Antique Cookie Jars

Control of Project Cash Flows

The development of information for the control of project costs with respect to the various functional activities appearing in the project budget. Project managers also are involved with assessment of the overall status of the project, including the status of activities, financing, payments and receipts. These various items comprise the project and financing cash flows described in earlier POME Chapters. These components include costs incurred (as described above), billings and receipts for billings to End Users (for contractors), payable amounts to suppliers and contractors, financing plan cash flows (for bonds or other financial instruments), etc.  Other short-term assets, including marketable securities, accounts receivable, inventory, and prepaid expenses, are part of the Project’s  cash flow. The rest of POME describes the management issues for each of these assets.

As an example of cash flow control, consider the report shown in Table below. In this case, costs are not divided into functional categories, such as labor, material, or equipment. Table below represents a summary of the project status as viewed from different components of the accounting system. Thus, the aggregation of different kinds of cost exposure or cost commitment shown in Table 12-0 has not been performed. The elements in Table below include:

Costs
This is a summary of charges as reflected by the job cost accounts, including expenditures and estimated costs. This row provides an aggregate summary of the detailed activity cost information For this example, the total costs as of July 2 (7/02) were $ 8,754,516, and the original cost estimate was $65,863,092, so the approximate percentage complete was 8,754,516/65,863,092 or 13.292%. However, the project manager now projects a cost of $66,545,263 for the project, representing an increase of $682,171 over the original estimate. This new estimate would reflect the actual percentage of work completed as well as other effects such as changes in unit prices for labor or materials. Needless to say, this increase in expected costs is not a welcome change to the project manager.
Billings
This row summarizes the state of cash flows with respect to the owner of the facility; this row would not be included for reports to End Users. The contract amount was $67,511,602, and a total of $9,276,621 or 13.741% of the contract has been billed. The amount of allowable billing is specified under the terms of the contract between an owner and an engineering, architect, or constructor. In this case, total billings have exceeded the estimated project completion proportion. The final column includes the currently projected net earnings of $966,339. This figure is calculated as the contract amount less projected costs: 67,511,602 – 66,545,263 = $966,339. Note that this profit figure does not reflect the time value of money or discounting.
Payables
The Payables row summarizes the amount owed by the contractor to material suppliers, labor or sub-contractors. At the time of this report, $6,719,103 had been paid to subcontractors, material suppliers, and others. Invoices of $1,300,089 have accumulated but have not yet been paid. A retention of $391,671 has been imposed on subcontractors, and $343,653 in direct labor expenses have been occurred. The total of payables is equal to the total project expenses shown in the first row of costs.

One of the principal ways that many companies generate sales is by offering to sell their products on credit. This is particularly true when the Projects is selling to other businesses. The sale on credit enables the purchasing Projects to use the product for a period of time before paying for it. They may convert the purchased product into some other product for ultimate sale, or they may resell the purchased product to downstream customers, or they may consume the product themselves. In any event, the payment for the purchase is delayed, enabling the buyer to retain its funds and use them to generate income for the Projects.

The delay in receiving payment for your sale increases the risk to your Projects, risk that you might not get paid at all, and risk because you need to borrow funds for the time you wait, lowering the return that you can earn because you do not have the money. Therefore, if you choose to sell on credit, it is important to manage your receivables to assure that you receive the funds when you want and expect them.

Managing accounts receivable involves the assessment of credit risk, as well as following up with customers to assure that they are satisfied with their purchase and will, therefore, pay for it when payment is due. The management of accounts receivable includes the maintenance of accurate and complete records of all sales and payments, monitoring the status of all accounts, and undertaking the collection effort necessary to keep your investment in accounts receivable at the lowest level consistent with your other management policies.

Most Project Managers do not like to call asking for money. Therefore, in many companies, accounts receivable are not well managed and customers are allowed to set their own schedule for payment. Because most companies, just as most people, pay their bills on time, that is, within the terms set by the seller, the longer a receivable remains unpaid, the riskier it is. Some companies borrow money, using accounts receivable as security for the loan. The bank, in assessing the accounts receivable, will limit the amounts that will be considered to those amounts that are current or only a little past due. The lender knows that receivables unpaid more than 30 days past due fall into the problem category, because the customer either can’t pay (doesn’t have the money) or won’t pay (has a problem with the product or service). In either event the security for the loan is gone and the lender will not consider such an account as valuable.

