a product, whether the product is consumer
or manufacturer oriented, will have current assets and fixed assets. If a firm grows, those
assets are likely to increase over time. The key to current asset planning is the ability of
management to forecast sales accurately and then to match the production schedules with
the sales forecast. Whenever actual sales are different from forecast sales, unexpected
buildups or reductions in inventory will occur that will eventually affect receivables and
cash flow.
In the simplest case, all of the firm’s current assets will be self-liquidating assets
(sold at the end of a specified time period). Assume that at the start of the summer you
buy 100 tires to be disposed of by September. It is your intention that all tires will be
sold, receivables collected, and bills paid over this time period. In this case, your working
capital (current asset) needs are truly short term.
Now let us begin to expand the business. In stage two, you add radios, seat
covers, and batteries to your operation. Some of your inventory will again be completely
liquidated, while other items will form the basic stock for your operation. To stay in
business, you must maintain floor displays and multiple items for selection. Furthermore,
not all items will sell. As you eventually grow to more than one store, this “permanent”
aggregate stock of current assets will continue to increase. Problems of inadequate
financing arrangements are often the result of the businessperson’s failure to realize the
firm is carrying not only self-liquidating inventory but also the anomaly of “permanent”
current assets.
The movement from stage one to stage two of growth for a typical business is
depicted. In panel A, the buildup in current assets is temporary—while in panel B, part of
the growth in current assets is temporary and part is permanent. (Fixed assets are
included in the illustrations, but they are not directly related to the present discussion.)
b. Controlling Assets-Matching Sales and Production
In most firms, fixed assets grow slowly as productive capacity is increased and
old equipment is replaced, but current assets fluctuate in the short run, depending on the
level of production versus the level of sales. When the firm produces more than it sells,
inventory rises. When sales rise faster than production, inventory declines and
receivables rise.
As discussed in the treatment of the cash budgeting process in, some firms
employ level production methods to smooth production schedules and use manpower and
equipment efficiently at a lower cost. One consequence of level production is that current
assets go up and down when sales and production are not equal. Other firms may try to
match sales and production as closely as possible in the short run. This allows current
assets to increase or decrease with the level of sales and eliminates the large seasonal
bulges or sharp reductions in current assets that occur under level production.
Seasonal industries can be found in manufacturing, retailing, electricity, and
natural gas. Demand is uneven in these industries, and many exhibit a seasonal demand.
For example, electricity producers have more demand in the summer for air conditioning,
while natural gas companies have more demand in the winter for heating. One small
manufacturing company that exhibits this type of seasonal demand is Briggs & Stratton
Corporation from Wauwatosa, Wisconsin.
Briggs & Stratton is the largest maker of 3.5- to 25-horsepower air-cooled
gasoline engines. If you’ve ever mowed a lawn, there is a good chance your lawnmower
had a Briggs & Stratton engine. Its motors can be found in pressure washers, compressors
and pumps, garden tillers, generators, small tractors, lawnmowers, and outboard marine
engines, and about 30 percent of the company’s overall sales are in the international
market.
Briggs & Stratton’s fiscal year ends in June, and demonstrates both the
seasonality of sales and the leverage impact on earnings per share that we discussed in.
Because Briggs sells most of its products to other manufacturers, who use the engines as
part of their finished products, a large percentage of sales must occur early in the year in
order to produce the garden equipment that would be in demand in spring and summer.
We can see from that sales are lowest in the July to September quarter, followed by the
September to December quarter. Peak sales are in the third quarter, beginning in January
and ending in March. There are carryover sales in the April to June quarter, which is the
second-best period for Briggs & Stratton.
Notice that the first quarter of the year always generates negative earnings per
share as the costs of production outweigh the revenue produced. This is most likely
caused by the costs of building inventory. Earnings in the second and fourth quarters are
small, with most of the earnings coming in the peak sales period of the third quarter. For
example, in 2016, Briggs & Stratton earned $57 million for the year with $36 million
coming in the third quarter; in 2017 the firm earned $27 million with all of it coming in
the third quarter. The seasonal nature of the company’s sales can be exacerbated by
inventory buildup at the end user and a fall in orders for the next season.
Retail firms such as Target and Macy’s also have seasonal sales patterns. On the
next page shows the quarterly sales and earnings per share of these two companies, with
the quarters ending in April, July, October, and January. These retail companies do not
stock a year or more of inventory at one time. They are selling products that are either
manufactured for them by others or manufactured by their subsidiaries. Most retail stores
are not involved in deciding on level versus seasonal production but rather in matching
sales and inventory. Their suppliers must make the decision to produce on either a level
or a seasonal basis. Since the selling seasons are very much affected by the weather and
holiday periods, the suppliers and retailers cannot avoid inventory risk. The fourth quarter
for retailers, which begins in November and ends in January, is their biggest quarter and
accounts for more than half of their earnings. You can be sure that inventory not sold
during the Christmas season will be put on sale during January.
Both Target and Macy’s show seasonal peaks and troughs in sales that will also
be reflected in their cash balances, accounts receivable, and inventory. Notice that Target
has higher sales than Macy’s. Even so, Macy’s peak earnings per share are often higher
than Target’s earnings per share when the fourth quarter sales peak out. Both companies
illustrate the impact of leverage on earnings as discussed, but we can tell that Macy’s has
higher leverage because its EPS rises and falls with sales more than Target’s EPS. We
shall see as we go through the that seasonal sales can cause asset management problems.
A financial manager must be aware of these problems to avoid getting caught short of
cash or unprepared to borrow when necessary.
Many retail-oriented firms have been more successful in matching sales and
orders in recent years because of computerized inventory control systems linked to online
point-of-sales terminals. These point-of-sales terminals allow either digital input or use of
optical scanners to record the inventory code numbers and the amount of each item sold.
Managers can continuously examine sales and inventory levels item by item and, if need
be, adjust orders or production schedules. The predictability of the market will influence
the speed with which the manager reacts to this information, while the length and
complexity of the production process will dictate how fast production levels can be
changed.
