Expert answer:Need health and medical help with Measure of Succe
Answer & Explanation:Measures for Success Secenerio: Purchase of MRI machine instead of leasing. CFO and Radiology Director will be used in answering the questions below.Financial managers may work alongside general services managers to address certain measures of liquidity. How might a financial manager and the department administrator for your chosen capital investment plan work together to make an effort on reducing days in accounts receivable? If you are successful with your financial performance and are paid a bonus based on profitability , which measure should be used?08CH_Smith_Healthcare.pdf09CH_Smith_Healthcare.pdf
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8
Time Value of Money
Fuse/Thinkstock
Learning Outcomes
By the end of this chapter, you will be able to:
• Explain the role of corporate finance in a healthcare organization
• Explain the time value of money in terms of opportunity cost
• Calculate the future value of single and multiple cash amounts, as well as with compounding interest
• Calculate the present value of single and multiple cash amounts, as well as perpetuities
and annuities
• Calculate payments and investment amounts
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Section 8.1
Introduction to Corporate Finance
Introduction
In order to remain profitable in the face of declining numbers of inpatient admissions and
patient days, Bixby Hospital is evaluating a number of possible services that would better
meet the needs of patients requiring higher levels of medical technology than are currently
available. One possible area of interest is a sleep lab. Diagnosis of sleep apnea and other sleep
disorders will require some renovations to clinic space for which Bixby might use current
resources, solicit donations, save money for the investment, or borrow from a bank. The decision by itself may not be difficult, but a sleep lab is only one of a number of areas of interest
that have been raised by the medical staff and managers. The medical needs of the community will be an important part of the investment decision. The financial impact on the organization over several years will also be important.
In this chapter, the focus will be on tools to enable analyses of financial impact over time.
Knowing the future value of funds that are invested now and the present value of amounts
that will be received in the future is the foundation for analyses in corporate finance.
8.1 Introduction to Corporate Finance
The field of healthcare finance has three main components: financial accounting, managerial accounting, and corporate finance. Corporate finance involves decision making about
asset acquisition and other long-term investment decisions. In addition to decisions about
which assets to invest in, finance is also concerned with the determination of methods to pay
for investments, through the use of debt and equity. The capital expenditure budget and the
planned balance sheet are important products of corporate finance.
Financial management involves many trade-offs. As discussed in Chapter 7, many components of the budgeting process involve trade-offs between planning and control. Decision
making for the short-term operating budget also involves making trade-offs among organizational goals, especially among profitability, viability, and service missions. Profitability of
the healthcare organization itself involves trade-offs between risk and return. Quite simply,
to earn higher expected profits, organizations must take more risks. The risk-return trade-off
will be the focus of Chapter 9.
Viability also involves a trade-off between liquidity and investments in plant and equipment.
In the short run, it is safe to invest funds in marketable securities where the organization can
gain access to cash quickly if needed. In the long run, it is necessary to invest funds in plant
and equipment. Decision making among alternative investments in plant and equipment to
provide healthcare services will be the focus of Chapter 10.
The current chapter develops the tools required for corporate finance and long-term financial decision making. Information provided on current financial statements and budgets is
usually adequate for short-run decisions. Calculating the number of patient visits required
for a clinic to break even only requires information on the fixed cost, average variable cost,
and price of patient visits. Determining whether it is appropriate to take the risk of building
a new clinic that will serve patient needs over the next 20 years requires substantially more
information and more tools for analysis. Tools for analyzing flows of funds that occur over the
long-term planning are presented here.
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Section 8.2
Time Value of Money
For Review:
1. How is corporate finance different from accounting?
Corporate finance is a process of analysis and decision making, focused on long-term
asset acquisition and how to pay for it. Managerial accounting is a process of analysis and decision making, focused on short-term operations of an organization. Financial accounting is a process of recordkeeping and reporting, not decision making.
8.2 Time Value of Money
The concepts of inflation and interest are common in everyday life. Almost every year,
goods and services cost more the next year than the previous year due to inflation. Workers
seek higher wages because the value of what they can buy with the same amount of money
decreases with inflation. As displayed in Figure 8.1, prices paid by consumers for all items
have increased in all recent years, except during the worst part of the recession in 2009
(United States Department of Labor, n.d.). For a consumer to purchase the same set of items
in 2012 as they did in 2004, they would need to have had wage increases averaging 2.5% per
year. The consumer cost for medical services has also increased in recent years and has usually increased by more than the average of all items.