As part of managing accounts receivable, management assesses the probability of collecting the amounts due. If there is some question as to whether the customer will pay the amount due, a reserve may be established. It might even be reasonable to create such a reserve based on the percentage of receivables, and therefore of sales, that has historically been uncollectible. This reserve, created by recording a “Bad Debt Expense” in the Income Statement and a “Reserve for Bad Debts” or an “Allowance for Doubtful Accounts” on the Balance Sheet, reduces the profits for the period and lowers the net balance of accounts receivable on the Balance Sheet. If a Projects chooses not to recognize this probability, no adjustment to income or assets occurs. As you can see, the evaluation of accounts receivable can change financial performance.

In the past some companies adjusted their reported profits by manipulating this and other reserves, raising and lowering profits according to management choice or investor expectations. The Internal Revenue Service (IRS), Securities and Exchange Commission (SEC), and the Financial Accounting Standards Board (FASB) all felt this practice was sufficiently misleading that they established rules to limit the use of reserves. Today, reserves for bad debts must be specific, that is, based on specific accounts considered potentially uncollectible rather than on a percentage of receivables. Other reserves, such as a reserve for inventory obsolescence, may no longer be recorded on the Balance Sheet, but must be specifically identified and written off through the Income Statement, reducing the Balance Sheet balance. Any inventory thus written off must be disposed of. It cannot be held, to be sold at a later date, permitting the Projects to transfer the profits to the future.

POME considered the calculation of the Average Collection Period, a measure of the effectiveness of the management of accounts receivable. This ratio tells us a lot about the credit management and the overall management of the Projects, the quality of the accounts receivable, and something about the future profitability of the business. As such this ratio is one of the first computed when a Projects is being analyzed, whether by an investor, a customer, or a competitor.

Receivables
This row summarizes the cash flow of receipts from the owner. Note that the actual receipts from the owner may differ from the amounts billed due to delayed payments or retainage on the part of the owner. The net-billed equals the gross billed less retention by the owner. In this case, gross billed is $9,276,621 (as shown in the billings row), the net billed is $8,761,673 and the retention is $514,948. Unfortunately, only $7,209,344 has been received from the owner, so the open receivable amount is a (substantial!) $2,067,277 due from the owner.
Inventory

For many companies, inventory is as important, or more important, as accounts receivable. The money spent on inventory takes longer to convert to cash, because it must be sold and the revenue collected, and is therefore more risky than accounts receivable. Because in many cases inventory goes through stages, it is more complicated to manage as well.

In a manufacturing Projects, inventory goes through three stages: raw material, work-in-process, and finished goods. In these companies the management function is more complex, requiring forecasts of requirements, an understanding of the production process, and an estimate of end customer demand. In other companies, ones that only handle the product after it is finished, the stages of inventory are not important, but the forecasting is more critical because, although raw materials may be used for several end products, and even work-in-process may be finished into a number of different items, finished goods are not easily changed into something else.

Because managing inventory is so critical, companies have developed complex systems to control inventory and keep track of it. In recent years some of these systems, drawing on the capabilities of computers and systems, have been expanded to control all aspects of the manufacturing process. In the early years of computerization, companies developed inventory control systems that tracked the quantities, cost, and physical location of stocks held. Later these systems were expanded to recognize ordered but not received materials as well as work-in-process by stage of processing. These systems evolved into planning and forecasting tools that took on the projection of materials requirements and the first Materials Requirements Planning (MRP) systems were developed. Rapidly, MRP systems evolved into Manufacturing Resource Planning (MRPII) tools, and from there to Enterprise Resource Planning (ERP) systems. These have in recent years been further expanded to recognize that the requirements for resources extend beyond the Projects to the suppliers and their suppliers and to the customers and their customers. Today companies are developing comprehensive computerized planning systems to tie the needs of all the parts of the supply chain into an integrated planning system that will provide status information about any stage of the entire processing chain from the very beginning to the very end to anyone with a need to know.

The discussion of reserves  is applicable here as well. Forecasts guide management’s inventory decisions and forecasts can be wrong. However, because of the potential for misuse, reserves for inventory may not be used for financial or tax reporting. Any inventory considered unsalable, and therefore worthy of write-off, must be disposed of, thereby assuring that the reduction in profits is not just a “cookie jar” reserve, to be recovered in some future period when profits need a boost. As you can see, regulators are continuously trying to assure that financial results are meaningful and reliable.

