MAT/543 MAT543 MAT 543 WEEK 3 HOMEWORK

MAT 543 WEEK 3 HOMEWORK

Week 3 Homework

• Homework
• Chapter 3: Exercise 3-3 (page 61 of the text)
• Chapter 4: Exercise 4-1 through 4-4 (page 72 of the text)

 Flow Chart: To Complete an Acceptable Term Paper

As can be seen from this example, more detail could have been added by expanding the number of steps in this chart. The example could be considered a Level I or macro chart with other more detailed charts (Level II) to cover each individual work process such as collect data, write first draft, etc.

This chapter has established general rules and conventions associated with general systems flow charting. Developing the skill to flow chart requires practice as well as patience. Although a basic method, it is very robust in identifying the operation of current work processes and options to enhance the efficiency and quality of work processes. Be aware that contemporary attempts to improve service quality, such as total quality management (TQM) and continuous quality improvement (CQI) rely upon general systems flow charting as a basis for system and process analysis.

Unlike other management methods that rely upon mathematics, general systems flow charting does not involve numbers and equations. In this sense it is not a quantitative method. It does, however, provide the manager a form of symbolic logic to use to describe and improve operations and design new systems. As such, general systems flow charting is a systematic method that should be incorporated into the repertoire of any health services manager.

EXERCISES

    3-1 Develop a general systems flow chart that describes the process of filling a car with gasoline. After “start” have as the first process “Arrive at Gas Station.” Immediately before “stop” have as the last process “Leave Gas Station.”

    3-2 Using a general systems flow chart design a system for arrivals at an emergency room of a hospital.

    3-3 Using the following narrative, create a general system flow chart. When a patient arrives at the clinic the patient first sees the receptionist, who checks to see if the patient was seen before. If so, the receptionist pulls the medical record from the file. If the patient is new, the receptionist has the patient complete the necessary forms and creates a medical record. Patients are seen by the physician in the order they arrive. If one of the two examination rooms is empty, the nurse escorts the patient to the examination room and records the complaint. The nurse performs routine tests. The nurse writes the complaint and findings on a medical examination form, a form that will be subsequently filed with the patient’s medical record. The physician examines the patient and orders medical tests, if necessary. A diagnosis and treatment plan is presented to the patient by the physician; a written copy of this plan and any other appropriate instructions. [Notes are written on the medical examination form.] When the physician releases the patient, the patient returns to the receptionist, who prepares a bill. If the patient has health insurance, the bill is sent to the health insurance carrier. The patient leaves after either paying the bill (by cash, check, or credit card) or signing the forms to authorize payment by his or her health insurance company. If the health insurance company refuses to pay or partially pays the bill, the receptionist bills the patient by mail. Any patient with an unpaid bill or bad credit history is refused subsequent treatment until the old bill is paid.

REAL WORLD SCENARIO

Eugene Righter is manager of strategy for St. Clement’s, Mercy Medical Center in a Midwestern city. He is presented with an offer of $100,000 to purchase a new piece of laboratory equipment that the medical center has begun developing. The prospective purchaser of this equipment has offered him an option of receiving the $100,000 for the rights to the equipment immediately or in 12 months. Righter is planning to sell the rights anyway, and there is no prospect of generating any revenue from the use of the equipment in the coming 12 months. Should he accept the money now or in 12 months? This is an easy choice: Righter elects to receive the $100,000 now, rather than waiting for 1 year. But what were the reasons behind his decision?

There are at least two factors that influenced the decision:

    1. Assuming that some level of inflation will occur within the next 12 months, $100,000 can buy more today than in 12 months.

    2. There is always an option of investing the $100,000 today or during the next year, an option that may result in greater financial return or gain in 12 months than accepting $100,000 in 12 months. At a minimum, the $100,000 could be used to purchase a certificate of deposit or a government note of minimum risk, where it would earn interest for the period of the investment.

LEARNING OBJECTIVE 1: TO UNDERSTAND THE CONCEPT OF THE TIME VALUE OF MONEY

This simple example illustrates one of the fundamental concepts of management: There is a time value associated with money. All other things being equal, money that you have today is worth more than the same amount of money received in the future. This concept, known as the time value of money, comes from the field of finance.

Issues related to the time value of money become more critical as the period of time in question increases. As many accounting issues pertain to issues with relatively short time horizons; e.g., less than 12 months, managers may not consider the time value of money in analyzing strategic decisions. Over longer periods of time, however (and occasionally shorter as well), the relationship between time and the value of money is a critical management consideration. Given the fact that most investments or project opportunities have “lives” extending over time horizons greater than 12 months, the importance of the time value of money is magnified. Effective managers take a financial perspective of projects, including considerations of the time value of money, not simply an accounting perspective (such as short-term profit or loss), although both are important.