To get a better understanding of how current assets fluctuate, let us use the
example of the Yawakuzi Motorcycle Company, which manufactures and sells in the
snowy U.S. Midwest. Not too many people will be buying motorcycles during October
through March, but sales will pick up in early spring and summer and will again trail off
during the fall. Because of the fixed assets and the skilled labor involved in the
production process, Yawakuzi decides that level production is the least expensive and the
most efficient production method. The marketing department provides a 12-month sales
forecast for October through September.
After reviewing the sales forecast, Yawakuzi decides to produce 800 motorcycles
per month, or one year’s production of 9,600 divided by 12. How level production and
seasonal sales combine to create fluctuating inventory. Assume that October’s beginning
inventory is one month’s production of 800 units. The ending inventory level is computed
for each month and then multiplied by the production cost per unit of $2,000.
The inventory level at cost fluctuates from a high of $9 million in March, the last
consecutive month in which production is greater than sales, to a low of $1 million in
August, the last month in which sales are greater than production. Combines a sales
forecast, a cash receipts schedule, a cash payments schedule, and a brief cash budget to
examine the buildup in accounts receivable and cash.
The unit volume of sales is multiplied by a sales price of $3,000 to get sales
dollars in millions. Next, cash receipts represent 50 percent collected in cash during the
month of sale and 50 percent from the prior month’s sales. For example, in October this
would represent $0.45 million from the current month plus $0.75 million from the prior
month’s sales.
Cash payments in are based on an assumption of level production of 800 units per
month at a cost of $2,000 per unit, or $1.6 million, plus payments for overhead,
dividends, interest, and taxes. Finally, the cash budget represents a comparison of the
cash receipts and cash payments schedules to determine cash flow. We further assume the
firm desires a minimum cash balance of $0.25 million. Thus in October, a negative cash
flow of $1.1 million brings the cumulative cash balance to a negative $0.85 million and
$1.1 million must be borrowed to provide an ending cash balance of $0.25 million.
Similar negative cash flows in subsequent months necessitate expanding the bank loan.
For example, in November there is a negative cash flow of $1.325 million. This brings
the cumulative cash balance to −$1.075 million, requiring additional borrowings of
$1.325 million to ensure a minimum cash balance of $0.25 million. The cumulative loan
through November (October and November borrowings) now adds up to $2.425 million.
Our cumulative bank loan is highest in the month of March.
We now wish to ascertain our total current asset buildup as a result of level
production and fluctuating sales for October through September. The cash figures come
directly from the last line. The accounts receivable balance is based on the assumption
that accounts receivable represent 50 percent of sales in a given month, as the other 50
percent is paid for in cash. Thus the accounts receivable figure represents 50 percent of
the sales figure from the second numerical line. Finally, the inventory figure in is taken
directly from the last column, which presented the production schedule and inventory
data.
Total current assets start at $3.3 million in October and rise to $10.35 million in
the peak month of April. From April through August, sales are larger than production,
and inventory falls to its low of $1 million in August, but accounts receivable peak at $3
million in the highest sales months of May, June, and July. The cash budget in explains
the cash flows and external funds borrowed to finance asset accumulation. From October
to March, Yawakuzi borrows more and more money to finance the inventory buildup, but
from April forward it eliminates all borrowing as inventory is liquidated and cash
balances rise to complete the cycle. In October, the cycle starts over again; but now the
firm has accumulated cash it can use to finance next year’s asset accumulation, pay a
larger dividend, replace old equipment, or—if growth in sales is anticipated—invest in
new equipment to increase productive capacity. Under a simplified no-growth
assumption, the monthly cash flow is the same as that of the first year, but beginning cash
in October is much higher than the first year’s beginning cash balance, and this lowers
the borrowing requirement and increases the ending cash balance and total current assets
at year-end. Higher current assets are present despite the fact that accounts receivable and
inventory do not change.
c. Patterns of Financing
The financial manager’s selection of external sources of funds to finance assets
may be one of the firm’s most important decisions. The axiom that all current assets
should be financed by current liabilities (accounts payable, bank loans, commercial
paper, etc.) is subject to challenge when one sees the permanent buildup that can occur in
current assets. In the Yawakuzi example, the buildup in inventory was substantial at $9
million. The example had a logical conclusion in that the motorcycles were sold, cash
was generated, and current assets became very liquid. What if a much smaller level of
sales had occurred? Yawakuzi would be sitting on a large inventory that needed to be
financed and would be generating no cash. Theoretically, the firm could be declared
technically insolvent (bankrupt) if short-term sources of funds were used but were unable
to be renewed when they came due. How would the interest and principal be paid without
cash flow from inventory liquidation? The most appropriate financing pattern would be
one in which asset buildup and length of financing terms are perfectly matched.
In the upper part of, we see that the temporary buildup in current assets
(represented by teal) is financed by shortterm funds. More importantly, however,
permanent current assets and fixed assets (both represented by blue) are financed with
long-term funds from the sale of stock, the issuance of bonds, or the retention of earnings.
Only a financial manager with unusual insight and timing could construct a
financial plan for working capital that adhered perfectly to the design. The difficulty rests
in determining precisely which part of current assets is temporary and which part is
permanent. Even if dollar amounts could be ascertained, the exact timing of asset
liquidation is a difficult matter. To compound the problem, we are never quite sure how
much short-term or long-term financing is available at a given time. While the precise
synchronization of temporary current assets and short-term financing depicted in may be
the most desirable and logical plan, other alternatives must be considered.
To protect against the danger of not being able to provide adequate short-term
financing in tight money periods, the financial manager may rely on long-term funds to
cover some short-term needs. As indicated, long-term capital is now being used to
finance fixed assets, permanent current assets, and part of temporary current assets.
By using long-term capital to cover part of short-term needs, the firm virtually
assures itself of having adequate capital at all times. The firm may prefer to borrow a
million dollars for 10 years—rather than attempt to borrow a million dollars at the
beginning of each year for 10 years and pay it back at the end of each year.