The representative Manufacturing Cash Cycle presented in Exhibit below helps clarify the importance of the planning as well as the interrelationships among the different disciplines within a Projects. Think about the timing of actions within this example.

Exhibit: Manufacturing Cash Cycle

This gap between cash out and cash in, known as the cash conversion cycle, requires the Projects to borrow funds or use equity resources to continue to operate during this time period. In this example we have assumed that our Projects and our customers pay their bills on time. If we delayed our payments, the amount of time from cash out to cash in would be reduced. If our customers were at all delinquent (and on the average companies’ collection periods are longer than the credit terms), the period from cash out to cash in would be longer.

In this case the length of the conversion cycle is caused primarily by the need to hold inventory, a need that is based on the difficulty of forecasting demand. It highlights the importance of developing good forecasts and emphasizes the interrelationships among forecasting, management of assets, and the cost of managing the Projects. Consider the costs associated with carrying inventory in a Projects. The list of such expenses is shown in Exhibit below.

Exhibit: Inventory Carrying Costs

It is estimated that when all these costs are added together, they equal approximately 30 percent of the value of the average annual inventory balance. This amounts to a substantial percentage of Projects profits and excess inventory held “just-in-case” severely impacts potential profitability. This is one reason for the “just-in-time” emphasis on inventory management today.

Cash Position
This row summarizes the cash position of the project as if all expenses and receipts for the project were combined in a single account. The actual expenditures have been $7,062,756 (calculated as the total costs of $8,754,516 less subcontractor retentions of $391,671 and unpaid bills of $1,300,089) and $ 7,209,344 has been received from the owner. As a result, a net cash balance of $146,588 exists which can be used in an interest earning bank account or to finance deficits on other projects.

Each of the rows shown in Table 12-8 would be derived from different sets of financial accounts. Additional reports could be prepared on the financing cash flows for bonds or interest charges in an overdraft account.

TABLE: An Example of a Cash Flow Status Report

Costs
7/02

Charges
8,754,516

Estimated
65,863,092

% Complete
13.292

Projected
66,545,263

Change
682,171

Billings
7/01

Contract
67,511,602

Gross Bill
9,276,621

% Billed
13.741

Profit
966,339

Payables
7/01

Paid
6,719,103

Open
1,300,089

Retention
391,671

Labor
343,653

Total
8,754,516

Receivable
7/02

Net Bill
8,761,673

Received
7,209,344

Retention
514,948

Open
2,067,277

Cash Position

Paid
7,062,756

Received
7,209,344

Position
146,588

The overall status of the project requires synthesizing the different pieces of information summarized in Table above Each of the different accounting systems contributing to this table provides a different view of the status of the project. In this example, the budget information indicates that costs are higher than expected, which could be troubling. However, a profit is still expected for the project. A substantial amount of money is due from the owner, and this could turn out to be a problem if the owner continues to lag in payment. Finally, the positive cash position for the project is highly desirable since financing charges can be avoided.

The job status reports illustrated in this and the previous sections provide a primary tool for project cost control. Different reports with varying amounts of detail and item reports would be prepared for different individuals involved in a project. Reports to upper management would be summaries, reports to particular staff individuals would emphasize their responsibilities (eg. purchasing, payroll, etc.), and detailed reports would be provided to the individual project managers. Coupled with scheduling reports, these reports provide a snapshot view of how a project is doing. Of course, these schedule and cost reports would have to be tempered by the actual accomplishments and problems occurring in the field. For example, if work already completed is of sub-standard quality, these reports would not reveal such a problem. Even though the reports indicated a project on time and on budget, the possibility of re-work or inadequate facility performance due to quality problems would quickly reverse that rosy situation.

Accounts Payable:

The purpose is to ensure vendor inoivces are processed and paid

Step

Who

Steps/Notes

1

Vendor

Submission of Invoice to Company

Vendor generates invoice and references the related Company purchase order number. .

Invoice must be submitted to the Bill To Address as stipulated on the purchase order.