The preceding example is simple; however, most decisions faced by managers are not as straightforward. For example, suppose the manager is offered the same $100,000 now for the equipment rights or $110,000 in 12 months. Should the manager sell the rights now, or sign an agreement to sell at the later time? Is it more beneficial financially to have the $100,000 in hand now, or is it more advantageous to wait for a year and receive a larger sum of money?

Responding to opportunities such as this requires competency in the management skill of calculating what is known as the present value of money received at a later time. This competency enables managers to assess opportunities on an “apples to apples” perspective financially; in other words, it takes into account the time value of money. The overall objective of this chapter is to introduce the key management methods associated with the time value of money. It must be added that, although financial factors should never be the only criterion used in making management decisions, particularly in health care, it is also true that such factors often take precedence in decision making.

LEARNING OBJECTIVE 2: TO BE ABLE TO COMPUTE THE FUTURE OR PRESENT VALUE OF MONEY (I.E., COMPOUNDING AND DISCOUNTING)

The fundamental concepts underlying the idea that the value of money changes in relation to time are known as compounding and discounting. Compounding refers to the idea that, if money is invested (e.g., put in the bank or used to buy a bond with fixed returns in the future), this amount of money grows or compounds in the future. Compounding refers to the process of going from today’s value of money, known as the present value, to some future value of money.

It is useful to think of discounting as the inverse of compounding. Discounting is a way of looking at some future amount of money, known as the future value, and calculating its value today (i.e., calculating its present value). The following sections present the ideas of compounding and discounting and give several examples of how to compute future and present value. Additional examples of how to apply the ideas and tools introduced in this chapter are found later in the book, notably in Chapter 13.

Calculating the Future Value of Money: Compounding

The simplest example of money growing over time (compounding) is a savings account at a bank. Individuals choose to deposit money in the bank for a variety of reasons, including the knowledge that money invested in the bank grows because interest is earned on the money. For example, if an initial deposit of $100 is made in a bank that promises to pay 2% interest annually, at the end of 12 months a total of $102 is available. The original deposit has grown or compounded from $100 to $102. The additional $2 is the interest earned on the deposit.

If the money is left in the bank for another year, assuming no change in the interest rate, at the end of year 2 a total of $104.04 is available in the account. The original $100 has grown or compounded by $4.04 as a result of interest earnings on the account. Thus, using conventional terminology, the future value of $100 invested for 2 years at an interest rate of 2% compounded annually is $104.04. The increase in the account in the second year is $2.04, not $2.00, as was earned in year 1. This is because the amount in the account at the end of year 1 (i.e., the amount that is compounded for an additional [second] year) was $102 (the original $100 deposit + $2 of interest earned to that point in time). Thus, during year 2, 2% was earned on $102, not $100.

In situations involving compounding or discounting, it is helpful to create a “picture” or timeline of the investment scenario. A timeline is used to indicate the present and future value of money, the applicable interest rate, and the length of time involved. In fact, always beginning a time value of money analysis with a timeline may be a prerequisite for accurate calculations.

For example, Figure 4-1 depicts the situation just described. Note that time period “0” refers to the present time (i.e., now), and that the future value refers to the size of account at the end of the time period indicated. The compounding (interest) rate is shown on the timeline for the appropriate time periods. Creating a timeline is a simple, yet helpful tool to organize the “facts” of the investment opportunity and to help ensure that mangers have all the information required for decision making.

In general terms, compounding is represented by the following equation:

Future Value = Present Value + Interest Earned (I)

where

Interest Earned = Present Value * Interest Rate (i)

Figure 4-1 Timeline Showing Present Value (PV) and Future Value (FV) of $100 Invested for 2 Years at a 2% Annual Rate

Stated another way:

FV = PV + I

which is the same as:

FV = PV + (PV*i)

Simplifying:

FV = PV(1 + i)

Equation 4-1

Using Equation 4-1 for the preceding example described, where the present value is the amount of the original deposit (i.e., $100) and the interest rate is 2%, the future value at the end of year 1 is calculated as:

FVyear 1

=

$100(1 + 0.02)

=

$100(1.02)

=

$102

In the second year, another year’s interest is earned. To reflect this second year of interest, using Equation 4-1:

FVyear 2

=

PV(1 + i)(1 + i)