Figure 8.1: Consumer price index (inflation) and interest rates, 200422012
8%
6%
4%
2%
0%
2004
2005
2006
2007
2008
Year
2009
2010
2011
2012
–2%
Consumer Price Index–All Items
Consumer Price Index–Medical Care Services
Interest Rate–20 Year Baa Bond
Source: Bureau of Labor Statistics (http://www.BLS.gov), Consumer Price Index—All Urban Consumers—All items, Series ID:
CUUR0000SA0; Consumer Price Index—All Urban Consumers—Medical Care Services, Series ID: CUUR0000SAM2; Federal Reserve
(http://www.federalreserve.gov/), Moody’s Yield on Seasoned Corporate Bonds, All Industries, Baa, Unique Identifier: H15/H15/
RIMLPBAAR_N.A.
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Section 8.2
Time Value of Money
Data on interest rates tell a similar story over time. Interest is the price for borrowing money.
To obtain a loan to purchase buildings or equipment, healthcare organizations are charged
interest on the amount borrowed. As presented in Figure 8.1, the rate of interest per year on
20-year loans has been between 4.9% and 7.4% in recent years.
Consumers, organizations, and banks all have the same concerns about prices over time, all
recognizing the time value of money. The time value of money refers to the recognition
that, due to inflation and interest, holding a dollar today is different from receiving a dollar
one year from now. For a consumer, as well as for a healthcare organization, receiving a dollar one year from now is worth less than a dollar in hand today, due to inflation. For banks,
healthcare organizations, and consumers who have funds available for investing, receiving a
dollar one year from now is worth less than a dollar in hand today due to the opportunity
cost of investing. The opportunity cost of investing is the next best alternative use of dollars.
The cost of investing, and its relationship to risk and return, is a core concept in finance that
is elaborated upon in Chapter 9.
With a time value to money, recognizing the value of dollar amounts requires precise accounting for when dollar amounts are spent and received. For ease of presentation and explanation,
it is common in finance to display dollar amounts on timelines. A timeline is simply a visual
representation of cash flows for an organization. The first timeline shows that $1,000 is held
right now, at Time 0.
Time 0
Time 1
Time 2
Time 3
$1,000
The second timeline shows that $1,000 will be received at Time 1.
Time 0
Time 1
Time 2
Time 3
$1,000
The third timeline shows that $1,000 will be received at Time 1 and another $1,000 will be
received at Time 2.
Time 0
Time 1
Time 2
$1,000
$1,000
Time 3
Unless it is stated otherwise, the convention in financial calculations is to assume that dollar
amounts spent and received are done so at the end of a time period. If our example timelines
referred to years, then Time 0 might be December 31, 2013, Time 1 might refer to December
31, 2014, and so forth. When dollar amounts are spent and received at the beginning of the
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Section 8.3
Future Value
time period, this difference can be highlighted. The fourth timeline shows that $1,000 will be
received at Time 1 at the end of the period, and Time 2 at the beginning of the period.
Time 0
Time 1
Time 2
Time 3
$1,000
$1,000
For loans and payments of bills, the exact date of the payment is important as there may be
fees or penalties associated with late payments. For financial analyses conducted for planning
purposes, receipts on December 31 and January 1 are close enough to be thought of as happening at the same time.
For Review:
1. Create a timeline for cash amounts of $600 available for investing at Time 0 (December 31, 2014) and Time 1 (December 31, 2015).
Time 0
Time 1
$600
$600
Time 2
Time 3
8.3 Future Value
Financial analyses incorporating the time value of money take one of two perspectives: (1) the
dollar amount of money that will be held in the future, associated with earning interest (or
otherwise gaining value), and (2) the dollar value of money now, recognizing the effects of
inflation, interest, and opportunity costs generally. In this section, calculations of future values are presented. Calculations of present values are presented in the next section.
Future Value of a Single Cash Amount
The future value (FV) is the amount, expressed in financial terms, of an asset or a flow of
funds at a defined time in the future. Future values may refer to amounts that will have been
accumulated through profits or savings, and may include investment earnings on the profits
or savings. The basic equation for the future value of an amount of money (represented by the
letter C, for cash) that is held now and will be invested for one time period at a rate of interest
(r) is defined as
FV1 5 C0 3 (1 1 r)
where the subscripts (1 and 0) refer to the time periods involved. On the timeline:
Time 0
Time 1
C0
FV1
Time 2
Time 3
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Section 8.3
Future Value
For the $1,000 held at Time 0 and invested at a rate of 5% (r 5 0.05), the equation yields
FV1 5 $1,000 3 (1 1 0.05)
5 $1,050
An organization that can earn 5% on a $1,000 investment will have $1,050 after one year.