2

Accounts Payable

Invoice Received at Company

When the invoice is received, purchase order number is validated by checking the following:

1. Purchase order number referenced on invoice

If purchase order number is not referenced on invoice, it is returned to the vendor with standard explanation letter.  A log is maintained to record each instance of an invoice being returned to vendor.

3

Accounts Payable

Scan Invoice into PMIS/ERP

Validated invoice is scanned into the ERP system.

Once scanned into ERP, invoice is stamped with the marking ‘file only’ to prevent duplicate scans.

4

AP

Matching of Invoice

Invoice is retrieved from ERP system and is matched to purchase order.  The agreed SLA is retrieval within three (3) working days.

Variance reasons: not receipted (on hold), dispute (PO & invoice do not match).

5

AP

Facilitation of Payment

Once invoice is matched to purchase order, the three (3) way match applies.

PO number + Receipt + Invoice = Validated invoice

Once invoice is in validated status, payment is calculated based upon the payment terms assigned to the vendor account, based upon his paymeny terms.

A Project Manager of cash in Projects recognizes that earning interest on cash on hand increases the overall profits of a Projects. Therefore, many Project Managers take advantage of the bank’s need for cash to maintain their levels of reserves. Project Managers contract with the bank for the bank to use the cash the Projects has on deposit to increase the bank’s overnight balances in return for interest. These repurchase certificates or securities (Repos) provide a modest income for the Projects on funds that otherwise would not earn anything at all. If the funds are not needed for longer than just overnight, longer agreements will be established, and they will carry higher interest rates, to compensate for the longer time. The differences in interest rates are very slight, but if the balances involved are substantial, this may still result in some real income. If the funds will be available for longer, weeks or months, other investment instruments may offer higher rates of return.

As part of this cash management process, companies with multiple locations will arrange to bring the cash from all the locations into a central account where it can be managed and invested more effectively. A Project Manager can earn more money if there are larger amounts to invest as well as if the money can be invested for longer periods of time. The sweeping of these funds into a concentration account gives the Project Manager more opportunities to manage the funds effectively.

Nevertheless, used properly, the techniques of cash management, getting money into a central account and investing the funds intelligently, offer an opportunity to contribute significantly to the financial success of a Projects. These funds are often invested in short-term securities, known as marketable securities.

Managing Marketable Securities

Numerous instruments are available to the Projects treasurer to help generate income while holding liquid assets. The list of such investments grows daily and includes instruments called derivatives, whose value is “derived” from underlying assets or arrangements. One of the most interesting aspects of the derivatives market is the flexibility of the instruments that are being developed. Derivatives, which have received a lot of negative publicity in recent years but which offer the ability to tailor investments to particular needs or situations, may carry a level of risk inappropriate for liquid resources that a Projects will need in the near future.

Exhibit: Short-Term Investment Choices

Clearly, the array of choices offers great flexibility at a broad range of risk levels. Common stock is far riskier than savings accounts, but for the right situation it may offer the prospect of sufficiently high return to make the risk worthwhile.

In any discussion of short-term investments, we must remember the effect of changes in interest rates. In recent years the Federal Reserve, in its efforts to manage the economy and control inflation, moved interest rates down, in a series of steps, as the economy slowed in 2001 and 2002, and then up, again in a series of steps, as the economy strengthened in 2004 and 2005. With each change in interest rates, specifically the short-term federal funds rate, but, affecting all other rates through a reference to the prime interest rate, there was a ripple effect through all financial markets. As banks and businesses have become used to the Federal Reserve rate-setting process, responses have become swift and predictable. The federal funds rate is the rate that banks charge other banks for overnight loans. The prime interest rate, approximately three percentage points higher than the federal funds rate, generally moves in concert with the federal funds rate. The prime interest rate is the short-term interest rate that banks charge their best (most creditworthy) customers.

Estimating Interest Rates

Using the preceding section as a guide, the formula for interest rates would be:

I = BR + DP + IP + MP + LP

Recognizing the premiums described we can easily arrive at an approximation for the “risk-free” rate, the interest rate paid by the U.S. Treasury. The risk-free rate, designated RF, includes the basic rental cost of money, plus the premiums for inflation and maturity, the nondiversifiable risk elements.