Equation 4-1

=

PV(1 + i)2

This is the same as:

FVyear 2 = FVyear 1(1 + i)

Each term (1 + i), known as the compounding factor, indicates an additional period during which interest is being earned. In this example, it is said that interest is compounded for two periods. Substituting numbers in the equation, the future value at the end of year 2 is calculated to be:

FVyear 2

=

$100(1 + 0.02)(1 + 0.02)

=

$100(1 + 0.02)2

=

$100(1.02)2

=

$100(1.0404)

=

$104.04

Equation 4-2 is a general equation for compounding that takes into account the number of compounding periods (n):

The General Compounding Formula

FVn

=

PV(1 + i)n

Equation 4-2

where FVn

=

future value in time period n

PV

=

present value

i

=

stated interest rate

n

=

number of time periods

For example, if the original $100 investment remains in the bank and is compounded annually for a period of 5 years, the future value calculation is:

FVyear 5

=

$100(1.02)(1.02)(1.02)(1.02)(1.02)

=

$100(1.02)5

=

$100(1.1041)

=

$110.41

Equation 4-2 can be used without modification in any compounding problem as long as there are no changes in the interest rate or the compounding period. (Examples in which these factors do change are considered later.) Any standard calculator with an exponent key can be used to calculate future value easily. A business/financial calculator has special keys, and spreadsheet software, such as Microsoft Excel, contain functions to simplify the calculation.

Compounding More Frequently Than Annually

In the simplest cases, as shown in the preceding, the value of money compounds once a year. In many cases, however, compounding occurs more frequently than annually. For example, interest on a savings account may be compounded semiannually (i.e., twice a year). In this case, the number of compounding periods doubles, but the interest rate at which the money grows is divided by two to account for the two periods in each year. The timeline in Figure 4-2 shows a situation in which the $100 in the earlier example is placed into an account that compounds interest semiannually.

Figure 4-2 Timeline Showing Present Value (PV) and Future Value (FV) of $100 Invested for 2 Years at a 2% Annual Rate, Compounded Semiannually

The $100 deposit will grow to $102.01 in 1 year when the 2% interest compounds semiannually. Using Equation 4-2, this calculation is:

Fvn

=

PV(1 + i)n

FVyear 1

=

$100(1.01)2

=

$100(1.0201)

=

$102.01

Note that the number of compounding periods (n) has increased to 2, and the interest rate is now 1% for each compounding period. At the end of year 2, the account will be $104.06. This simple example demonstrates one important characteristic of the time value of money: As the frequency of compounding increases, the future value increases as well. For example, if the frequency of compounding is quarterly, the initial deposit of $100 will grow to $104.07, and for monthly compounding it will grow to $104.08. In this example, the difference in the future value of the account under varying compounding frequencies is obviously quite small; however, the differences will become more substantial as the size of the account increases.

Using Effective Annual Rates to Assess Opportunities

It is often important for a manager to compare different investment opportunities involving compounding, and these opportunities may not have the same compounding periods. In the examples described in the preceding, the stated annual interest rate is 2% (also known as the nominal annual interest rate), but because the compounding frequencies differ, the future values of the investments differ. To facilitate a meaningful comparison among investment opportunities, it is important that adjustments be made to account for the differing compounding periods. This adjustment is made by calculating what is known as the effective annual rate (EAR).

The EAR is the compounding rate that would have increased the initial investment to the higher future value (i.e., the amount calculated for the scenario with more frequent compounding), assuming annual compounding. In the example with semiannual compounding, the effective annual rate is the rate that would have increased the initial $100 deposit to $102.01 after 1 year, assuming annual compounding. This EAR is calculated as follows:

$100(1 + i)

=

$102.01

(1 + i)

=

($102.01/$100)

i

=

($102.01/$100) − 1

=

(1.0201 − 1.000)

=

.0201

=

2.01%

The EAR of 2.01% is greater than the stated or nominal rate of 2%. Therefore, the opportunity with semiannual compounding is more attractive.

When compounding occurs annually, the EAR is equal to the nominal or stated rate. A manager evaluating the impact of different compounding periods should compare the EARs and draw conclusions about the relative attractiveness of the opportunities. When assessing opportunities, assuming comparable risk levels, the same stated interest rates, and the same present value, those opportunities with more frequent compounding have higher future values.