This basic equation for future value includes only two factors, each one of which requires
some careful analysis. The first factor, the amount of money to be invested, C, must be decided
upon. If the amount of money to be invested is currently in a bank account, the decision may
be very simple. If the amount of money to be invested is a forecast of an amount that will be
in a bank account, the decision requires an explanation of the forecast.
The second factor, the interest rate that will be earned on the investment, r, must be determined by the organization. The amount of interest that an organization will pay to borrow
money will vary depending on the amount of money to be borrowed, the length of time of
the loan, and the financial status of the organization seeking the loan. Borrowing a small sum
of money for a short period of time by an organization with good profitability and liquidity
indicators (as defined in Chapter 3) will involve a low rate of interest. Borrowing a large sum
of money for a long period of time by an organization with poor profitability and liquidity
indicators will involve a high rate of interest.
Analyze This
Suppose that a clinic uses the clinic’s credit card to borrow $750 from a bank to purchase a new
refrigerator for storing medication. This credit card purchase provides the bank with a financial
investment. The bank will be repaid the $750 plus interest. If the bank charges 13.90% annual
interest on credit card amounts, how much will the clinic that purchased the refrigerator repay
the bank at the end of one year?
The calculation becomes only slightly more complicated when the investment is for two time
periods, as shown on the timeline.
Time 0
Time 1
Time 2
Time 3
FV2
C0
The reason the calculation is more complicated is because of how the interest earned in the
first time period is treated. If interest is stated as an amount of interest per time period, say
5% per year, then at the end of the first year, interest has been earned. Between the first time
period and the second time period, interest must be paid on the interest, as shown on the
timeline.
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Section 8.3
Future Value
Time 0
Time 1
$1,000
$1,000 + $50
Time 2
Time 3
FV2 5 $1,000 3 (1 1 0.05) 1 $50 3 (1 1 0.05)
5 $1,050 1 $52.50
5 $1,102.50
The organization has not only earned interest for two periods on the initial investment, it has
also earned interest on the interest. The phenomenon of earning interest upon the interest
from prior periods is called compound interest. The process by which this happens is called
compounding. To reflect compounding on funds invested over multiple time periods, the
future value equation can be rewritten as
FVt 5 C0 3 (1 1 r)t
where the exponent (t) indicates the number of time periods. For two time periods, t 5 2, the
future value equation is written as
FV2 5 C0 3 (1 1 r)2
5 C0 3 (1 1 r) 3 (1 1 r)
For three time periods, t 5 3, the future value equation is written as
FV3 5 C0 3 (1 1 r)3
5 C0 3 (1 1 r) 3 (1 1 r) 3 (1 1 r)
Analyze This
Suppose the clinic that purchased the new refrigerator for $750 using a credit card does not pay
the bank until the end of three years. At 13.90% annual interest on credit card amounts, how
much will the clinic repay the bank at the end of three years?
Future Value of Multiple Cash Amounts
The examples provided have considered single-period cash amounts and single-period interest. The timelines and calculations become more complicated when there are multiple cash
amounts. Consider the case where $1,000 will be invested at Time 0 and Time 1, with the
returns being available at Time 2.
Time 0
Time 1
Time 2
$1,000
$1,000
FV2
Time 3
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Section 8.3
Future Value
These two cash amounts could be treated as separate transactions and evaluated using two
equations. For the cash amount from Time 0, the equation is
FV2 5 C0 3 (1 1 r)2
and for the cash amount from Time 1, the equation is
Together,
FV2 5 C1 3 (1 1 r)
FV2 5 ($1,000 3 (1 1 0.05)2) 1 ($1,000 3 (1 1 0.05))
5 $1,102.50 1 $1,050.00
5 $2,152.50
When the cash amounts (C) are different among time periods, it is necessary to separate each
cash amount and calculate its future value. When the cash amount (C) is the same in every
time period, the future value can be calculated using one general equation:
FVt 5 C 3
11 1 r2t 2 1
3 (1 1 r)
r
For the same example of $1,000 invested in Time 0 and Time 1, the future value in Time 2 is
calculated as
FV2 5 $1,000 3
1 1 1 0.05 2 2 2 1
3 (1 1 0.05)
0.05
5 $1,000 3 2.05 3 1.05
5 $2,152.50
For more than two time periods, the general equation for the future value of a set of investments of the same amount can be calculated more quickly than calculating the future value
of each year’s investment amount. Using a financial calculator or an electronic spreadsheet,
it can be done even more quickly. In Appendix B instructions are provided on the use of an
electronic spreadsheet for time value of money calculations.