As an example, U.S. Treasury bonds, the long-term bonds the U.S. government issues, are currently offering an interest rate of approximately 5.0 percent. If we consider the basic rent plus the inflation premium plus the maturity premium, the risk premiums discussed above that apply to the U.S. government’s obligations, we find that:

Where:

I

= the Interest Rate

BR

= Basic Rental cost of money, approximately 2 percent

DP

= Default Premium

IP

= Inflation Premium, currently running about 4 percent, increased

because the Federal Reserve is concerned that the strength of

the economy would cause prices to rise

MP

= Maturity Premium

LP

= Liquidity Premium

Interest rates move in response to the general level of business activity in the economy. If the economy is strong, interest rates, which are the price of money, rise as demand for money rises. The financial markets see this interest rate movement in the market for U.S. Treasury securities. By monitoring this market, business Project Managers are in a position to make decisions regarding the financing of their business, as the interest rates they will be charged are generally determined in relation to the Treasury security interest rates.

Capital Asset Pricing Model

This interest discussion establishes a basis for looking at other securities. After all, equity investors want a return that recognizes these same risk premiums and rewards the investor for giving up the right to a defined maturity, for taking a subordinated, lower priority role to other financing, and for giving up the right to a regular payment of income. Scholars have analyzed this relationship and identified a relationship that describes these needs. Finance theoreticians have described the Capital Asset Pricing Model (CAPM) as an equation that determines the return required of an investment having a particular risk relationship to the general market. This equation is:

kj = RF + bj(km – RF)

The measure of beta has been the subject of much academic debate, but generally it relates the volatility or riskiness of a particular security to the general market for similar securities. That is, it relates a particular stock, j, to the performance of the Standard & Poor’s 500 Average, the Dow Jones Industrial Average, or some similar well-known market measure.

Relating Risk and Return

Though the CAPM equation, in current markets, does not really present a definitive market value relationship for an investment, by relating risk and required return for a prospective investment to the risk-free rate (RF—the government bond rate) and the market (km) through an assessment of riskiness (bj), an investor is able to apply a rational assessment of validity to a projected, estimated, or definitively required rate of return. The investor is then in a position to decide whether the investment is attractive or not.

This defined relationship between risk and return leads to the old adage, “If it sounds too good to be true, it probably is.” This saying applies to investments as well as, if not better than, to other situations. If someone offers an extraordinarily high rate of return, it must mean that there is an extraordinarily high risk associated with the opportunity. Despite any objections that might be raised, the relationship of risk and return is clearly valid and as such should be heeded.

Extending the Theory

Over the years many sources of investment guidance have estimated the beta coefficients for different stock issues. Drawing on the difficulty of establishing just how much riskier one situation or investment is than another, we find that in these estimates of beta, very few Projects stocks are evaluated at a beta higher than 2.The consequence of this leads to an important result in the financial marketplace. Taking the CAPM equation and using 2 as beta, recognizing that historically RF has been 6.0 percent and km is estimated long-term to be approximately 10 percent, the consequence is a required rate of return of:

Where:

kj

= the Required Rate of Return on an investment j

RF

=the risk-free rate, usually the rate on a 10-year or 20-year U.S.Treasury bond

bj

= “beta sub j” is the risk coefficient that relates investment j to the market

km

= the rate of return available on a known portfolio in the relevantmarket, the basis for the comparison to j

kj = RF + bj(km – RF)
kj = 6 + 2(10 – 6)
kj = 14

If beta is 2, frequently the highest beta coefficient because it is so hard to say that one opportunity is more than twice as risky, twice as volatile, as the market, then to be attractive, a risky investment must offer the investor a rate of return greater than 14 percent. It is this recognition that has established a market for high-risk, non-investment-grade securities. If a Projects that does not qualify as an investment-grade borrower offers a bond at a rate of, say, 15 or 16 percent interest, there will be some investors—risk takers— who, seeing a rate of return higher than their required rate of return, will invest, establishing the junk bond market and making it possible for riskier companies to attract the funding they need to move their businesses forward. To further explain how this works, remember that interest expense is deductible before computing taxes..

Time Value of Money

The importance of determining the risk-based required rate of return, k, cannot be overstated. All financial decisions should incorporate an assessment of this risk and the return required as a basis for action.

In essence, we use “k” to assess the real value of whatever we are considering. An essential element of understanding our business system is the recognition that we can always earn a return—an income—however modest, by investing our money in a low- or no-risk investment offering a basic interest rate—a basic rental cost for the use of our money.