This is not to say that all financial managers utilize long-term financing on a large
scale. To acquire long-term funds, the firm must generally go to the capital markets with
a bond or stock offering or must privately place longer-term obligations with insurance
companies, wealthy individuals, and so forth. Many small businesses do not have access
to such long-term capital and are forced to rely heavily on short-term bank and trade
credit.
Furthermore, short-term financing offers some advantages over more extended
financial arrangements. As a general rule, the interest rate on short-term funds is lower
than that on long-term funds. We might surmise, then, that a firm could develop a
working capital financing plan in which short-term funds are used to finance not only
temporary current assets but also part of the permanent working capital needs of the firm.
As depicted, bank and trade credit as well as other sources of shortterm financing are now
supporting part of the permanent capital asset needs of the firm.
d. The Financing Decision
Some corporations are more flexible than others because they are not locked into
a few available sources of funds. Corporations would like many financing alternatives in
order to minimize their cost of funds at any point. Unfortunately, not many firms are in
this enviable position through the duration of a business cycle. During an economic boom
period, a shortage of low-cost alternatives exists, and firms often minimize their
financing costs by raising funds in advance of forecast asset needs.
Not only does the financial manager encounter a timing problem, but he or she
also needs to select the right type of financing. Even for companies having many
alternative sources of funds, there may be only one or two decisions that will look good
in retrospect. At the time the financing decision is made, the financial manager is never
sure it is the right one. Should the financing be long term or short term, debt or equity,
and so on?
A decision is made at each point until a final financing method is chosen. In most
cases, a corporation will use a combination of these financing methods. At all times, the
financial manager will balance short-term versus long-term considerations against the
composition of the firm’s assets and the firm’s willingness to accept risk. The ratio of
long-term financing to short-term financing at any point in time will be greatly influenced
by the term structure of interest rates.
The term structure of interest rates is often referred to as a yield curve. It shows
the relative level of short-term and longterm interest rates at a point in time. Knowledge
of changing interest rates and interest rate theory is extremely valuable to corporate
executives making decisions about how to time and structure their borrowing between
short- and long-term debt. Generally, U.S. government securities are used to construct
yield curves because they are free of default risk and the large number of maturities
creates a fairly continuous curve. Yields on corporate debt securities will move in the
same direction as government securities but will have higher interest rates because of
their greater financial risk. Yield curves for both corporations and government securities
change daily to reflect current competitive conditions in the money and capital markets,
expected inflation, and changes in economic conditions.
Three basic theories describe the shape of the yield curve. The first theory is
called the liquidity premium theory and states that long-term rates should be higher than
short-term rates. This premium of long-term rates over short-term rates exists because
short-term securities have greater liquidity and therefore higher rates have to be offered
to potential long-term bond buyers to entice them to hold these less liquid and more
price-sensitive securities. The market segmentation theory (the second theory) states that
Treasury securities are divided into market segments by the various financial institutions
investing in the market. Commercial banks prefer short-term securities of one year or less
to match their short-term lending strategies. Savings and loans and other mortgage-
oriented financial institutions prefer the intermediate-length securities of between 5 and 7
years, while pension funds and life insurance companies prefer long-term 20- to 30-year
securities to offset the long-term nature of their commitments to policyholders. The
changing needs, desires, and strategies of these investors tend to strongly influence the
nature and relationship of short-term and long-term interest rates.
The third theory describing the term structure of interest rates is called the
expectations hypothesis. This theory explains the yields on long-term securities as a
function of short-term rates. The expectations theory says long-term rates reflect the
average of short-term expected rates over the time period that the long-term security is
outstanding. Using a four-year example and simple averages, we demonstrate this theory.
In the left-hand panel of the table, we show the anticipated oneyear rate on T-bill
(Treasury bill) securities at the beginning of each of four years in the future. Treasury
bills are short-term securities issued by the government. In the right-hand panel, we show
the two-, three- and four-year averages of the one-year anticipated rates.
For example, the two-year security rate is the average of the expected yields of
two one-year T-bills, while the rate on the four-year security is the average of all four
one-year rates.1 In this example, the progressively higher rates for two-, three-, and four-
year securities represent a reflection of higher anticipated one-year rates in the future.
The expectations hypothesis is especially useful in explaining the shape and movement of
the yield curve. The result of the expectations hypothesis is that when long-term rates are
much higher than short-term rates, the market is saying it expects short-term rates to rise.
When long-term rates are lower than short-term rates, the market is expecting short-term
rates to fall. This theory is useful to financial managers in helping them set expectations
for the cost of financing over time and, especially, in making choices about when to use
shortterm debt or long-term debt.
The bottom axis shows time periods (months and years) and the vertical axis
indicates rates. In this figure, there are three curves: January 2016, January 2017, and
January 2018. We can see that short-term yields rose during 2017. However, 10-year
yields did not rise very much during 2016 and 2017. Using the January 2016 curve (the
red line), we can see that yields rose from less than 0.25 percent for three-month Treasury
bills to approximately 1.75 percent for 5-year Treasury notes and continued up to almost
2.25 percent for 10-year Treasury bonds. This upward-sloping yield curve has the normal
shape. The increase in rates from the three-month to the 10-year yield was 2.02 percent,
or 202 basis points. (A basis point represents 1/100th of 1 percent.) Over the last decade,
the Federal Reserve has kept all interest rates low, with short-term rates extremely low.
This action by the Fed was intended to help the economy recover from the most serious
recession since the Great Depression. By keeping the cost of borrowing low, the Federal
Reserve helps stimulate the economy. As the economy recovers, the yield curve will shift
up and become less steep, as we were already seeing in January 2018.
An upward-sloping yield curve is considered normal, but the difference between
short-term and long-term rates has often been quite wide, as in October 1993 when short-
term rates were less than 3 percent and long-term rates were close to 7 percent.
Generally, the more upward-sloping the yield curve, the greater the expectation that
interest rates will rise. When faced with a downward-sloping, or inverted, yield curve, the
expectation would be the opposite. A good example of this occurred in September 1981
when short-term rates were over 17 percent and long-term rates were close to 15 percent.
A little over one year later, in December 1982, short-term rates were 8 percent and long-
term rates were about 10.5 percent. This example also illustrates that interest rates can
move dramatically in a relatively short time (in this case, 15 months).