Future Value with More Frequent Interest Compounding
The calculations also become more complicated when the time period for the interest and
the time period of the cash amounts do not match. For example, it is quite common to invest
money in a bank account and be provided an annual interest rate and yet have interest that
is earned monthly.
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Section 8.3
Future Value
The basic future value equation can be rewritten to recognize more frequent interest compounding as follows:
FVt 5 C0 3 (1 1 r/m)(t3m)
where m indicates the number of compounding periods for each time period.
For the $1,000 held at Time 0 and invested at a stated annual rate of 5% (r 5 0.05), with
interest paid monthly (m 5 12), the 5% annual interest becomes 0.4167% monthly interest
(r/m 5 0.05 4 12), and the number of time periods becomes 12 (t 3 m, which is 1 3 12). The
complete set of calculations can be written as
FV12 5 C0 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m)
3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m) 3 (1 1 r/m)
5 $1,000 3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167)
3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167)
3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167) 3 (1 1 0.004167)
5 $1,051.16
Payment of interest on a monthly basis provides 12 opportunities for compounding during
a year, and therefore a higher return on the investment. Payment of interest on a daily basis
provides 365 opportunities for compounding during a year.
For the previous example of $1,000 invested at 5% (r 5 0.05) for one year, with interest
paid monthly, the total amount of interest received is $51.16. The interest rates on investments may be presented as the nominal annual percentage rate (APR), meaning that it is
the simple rate at which interest is earned (5% in this example). Alternatively, the amount
may be presented as the effective APR, meaning that it is the total interest that has been
earned once compounding has been included in the calculation (5.116% 5 $51.16 4 $1,000,
in this example).
Calculation Methods
The calculation of the future values of investments can be performed by hand or with a simple calculator. To ease the task when there are a number of analyses or many time periods
and frequent compounding, advanced calculators and electronic spreadsheets may be used
instead. Many popular calculators have a function key for exponents to permit the direct
entry of equations. As an added convenience, some calculators specialize in finance functions,
requiring only the entry of the cash amount, the interest rate, and the number of time periods.
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Section 8.3
Future Value
Electronic spreadsheets, such as Microsoft Excel/, permit calculations based on the use of
the exponent functions and prespecified finance functions. Four ways of calculating the future
value of $1,000 with 5% interest for two time periods are presented in Exhibit 8.1. Three ways
of calculating the future value of two payments of $1,000 with 5% interest are presented in
Exhibit 8.2. Definitions of the values in Exhibits 8.1 and 8.2 are provided Appendix B.
Exhibit 8.1 Spreadsheet calculations of future values of a single amount
A
Amount
Interest
Years
1
2
3
4
5
6
7
B
$1,000.00
5%
2
$1,102.50
$1,102.50
$1,102.50
$1,102.50
C
=1000*(1+0.05)*(1+0.05)
=1000*(1+0.05)^2
=B1*(1+B2)^B3
=FV(B2,B3,0,-B1,1)
Exhibit 8.2 Spreadsheet calculations of future values for multiple amounts
A
Amount
Interest
Years
1
2
3
4
5
6
7
B
$1,000.00
5%
2
C
=(1000*(((1+0.05)^2–1)/0.05))*(1+0.05)
$2,152.50
=(B1*((1+B2)^2–1)/B2)*(1+B2)
$2,152.50
=FV(B2,B3,–B1,0,1)
$2,152.50
For calculating the future value of multiple payments, such as in Exhibit 8.2, the use of a preprogrammed function (FV) reduces the chance of making an error in typing complicated
equations.
For Review:
1. What is the future value in four years of a dollar amount invested today?
FV4 5 C0 3 (1 1 r)4
2. Why do investors require interest? Would a healthcare organization be willing to put
$11,000 in the bank and have exactly $11,000 in that same account four years later?
Interest reflects the time value of money …
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