We further recognize that if we leave our money invested for periods longer than the stated interest period, the investment will continue to earn interest and will also earn interest on the interest. This lesson goes back to childhood when a parent took you to the savings bank and explained that if you deposit your money in the bank, the bank will pay you interest and that interest will compound, enabling your deposit to grow and grow. This understanding is our starting point. It can be described as, “A dollar today is worth more than a dollar tomorrow.”

Taking risk into account results in changing expectations of that return. The greater the risk, the greater the return must be to make taking that risk attractive to us. This premise makes it possible for us to evaluate alternative opportunities by judging the risk and then applying our requirements for return based on that risk. If after taking risk into account, the return is satisfactory, we will make the investment; if it is not, we will not.

The way we assess the investment is to relate the value of the money we pay out to the amount of money that we will receive would be worth if it were computed in today’s terms. Or, we relate the value that something will be worth in the future to what an acceptable investment would be worth, using the required rate of return, k, as the basis for the assessment.

To make this concept simple, assume you required a rate of return of 10 percent and you had $100 to invest for one year. To be attractive to you under these circumstances, you would need to receive at least your $100 back plus a 10 percent additional amount, or $10 ($100 × .10). Therefore, we can say that the future value, in one year, of the investment for which we will pay $100, must be $110.

Similarly, we can say that an investment that will pay us $110 in one year has a present value of $100 today if our required rate of return is 10 percent. It is important to recognize that such analysis goes both ways. We need to be able to compute the future value from the present and to compute the present value from the future. In fact, we can go either way. If we know any three of the four variables—Present Value, Future Value, Term, and Rate of Return—we can compute the missing variable and then assess the investment.

Present Value—the cost of an investment or the value today of monies to be received in the future
Future Value—the dollar yield of an investment or the value of monies to be received at some time in the future from an investment made today
Term—the life of the investment
Rate of Return—the rate of return offered by an investment or required by the investor

In some situations payments made are in equal instalments. In such cases we refer to the payments as annuities. An annuity is a series of equal periodic payments whose value may be determined by use of specialized computations or by summing the values derived by calculating the present value or the future value, whichever is appropriate, of each of the payments individually. One computation quirk to keep in mind is that in calculating the future value of an annuity, payments are assumed to begin at the end of the first period and to occur at the end of each subsequent period. If the payments begin at the beginning of the period and continue at the beginning of subsequent periods, the sequence of payments is known as an annuity due and the value of the annuity is increased by one interest computation.

In the Appendix at the end of the course are some tables that help relate present value to future value, both for individual sums of money and for annuities, which, as noted, are regular periodic payments of the same amount of money over a period of time extending beyond one period. , we can compute the present value of capital investments by applying the principles of time value of money to the facts that we determine.

Valuation

We can use our understanding of time value of money, along with the application of risk assessment, to evaluate investment opportunities. So, we can determine that the value of an investment is a function of what we will receive in the future, discounted to the date of the investment. Thus, if we want an investment of $100 to yield 10 percent over 5 years, we can compute $100 × 1.10 × 1.10 × 1.10 × 1.10 × 1.10, which equals $161.05. Therefore, the future value of an investment of $100 at 10 percent for five years is $161.05. A look at the future value table shown in the Appendix confirms that the future value of $1, at 10 percent interest, compounded annually for five years is $1.6105. Therefore, the future value of $100 computed the same way will be $100 × 1.6105, or $161.05.

All investments can be assessed the same way. Therefore, the determination of the value of an investment depends on the present value (PV), future value (FV), interest rate (I) and term (N, for number of periods). Present value and future value tables referred to in the following pages are in the Appendix to this manual. These same calculations can be done very easily using one of many financial calculators available from any office supply store. These calculators perform the same calculations demonstrated in the following pages. We can also determine how much we will need at some time in the future, to buy something or to reach a desired milestone. Let’s look at an example.

POME Case Study:

An Illustrative Example

Suppose you want to purchase a retirement home when you retire in 20 years. You have a specific home in mind that is currently available for $85,000. You expect market prices to increase an average of 6 percent per year for the next 20 years. What will the house be worth when you are ready to buy it? Looking at the table for future values in the Appendix, under the 6 percent column across the 20 period line, we find the factor of 3.207, which tells us that the value of the house will be $85,000 × 3.207 or $272,595.