In designing working capital policy, the astute financial manager is interested in
not only the term structure of interest rates but also the relative volatility and the
historical level of short-term and long-term rates. Covers a 20-year period and
demonstrates that short-term rates (green) are more volatile than long-term rates (red).
This volatility is what makes a short-term financing strategy risky. Note that rates
declined during the recession of 2007–2009, which is what is expected as demand
declines. As inflation goes up or down, so do interest rates. While we can see that short-
and long-term interest rates are closely related to each other and to inflation, the record of
the professionals for accurate interest rate predictions for periods longer than a few
months is spotty at best.
How should the financial manager respond to fluctuating interest rates and
changing term structures? When interest rates are high and expected to decline, the
financial manager generally tries to borrow short term (if funds are available). As rates
decline, the chief financial officer will try to lock in the lower rates with heavy long-term
borrowing. Some of these long-term funds will be used to reduce short-term debt, and the
rest will be available for future expansion of plant and equipment and working capital if
necessary
e. A Decision Process
Assume we are comparing alternative financing plans for working capital. As
indicated, $500,000 of working capital (current assets) must be financed for the Edwards
Corporation. Under Plan A, we will finance all our current asset needs with short-term
funds (fourth line), while under Plan B we will finance only a relatively small portion of
current assets with short-term money—relying heavily on long-term funds. In either case,
we will carry $100,000 of fixed assets with long-term financing commitments. As
indicated in part 3, under Plan A we will finance total needs of $600,000 with $500,000
of shortterm financing and $100,000 of long-term financing, whereas with Plan B we will
finance $150,000 short term and $450,000 long term.
In the realm of financial decision-making, the choice of financing strategy can
significantly influence a company's bottom-line earnings and overall profitability. When
evaluating financing options, factors such as the cost of capital, interest rates, and debt
obligations play a crucial role in determining the optimal approach. In this analysis, we
delve into the impact of different financing plans on bottom-line earnings, comparing the
outcomes of Plan A and Plan B in light of their respective costs of financing.
Understanding Financing Options: Before delving into the specifics of Plan A and
Plan B, it's essential to understand the underlying financing options and their
implications. Financing strategies typically involve a mix of equity and debt financing,
each carrying its own cost and risk profile. Debt financing, characterized by borrowing
funds from external sources such as banks or bondholders, incurs interest expenses but
allows companies to leverage their capital structure to amplify returns. Equity financing,
on the other hand, involves raising funds by issuing shares of ownership in the company,
thereby diluting existing ownership but avoiding interest expenses.
Analysis of Plan A and Plan B: In the scenario presented, Plan A carries a lower
cost of financing, with an interest rate of 6 percent on $500,000 of the $600,000 required.
Meanwhile, Plan B presumably entails a higher cost of capital, although specific details
are not provided. To assess the impact of these financing plans on bottom-line earnings,
we analyze the after-tax earnings generated under each scenario.
Impact on Bottom-Line Earnings: Assuming the firm generates $200,000 in
earnings before interest and taxes (EBIT), we can calculate the after-tax earnings under
each financing plan. Under Plan A, where the cost of financing is lower, the interest
expense is $30,000 (6% of $500,000), resulting in earnings before taxes (EBT) of
$170,000 ($200,000 - $30,000). After applying the corporate tax rate to calculate taxes,
the after-tax earnings amount to $120,000.
Conversely, under Plan B, with potentially higher financing costs, the interest
expense and subsequent earnings before taxes may differ. Without specific details on
interest rates or terms, we cannot provide precise calculations for Plan B. However,
assuming a higher cost of financing, the interest expense would likely be greater than
$30,000, resulting in lower after-tax earnings compared to Plan A.
Strategic Implications and Considerations: The choice between Plan A and Plan B
involves weighing the trade-offs between financing costs, risk exposure, and profitability.
While Plan A offers lower financing costs and higher after-tax earnings in the scenario
presented, Plan B may have other advantages such as greater flexibility, access to
additional funds, or strategic considerations that justify its higher cost of capital.
Conclusion: In conclusion, the impact of financing strategies on bottom-line
earnings underscores the importance of thoughtful analysis and strategic decision-
making. By evaluating the cost of capital, interest rates, and tax implications associated
with different financing options, companies can optimize their capital structure and
maximize profitability. While lower financing costs may seem favorable, it's essential to
consider the broader financial implications and strategic objectives to ensure sustainable
growth and value creation in the long term.
In the dynamic landscape of corporate finance, the choice between different
financing plans carries profound implications for a company's financial health and
strategic resilience. As businesses navigate through periods of economic volatility and
fluctuating money markets, evaluating financing options becomes paramount to mitigate
risks and seize opportunities. In this analysis, we explore the considerations and
implications of choosing between Plan A and Plan B under varying economic
assumptions, emphasizing the importance of adaptability and foresight in financial
decision-making.
Understanding Financing Plans A and B: Plan A entails employing cheaper short-
term sources of financing, potentially offering immediate cost savings and higher returns.
Conversely, Plan B may involve a more balanced mix of short-term and long-term
financing, providing greater stability and flexibility but potentially at a higher cost. While
Plan A appears to offer $10,500 more in return in the given scenario, it's essential to
recognize that this may not always hold true, especially during tight money periods
characterized by capital scarcity and elevated borrowing costs.
Economic Conditions: During periods of economic volatility, access to short-term
financing may become constrained, and interest rates may spike, rendering Plan A less
favorable. In contrast, Plan B, with its mix of short-term and long-term financing, may
provide greater resilience and certainty, albeit at a higher cost. Therefore, companies
must assess the prevailing economic conditions, interest rate trends, and credit market
dynamics to determine the most appropriate financing strategy.
Money Market Dynamics: Tight money periods, marked by liquidity constraints
and heightened risk aversion among lenders, can significantly impact the availability and
cost of short-term financing. In such environments, companies relying solely on short-
term sources of financing may encounter difficulties securing funding or face exorbitant
borrowing rates, jeopardizing their financial stability and operational continuity. Plan B,
with its diversified financing sources, offers a hedge against these uncertainties by
providing access to longer-term funding options.