Equation 4-3 is the general equation for the EAR:

EAR = [1 + (i/m)]m − 1.0

Equation 4-3

where i

=

stated or nominal interest rate

m

=

number of compounding periods per year

Calculating the Present Value of Money: Discounting

Earlier in the chapter, a manager was presented with an opportunity to receive $100,000 now or $110,000 in 12 months. This is a typical financial management decision. The manager’s choice is based on determining the present value of the amount of money to be received in the future, in this case $110,000. That is the same as asking, How much is that future sum of money worth today? This is essentially the reverse of the compounding question discussed in the first part of this chapter. Recall that Equation 4-2 states that:

FVn = PV(1 + i)n

where   FVn

=

future value in time period n

PV

=

present value

n

=

number of time periods

i

=

interest rate (discount rate)

This new problem requires solving for the present value, the equation for which is shown as 6 − 4 (the general discounting formula):

PV

=

FVn/(1 + i)n

Equation 4-4

where   PV

=

present value

FVn

=

future value in time period n

n

=

number of time periods

i

=

interest rate (discount rate)

Looking at this equation it should be apparent that, as it stands, there is not enough information to solve the problem—there is no interest rate (i) provided. Therefore, an interest rate must be assumed. The question is how to determine an appropriate rate. One way to determine such a rate is based on the concept of opportunity cost.

A manager typically has multiple options for investing money. For example, several certificates of deposit or bank savings options may be available, each paying a specified rate of return. Suppose the manager is considering two separate savings options. Option A pays 2.5% annually and option B pays 1.75% interest on savings. If the manager selects option B for investment, he or she is therefore foregoing the return available with option A. The rate of return on the option(s) not selected is known as an opportunity cost. So, in this example, selection of option A carries with it an opportunity cost of 2.5%.

Of course, not all investment opportunities are the same. For example, the manager could decide to take a very financially conservative approach and deposit money in a bank savings account. The financial return from this strategy is likely to be relatively modest, but the level of risk associated with this investment strategy is quite low. Alternatively, the manager might choose to invest available funds in the bonds of a highly speculative new company. Under this scenario it is likely that the potential financial return will be higher than the bank deposit, but this investment strategy carries substantially more financial risk. Note that in rational financial markets, there is a direct relationship between risk and potential reward; that is, as the level of riskiness increases, so too does the level of potential reward.

The key to selecting an appropriate interest (or discount) rate to use in an analysis is to use the interest rate available on an alternative investment of similar type, level of risk, and time horizon. In other words, the manager should identify an investment opportunity, with a stated interest rate that is similar to the project being considered and use that stated rate to compute the present value.

So, for example, following thorough research, the manager concludes that investments of similar type, risk, and time horizon pay a 3% return annually; this is the discount rate that should be used. A timeline for this project is shown in Figure 4-3.

Using Equation 4-4, the present value of the proposed investment is computed to be $106,796. This means that all other things being equal, the manager should be willing to invest no more than $106,796 in this project. If the manager can accept this opportunity at a cost of less than $106,796, it will yield a better financial return than the investment alternative; however, if the cost of this opportunity exceeds this amount, then the manager should decline this opportunity and pursue the alternative. That is, the manager—as a prudent investor—should be willing to pay no more than $106,796 for this opportunity.

Just as was the case with the compounding formula (Equation 4-2), a manager can use the discounting formula (Equation 4-4) to calculate crucial variables in addition to the present value. The formula can be used to calculate either the number of time periods required to generate a specified future value given a known present value and interest rate, or the discount rate given a known present value and number of periods.

CONCLUSION

All management decisions involving the time value of money require the use of the tools of compounding and discounting. Competency in these two skills enables the manager to evaluate a wide variety of situations. Often, the greatest challenges for managers involve identifying the unknown variable in the equation (i.e., deciding what needs to be determined or calculated), and determining the appropriate discount rate. Regardless of the situation being analyzed, however, the simplest tool and most important starting point for analysis is a timeline that indicates the information available and assists in identifying what variable or factor is missing. Therefore, the first step in assessing the time value of money always should be to draw such a timeline.

EXERCISES

    4-1 You decide to invest $100,000 in a program that is guaranteed to grow by 2.5% for each of the next 5 years. At the end of the 5 years, how much is your investment worth?

    4-2 What is the effective annual rate of an investment that pays 6% for 5 years, compounded semiannually?

    4-3 What is the present value of a single cash flow of $25,000 received at the end of 10 years, if we assume a discount rate of 5% annually? With a discount rate of 7%?

    4-4 Suppose you deposit $100 in a savings account that compounds annually at 2%. After 1 year at this rate, the bank changes its rate of compounding to 1.5% annually. Assuming the compounding rate does not change for 4 additional years, how much will your account be worth at the end of the 5-year period?

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