As a second part to this problem, let us determine how much we need to save each year if we can invest our savings at 10 percent for the entire time. Since we want to save the same amount each year for the twenty years, we are talking about an annuity. We need the annuity to be worth $272,595 in 20 years using a 10 percent interest factor. Looking at the future value of an annuity table (see Appendix), we see the factor for an annuity for 20 periods at 10 percent is equal to 57.275. Therefore, if we divide the $272,595 by the factor 57.275, we find that if we save $4,759.41 each year for the twenty years, we will have accumulated enough money to pay for the house. This example is illustrated in Exhibit below.

Exhibit: Valuation Computations

Assessing Investments

We can use these tools to assess any investment, recognizing that the value of the investment is whatever we receive, related to what we paid in, and related to our expectation of return, which, in turn, depends on our assessment of risk.

To determine the attractiveness of an investment in a bond, therefore, we evaluate the interest payments we will receive and the return of the face amount of the bond at maturity and compare that result to our investment amount. So, a bond that will pay us a coupon rate, the stated interest rate of the bond, of 10 percent, equal to $100 per year for five years, and will then pay us $1,000, the face amount of the bond, is worth $1,000.00 to us now if our required rate of return is 10 percent, but is worth $1,080.30 to us if our required rate of return is 8 percent, or $927.50 if our required rate of return is 12 percent.

Exhibit: Assessing Investments

These computations tell us many things. Not only do they tell us what such a bond is worth at different discount rates, but they also demonstrate the relationship between nominal interest rates, the 10 percent that the bond pays based on its face amount, and market rates. If the bond’s interest rate exceeds the current market, the bond will sell at a premium, and, conversely, if the bond’s interest rate is lower than the current market rate, the bond will sell at a discount. This enables an investor to receive a return competitive with the market rate. If that were not possible, there would be no market for securities that offered returns different from the current market.

Equity investments can be evaluated in a similar manner. The investor, in considering an equity investment, has a desired rate of return in mind. This return is invariably higher than would be required for a risk-free or a low-risk investment as equity investments are clearly riskier. Additionally, an equity investment does not promise regular cash income. Therefore, the expectation is that when the return is actually received, it will be significantly more rewarding.

The reward for an equity investment is a function, not of dividends, but of earnings. The earnings of a Projects belong to the shareholders so that a dividend, which is a distribution of the Project’s earnings to the shareholders, is actually a distribution by the Projects of money that already belongs to the shareholders. However, it is deemed to have a separate value. More important, however, than the dividends, is the market value of the stock. When investors purchase shares in a Projects, they do so in a market and with the expectation that, someday, they will resell those shares into the market. Therefore, the market price that investors pay for shares must be a reflection of the perceived present value of the money that the shareholder expects to receive in the future, when he or she sells the shares back into the market.

Unlike a bond, there is no certainty of timing for redemption or sale of the stock. The shareholder will hold the stock until the current market value of the shares is higher than the perceived present value of the future market performance, as determined using the investor’s required rate of return. This all makes sense, but is probably not a picture of reality. Most investors make investment decisions largely on the basis of past performance and intuitive perception. However, underlying this perception is an assessment that the future market price will be higher, and will be enough higher to make it worthwhile to buy and hold this stock.

Valuing an Investment

Valuing an investment involves applying the tools of time value of money to the expectation of return, recognizing the riskiness of the investment in determining the required rate that will be applied. That is, the value today of an investment is the present value of the future cash flows (whether periodic payments, maturity payment, or price received when sold) of the investment in question, discounted at a rate of return required by the investor and determined by applying a risk assessment to the investment.

The required rate of return that the investor establishes for a particular investment is used as the “k,” the discount rate used to convert future cash flows into present value for comparison to the price of the investment.

POME Case Study:

The following problem highlights the flexibility of this tool. Using the table below and the time value of money tables in the Appendix, answer the questions that follo

At what price will each of these investments yield 10 percent?
What is the approximate yield (return on investment) percentage of each if the investment required today is $8,000?

Investment

Value at Maturity

Maturity

A

$30,000

15 years

B

13,000

7 years

C

20,000

10 years

D

15,000

20 years

Finally, let’s consider a more comprehensive example related to personal financial planning. For this analysis, assume that you are a 25-year-old who wishes to retire in 40 years with $1,000,000 in the bank. Although a million dollars won’t be as attractive then as it is now, having it will be far better than not having it.