In evaluating Plans A and B, companies must consider the trade-offs between
cost, risk, and flexibility. While Plan A may offer immediate cost savings and higher
returns under favorable economic conditions, it also exposes the firm to greater risks
during periods of economic turmoil. Plan B, with its more conservative approach and
diversified funding sources, may offer greater stability and resilience, albeit at a higher
cost.
Furthermore, inadequate financing under Plan A during tight money periods may
result in lost sales opportunities, operational disruptions, or even financial
embarrassment, underscoring the importance of prudent risk management and
contingency planning. By evaluating financing plans based on differing assumptions
about the economy and money markets, companies can proactively adapt their strategies
to navigate uncertainties and position themselves for long-term success.
Conclusion: In conclusion, the evaluation of financing plans A and B requires
careful consideration of economic conditions, money market dynamics, and strategic
objectives. While Plan A may offer apparent cost advantages under certain
circumstances, it's essential to assess the resilience and flexibility of Plan B, especially in
the face of economic uncertainty and tight money periods. By adopting a dynamic and
adaptive approach to financial decision-making, companies can effectively manage risks,
seize opportunities, and safeguard their long-term viability and competitiveness.
In the dynamic landscape of corporate finance, the ability to anticipate and adapt
to changing economic conditions is essential for strategic decision-making. As companies
evaluate financing options, they must consider not only the immediate returns but also the
potential impact of uncertain events on profitability and resilience. In this analysis, we
explore the implications of different economic scenarios on the expected returns of Plan
A and Plan B for the Edwards Corporation, highlighting the importance of strategic risk
management and contingency planning.
Calculating Expected Value of Return: To assess the overall expected returns of
Plan A and Plan B, we compute the expected value, which represents the sum of the
expected outcomes under the two economic conditions. By weighting the returns of each
scenario by their respective probabilities, we can derive a comprehensive estimate of the
expected return for each financing plan.
Strategic Implications and Risk Mitigation: The calculation of the expected value
of return provides valuable insights into the risk-return profiles of Plan A and Plan B
under varying economic scenarios. While Plan A may offer superior returns under normal
conditions, its vulnerability to disruptive tight money periods poses significant risks to
profitability and financial stability. In contrast, Plan B, with its more balanced mix of
short-term and long-term financing, offers greater resilience and stability, albeit at a
potentially higher cost.
Strategic risk management involves evaluating the trade-offs between risk and
return and implementing mitigation strategies to safeguard against adverse events.
Companies may consider diversifying their financing sources, establishing contingency
plans, and maintaining financial flexibility to mitigate the impact of economic
uncertainties and optimize their overall risk-return profile.
Conclusion: In conclusion, assessing financing plans under uncertain economic
conditions requires a comprehensive understanding of risk factors, strategic objectives,
and potential outcomes. By incorporating historical data, economic forecasting, and
probability analysis, companies can make informed decisions to optimize their financial
strategies and enhance resilience in the face of uncertainty. Strategic risk management
practices, such as scenario analysis and contingency planning, play a crucial role in
mitigating risks and maximizing opportunities, enabling companies to navigate turbulent
economic environments and achieve sustainable growth and success.
f. Future Value-Single Amount
In determining the future value, we measure the value of an amount that is
allowed to grow at a given interest rate over a period of time. Assume an investor has
$1,000 and wishes to know its worth after four years if it grows at 10 percent per year. At
the end of the first year, the investor will have $1,000 × 1.10, or $1,100. By the end of
year 2, the $1,100 will have grown to $1,210 ($1,100 × 1.10). This process of earning
more interest on a previous period’s interest is called compounding.
Although the future value of a single amount is straightforward, we will encounter
cash flow patterns that are more complicated. To organize those cash flows and other
information in a useful manner, you will need to use a timeline. Using timelines is an
excellent habit to form. Many of the early examples shown will probably seem so simple
that a timeline adds little to your organizational abilities. However, by forming this good
habit early, you will be much more competent and confident when you begin to
encounter more difficult concepts.
The intervals between each of the periods represent the number of years. The
number “2” labels the end of the second year, and the label “4” marks the end of the
fourth year. Notice that the period markers are at the end of each year. Cash flows are
shown above the timeline. The present value of $1,000 grows at 10% for 4 years to the
future value of $1,464.10.
Understanding the concept of time and its representation on a timeline is
fundamental yet nuanced, especially in the context of financial analysis and planning.
The notion that a number marks both the end and the beginning of a period is not only a
fundamental aspect of chronological sequencing but also holds profound implications for
strategic decision-making and forecasting in various domains. Let's explore this concept
in greater depth and examine its significance across different contexts.
At its core, time is a continuous spectrum marked by sequential intervals, each
demarcated by distinct numerical values. Whether we measure time in years, months,
days, or other units, the transition from one period to the next is marked by the
culmination of one interval and the commencement of another. This continuous
progression underscores the cyclical nature of time and the perpetual cycle of beginnings
and endings.
In financial analysis and planning, the concept of time plays a pivotal role in
forecasting, budgeting, and decision-making. Periodic financial statements, such as
income statements, balance sheets, and cash flow statements, provide snapshots of an
organization's performance and financial position at specific points in time. However,
these points in time represent not only the culmination of the preceding period but also
the inception of the subsequent period, highlighting the interconnectedness and continuity
of financial data over time.
In strategic decision-making, recognizing the dual significance of numerical
markers is essential for aligning actions with long-term goals and objectives. For
instance, when projecting future revenues, expenses, and cash flows, analysts must
consider not only the numerical values at the end of each period but also their
implications for the beginning of the subsequent period. This forward-looking
perspective enables organizations to anticipate trends, identify opportunities, and mitigate
risks effectively.
Beyond its practical applications, the concept of time as a continuous spectrum
invites philosophical reflections on the nature of existence, change, and impermanence.