We know the future value: $1,000,000.
We know the term: 40 years.
We know the interest rate: 10 percent.

Using the future value tables, we find the factor related to 40 years at 10 percent: 45.259. Dividing $1,000,000 by 45.259 equals $22,095.54, which tells us that if we were to invest $22,095.05 today in an investment that promised a 10 percent interest rate compounded annually, at the end of 40 years we would have $1,000,000.

We can use the present value tables equally effectively. The present value interest factor for 40 years at 10 percent is .022. Multiplying $1,000,000, the future value, by .022, the present value interest factor, equals $22,000. This is essentially equivalent to the $22,095.05 determined using the future value interest factor. The difference is a result of rounding. In fact, if we had a table of four decimal places, the factor would be .0221 and the answer would be $22,100.00, very close to the $22,095.05.

Perhaps, however, as a 25-year-old, you do not have $22,000 available to invest for 40 years. You are able to save some money from your weekly salary. How much would you need to save each year from your compensation to accumulate a $1,000,000 fund when you retire (all tax considerations are ignored for this exercise).

Using the future value of an annuity table, we find the factor for the future value of an annuity for 40 years at 10 percent is 442.58. Dividing $1,000,000 by the factor 442.58 equals $2,259.48. Saving $2,259.41 over the course of each year for 40 years and investing that money at 10 percent will yield a retirement fund of $1,000,000.

Using the present value of an annuity table is slightly more complicated because we must cover two steps.

The present value of a $1,000,000 fund to be available in 40 years is, as we saw before, $22,100. The present value of an annuity factor for 40 years at 10 percent is 9.779. We need to work with the present value of the retirement fund to equate to the present value of the annuity that will equal that fund. Dividing the $22,100 by 9.779 equals $2,259.94, equal to the annuity computed using future value amounts.

As is obvious from all this, the use of time value of money techniques, coupled with an understanding of risk and return, enables an investor to decide whether an investment opportunity is appropriate for him or her or not. These tools are extremely powerful and are used for both personal and business investment decision making.

At the present time interest rates are relatively low and the prospect of earning 10% per year may seem unlikely. Although it is true that any bonds offering a 10% interest rate would be quite risky, a significant number of mutual funds, funds that invest investor deposits in a portfolio of corporate stocks, bonds, and other investments, have earned 10 percent or more for several years. Analysis of mutual fund investments through brokers or through Morningstar.com or Lipper.com will identify a number of alternatives at different risk levels.

Managing the time value of money has been part of our responsibility since we were very young. In business it takes on even more importance as we manage money on behalf of others: lenders, shareholders, and others in our Projects. The essence of time value of money is that, “A dollar today is worth more than a dollar tomorrow.” However, the things that affect this value are volatile and must be taken into account:

Risk: the higher the risk, the higher the return must be.
Specific Risks: default, inflation, maturity, liquidity.
Required Return: the rate we must earn to satisfy the funding sources, a function not only of financial risk, but also of alternative opportunities, Project Managerial philosophy, and general economic conditions.

The Project Manager/ Finance Manager must take into account all of these factors when looking at investment alternatives.

To solve this problem, you could also use the future value interest factor by dividing the future value by the future value interest factor.

Part 1

Present Value

Future Value

Term

Interest Rate

Factor

Present Value

A

$30,000

15 yrs.

10%

.239

$7,170

B

$13,000

7 yrs.

10%

.513

$6,669

C

$20,000

10 yrs.

10%

.386

$7,720

D

$15,000

20 yrs.

10%

.149

$2,235

To arrive at the correct answers, you need to divide the future value by the present value to determine the future value interest factor.

Part 2

Present

Future

Interest

Interest

Investment

Value

Value

Term

Rate

Rate

Factor

A

$8,000

$30,000

15 yrs.

3.750

Between 9% and

10%

B

$8,000

$13,000

7 yrs.

1.625

Between 7% and

8%

C

$8,000

$20,000

10 yrs.

2.500

Between 9% and

10%

D

$8,000

$15,000

20 yrs.

1.875

Between 3% and

4%

To solve this problem you could also use the present value interest factor by dividing the present value by the future value.