Philosophers throughout history have pondered the nature of time, contemplating its
relationship to consciousness, memory, and human experience. From ancient
philosophers like Heraclitus, who famously stated that "you cannot step into the same
river twice," to modern thinkers grappling with the mysteries of space-time and relativity,
the concept of time remains a perennial subject of inquiry and contemplation.
In conclusion, the concept that a number marks both the end and the beginning of
a period underscores the interconnectedness and cyclical nature of time. Whether in
financial analysis, strategic decision-making, or philosophical reflections, understanding
this fundamental aspect of temporal progression enriches our comprehension of the world
around us and invites deeper reflections on the nature of existence and change. As we
navigate the complexities of time, both as a practical tool and a philosophical inquiry, we
gain valuable insights into the continuum of beginnings and endings that shape our lives
and experiences.
The keystrokes for this calculator example are presented in the margin. Notice
that we enter the appropriate value for each variable prior to pressing the appropriate
function key. The calculator assumes that either the PV key or the FV key is a cash
outflow, and the solution will have the opposite sign. Because we enter a negative value
for PV , the final solution is positive. If you enter a positive value for PV , the FV
solution will have a negative sign. Also notice that we enter the interest rate as a whole
number, 10. With a nonfinancial calculator you would need to enter the value as 0.10, but
most financial calculators assume that the number entered for the I/Y key is a percentage.
To enter the value 0.065 or 6.5%, you would enter 6.5 before striking the I/Y key. In the
margin example, the CPT key shown above FV stands for “compute.” Not all financial
calculators use a CPT key.
Time value of money problems can also be solved using Excel functions. There
are dozens of financial functions available in Excel, but a student who can use five basic
functions can solve almost any problem. These functions are the FV, PV, RATE, NPER,
and PMT functions. Each of these functions requires inputs (called arguments) that
correspond to the variables in the time value equations. Since we are currently interested
in solving for future values as in Formula 9-1, we will discuss Excel’s FV function.
Excel’s FV function can be used to calculate the future value of a single payment.
The following Excel spreadsheet shows two examples of the FV function. In cell D1, the
FV function references cells B1 to B4 for each argument. When a user begins to type the
FV function, Excel provides some help by displaying a screen tip showing the arguments
required in the function. Here you see the on-screen tip provided by Excel as a banner in
cell D2. Cells D1 and D2 (in combination) show how the function appears as you type in
the required arguments. Cell D3 shows the calculated answer for cell D1 after the enter
key has been pressed. Once the enter key is pressed, the tip in cell D2 will disappear.
The FV function in cell D5 uses numerical values for each argument rather than
cell references. The method used in cell D5 is called hardcoding. In general, cell
references are preferred to hardcoded solutions. Excel’s ability to accept cell references
in formulas is one of its greatest strengths as a spreadsheet tool. Excel’s on-screen help is
shown in cell D6, and the ultimate value produced after striking the enter key is shown in
cell D7. Of course, the values in D3 and D7 are identical to the calculator solution.
g. Number of Periods-Single Amount
Understanding the time value of money and the mathematics behind investment
growth is crucial for financial planning and decision-making. In this scenario, we're
presented with an investment opportunity offering a 10% annual return, and we seek to
determine the number of years required for a $1,000 investment to grow to $1,464.10.
While financial calculators and Excel's NPER function provide convenient solutions, it's
valuable to comprehend the underlying principles and mathematical concepts involved.
The logarithmic function, denoted as ln(x), is a powerful mathematical tool used
to solve exponential growth problems and calculate time periods required to achieve
specific investment goals. In this case, we can apply the natural logarithm to determine
the number of compounding periods necessary for the investment to reach $1,464.10 at a
10% annual interest rate.
The time value of money principle posits that the value of money changes over
time due to factors such as inflation, opportunity costs, and risk. By recognizing the
relationship between present value, future value, interest rate, and time, investors can
assess the attractiveness of investment opportunities and make informed decisions to
maximize returns.
While financial calculators and spreadsheet functions provide efficient solutions
to complex calculations, it's essential for users to understand the underlying mathematical
concepts and assumptions driving these calculations. By gaining proficiency in
mathematical principles such as logarithms, compound interest, and time value of money,
individuals can enhance their analytical skills, interpret results with greater confidence,
and make more informed financial decisions.
In conclusion, the ability to calculate investment growth and time periods using
logarithmic functions, financial calculators, and spreadsheet functions like Excel's NPER
function is a valuable skill for individuals and professionals in the field of finance. By
mastering these mathematical techniques and understanding the principles of time value
of money, investors can navigate the complexities of investment planning, assess risks
and opportunities, and work towards achieving their financial goals with clarity and
precision.
Understanding the various formulas and calculations involved in financial
analysis is essential for making informed decisions and effectively managing
investments. While determining present value (PV) and future value (FV) of a single
amount is relatively straightforward using algebraic formulas, solving for interest rate or
compounding periods can be more complex. As a result, many students and professionals
often rely on financial calculators or Excel functions to perform these calculations
efficiently. Let's delve deeper into this concept and explore why these tools are
commonly utilized in financial analysis.
Solving for interest rate (I) or the number of compounding periods (N) involves
nonlinear equations that may require iterative methods or trial-and-error approaches to
find a solution. These calculations can become cumbersome and time-consuming,
particularly when dealing with complex financial scenarios or multiple variables. As a
result, students and practitioners often opt for more efficient computational tools to
streamline the process.
Financial calculators offer built-in functions and algorithms specifically designed
for solving common financial problems, including interest rate determination and period
calculation. By inputting relevant variables such as PV, FV, and payment amounts, users
can quickly obtain accurate results without the need for manual algebraic manipulation.
This saves time and reduces the likelihood of computational errors, especially in high-
stakes financial decision-making scenarios.
Incorporating real-world examples and practical applications into financial
education can enhance students' ability to apply theoretical concepts to practical
scenarios. By engaging in hands-on exercises and case studies, students gain valuable
experience in using financial tools and techniques to solve complex problems, preparing
them for the challenges of real-world financial analysis and decision-making.
In conclusion, while algebraic formulas provide a theoretical framework for
financial calculations, the complexity of solving for interest rate or compounding periods
often necessitates the use of financial calculators or Excel functions. These tools offer
efficiency, accuracy, and convenience in performing iterative or nonlinear calculations,
enabling students and professionals to focus on understanding financial concepts and
making informed decisions. By combining theoretical knowledge with practical skills,
individuals can navigate the complexities of financial analysis with confidence and
competence.
h. Graphical Presentation of Time Value Relationships
In the realm of finance, understanding the fundamental concepts of future value,
present value, and annuities is essential for making sound investment decisions and
financial planning. To supplement previous discussions and reinforce your understanding
of these concepts, we will explore them further through a non-mathematical, visual
approach. By illustrating key principles using visual aids and examples, we aim to
enhance your comprehension and retention of these crucial concepts before delving into
more advanced topics.
Future value represents the value of an investment at a specified point in the
future, taking into account compounding interest or investment returns. Visualizing future
value involves picturing how an initial investment grows over time due to the effect of
compound interest. Through graphical representations such as line graphs or compound
interest tables, we can observe the exponential growth of investments over time and
understand the importance of long-term compounding in wealth accumulation.
Present value, on the other hand, reflects the current worth of future cash flows,
discounted at an appropriate interest rate. Visualizing present value entails
conceptualizing the value of future cash flows in today's terms, accounting for the time
value of money. By discounting future cash flows back to their present value using
discounting factors or discount rate, we can assess the attractiveness of investment
opportunities and evaluate alternative financial choices.
In previous sections, we explored the concepts of future value, present value, and
annuities, each playing a crucial role in financial decision-making. To enhance
understanding and clarity, we will employ color-coding techniques to illustrate the
relationships between future and present value. By visually distinguishing key
components and highlighting their interconnections, we aim to provide a comprehensive
and intuitive understanding of these fundamental concepts.
In conclusion, employing color-coded techniques to visualize the relationships
between future and present value enhances understanding and clarity in financial
analysis. By associating green with growth, blue with current worth, and yellow with
regular cash flows, individuals can intuitively grasp the dynamics of time value concepts
and their applications in investment analysis, loan evaluation, and retirement planning.
As we navigate the complexities of financial decision-making, the integration of color-
coded representations serves as a valuable tool for learning, comprehension, and practical
application in real-world scenarios.
Future value takes a value today, such as $0.68, and computes its value in the
future assuming that it earns a rate of return each period. Because we want to avoid large
mathematical rounding errors, we actually carry the decimal points three places. The
$0.683 that we invest today (period 0), grows to $0.751 after one period, $0.826 after two
periods, $0.909 after three periods, and $1.00 at the end of the fourth period. In this
example, the $0.68 is the present value and the $1.00 is the future value.
In the present value table, it becomes clear that if I have $1.00 in period 0, it is
worth its present value of $1.00. However, if I have to wait one period to receive my
dollar, it is worth only $0.909 if I can earn a 10 percent return on my money. We can see
that are mirror images of one another. The $0.909 at the end of period 3 will grow to
$1.00 during period 4. Or by letting $0.909 compound at a 10 percent rate for one period,
you have $1.00.
Because you can earn a return on your money, $1.00 received in the future is
worth less than $1.00 today, and the longer you have to wait to receive the dollar, the less
it is worth. For example, if you are to receive $1.00 at the end of four periods, how much
is its present value? As you change the rate of return that can be earned, but the
relationship will remain the same as presented in this example.
The assumption is that you will receive $1.00 at the end of each period. This is the
same concept as a lottery, where you win $2 million over 20 years and receive $100,000
per year for 20 years. In this example, we receive only four payments of $1.00 each and
we use color coding to build up one year at a time.
Understanding the present value of future cash flows is fundamental in finance
and investment analysis. The present value of $1.00 received at different points in time,
as you mentioned, reflects the discounted value of that amount at a specific interest rate.
These numbers indeed should look familiar, as they correspond to the discounted values
of future cash flows based on the time value of money principles and discounting at a
given interest rate.
In conclusion, the present value figures you provided represent the discounted
values of $1.00 received at different points in time, reflecting the time value of money
principle and the discounting effect at a given interest rate. These figures are fundamental
in financial analysis and decision-making, allowing analysts and investors to evaluate
investment opportunities and make informed choices based on present value
considerations.
Looking at the second column for two periods, you see that if you receive two
$1.00 payments, the first at the end of period 1 and the second at the end of period 2, the
total present value will simply be the sum of the present value of each $1.00 payment.
You can see that the total present value of $1.74 represents the present value of $1.00 to
be received at the end of the first period ($0.909) and the present value of $1.00 to be
received at the end of the second period. In the third column we add the present value of
$0.751, received at the end of the third year, to end up with the present value of a three-
period annuity equaling $2.49. The fourth column adds another $0.683 to column 3 and
illustrates the present value of four $1.00 payments equaling $3.17.
This $3.17 is the sum of each present value. The color coding helps illustrate the
relationships. The top box is always $0.909 and represents the present value of $1.00
received at the end of the first period; the second box from the top is always $0.826 and
is the present value of the $1.00 received at the end of the second year; the box third from
the top is $0.751 and is the present value of the $1.00 received at the end of the third
year; and finally, the present value of the $1.00 received at the end of the fourth year is
$0.683.
The next relationship is between the future value of a single sum and the future
value of an annuity. We start, which graphically depicts the future value of $1.00 that is
growing at a 10 percent rate of return each period. If we start with a present value of
$1.00 today (period 0), at the end of period 1 we will have $1.10; at the end of period 2
we will have $1.21; and at the end of period 3 the $1.00 will have grown to $1.33.
One of the confusing features between the future value of $1.00 and the future
value of a $1.00 annuity is that they have different assumptions concerning the timing of
cash flows. The future value of $1.00 assumes the $1.00 is invested at the beginning of
the period and grows to the end of the period. The future value of an ordinary annuity
assumes $1.00 is invested at the end of the period and grows to the end of the next period.
This means the last $1.00 invested has no time to increase its value by earning a return.
This relationship is shown by adding a period 0 to the future value graph.
The calculation for the future value of a $1.00 annuity simply adds together the
future value of a series of equal $1.00 investments. Since the last $1.00 invested does not
have a chance to compound, the future value of a two-period annuity equals $2.10. This
$2.10 comes from adding the $1.00 invested at the end of period 2 plus the first $1.00
that has grown to $1.10. When you look at column three, notice the future value of a
three-period annuity is $3.31. This $3.31 is a combination of the $1.00 invested at the end
of period 3, the $1.10 from the second $1.00 invested, and $1.21 from the first dollar
invested.
Finally, the last column demonstrates that the future value of a four-period
annuity totals $4.64. The explanation of how each value creates the total is given in the
figure. Since is color-coded, you might notice the pattern that exists. The $1.00 amount is
always the top box and is the same color. This is the $1.00 that is always invested at the
end of the period and has no time to compound. The $1.10 is always the second box from
the top and represents the $1.00 that has been invested for only one period, while the
$1.21 is always the third box from the top and represents the $1.00 invested for two
periods. The $1.33 is the fourth box from the top and represents $1.00 invested for three
periods.
i. Determining the Annuity Value
Next assume you know the present value and you wish to determine what size
annuity can be equated to that amount. Suppose your wealthy uncle presents you with
$10,000 now to help you get through the next four years of college. If you are able to
earn 6 percent on deposited funds, how many equal payments can you withdraw at the
end of each year for four years? We need to know the value of an annuity equal to a
given present value.
Notice in this table that each year’s annual payment is $8,148. Each payment is
split between interest and repayment of the loan principal. The interest (8 percent of each
line’s beginning balance) is paid first, and the remainder of the payment reduces the
outstanding balance on the loan. For each line, the difference between the beginning
balance and the ending balance is the repayment amount.
Suppose that you have $3,169.87 in a bank account when you start college, and
you intend to take out an equal payment amount at the end of each year for four years
when interest rates are 10 percent. How much can you take out at the end of each year?
Answering this question requires that you recognize you are trying to find the PMT for an
annuity. As expected, the financial calculator solution shows that the annuity amount is
$1,000 per year.
Excel’s PMT function can calculate the annuity payment amount given the
present value or future value of an annuity. The PMT function assumes that each
payment is at the end of a period as shown in the previous timeline. Either the pv or fv
argument must be entered. The function in cell D1 references the arguments in cells B1 to
B4. The function in cell D5 uses numerical inputs instead. In both cases, the values
produced by the PMT function are identical to the calculator solution.
j. Finding Interest Rates and the Number of Payments
Now suppose that an insurance company offers to pay you an annuity of $1,000
per year for 4 years in exchange for $3,169.87 today. To compare this offer to what you
could earn in a bank account, you must determine what interest rate of return you are
being offered. Calculator keystrokes in the margin show that the rate of return being
offered is 10%. In this example, the PMT key and the PV key must be assigned different
signs. If both are assigned a positive value, the calculator will return an error alert.
Excel’s RATE function can calculate the interest rate that equates the value of an
annuity payment stream with the present value or future value of an annuity. The RATE
function assumes that each payment is at the end of a period as shown in the previous
timeline. Either the pv or fv argument must be entered, as well as a pmt argument. The
function in cell D1 references the arguments in cells B1 to B4. The function in cell D5
uses hardcoded numerical inputs instead. In both cases, the values produced by the RATE
function are identical to the calculator solution.
As our final example, suppose that an insurance company offers to pay you an
annuity of $1,000 per year in exchange for $3,169.87 today. They promise you a 10%
return until the money runs out. How many years will you receive payments? Making
sure that the PMT key and the PV key are given opposite signs, we find on the right that
the annuity will last for 4 years.
Excel’s NPER function calculates the interest rate that equates the annuity
payment stream with the present value or future value of the annuity. The NPER function
assumes that each payment is at the end of a period as shown in the previous timeline.
Either the pv or fv argument must be entered, as well as a pmt argument. The function in
cell D1 references the arguments in cells B1 to B4. The function in cell D5 uses
hardcoded numbers instead of cell references. In both cases, the values produced by the
NPER function are identical to the calculator solution.
k. Compounding over Additional Periods
We have assumed interest was compounded or discounted on an annual basis.
This assumption will now be relaxed. Contractual arrangements, such as an installment
purchase agreement or a corporate bond contract, may call for semiannual, quarterly, or
monthly compounding periods. The adjustment to the normal formula is simple. To
determine n, multiply the number of years by the number of compounding periods during
the year. The factor for i is then determined by dividing the quoted annual interest rate by
the number of compounding periods.
Time value of money problems may revolve around a number of different
payment or receipt patterns. Not every situation will involve a single amount or an
annuity. For example, a contract may call for the payment of a different amount each year
over a three-year period. To determine present value, each payment is discounted to the
present and then summed.
A more involved problem might include a combination of single amounts and an
annuity. If the annuity will be paid at some time in the future, it is referred to as a
deferred annuity and requires special treatment. Assume the same problem as above, but
with an annuity of $1,000 that will be paid at the end of each year from the fourth
through the eighth years. With a discount rate of 8 percent, what is the present value of
the cash flows?
As stated earlier in the, annuity payments are assumed to come at the end of each
payment period. An annuity payment stream of this type is referred to as an ordinary
annuity. However, we should also address how to value annuity payments that come at
the beginning of each period (called an annuity due). As an example, rental payments are
usually required at the beginning of each month.
Both of these are slight variations on the previous formulas shown for ordinary
annuities. When using a financial calculator, modifications must be made so that the
calculator recognizes that the annuity payments are being made at the beginning of each
period. These adjustments differ for various calculators. The website www.tvmcalcs.com
has examples of the appropriate calculator adjustments for numerous commonly used
financial calculators. Using Excel to solve for the future value or present value of an
annuity due is straightforward. To this point, we have ignored the [type] argument in
Excel’s PV and FV functions. When the [type] argument is ignored (or [type = 0]), Excel
regards the annuity payments as ordinary. If [type = 1], Excel values the cash flows as an
annuity due. The following spreadsheet illustrates this point. Notice that the last argument
is [type].
