HCM 570 Financial Management in Healthcare August 14-December 18, 2004

1
HCM 570 Financial Managementin
HealthcareAugust 14-December 18, 2004

• Joseph Callaghan, Ph.D.
• Oakland University
• Accounting and Finance

2
Mathematics and Tools of Finance

• Basics
• Intermediate
• Case 11

3
Time Value Analysis

• Future and present values
• Lump sums
• Annuities
• Uneven cash flow streams
• Solving for i and n
• Investment returns
• Amortization

4
Time Value of Money

• Time value analysis is necessary because money
  has time value.
• A dollar in hand today is worth more than a
  dollar to be received in the future. Why?
• Because of time value, the values of future
  dollars must be adjusted before they can be
  compared to current dollars.
• Time value analysis constitutes the techniques
  that are used to account for the time value of
  money.

5

• Time Lines

1
2
0
3
i
CF0
CF1
CF3
CF2
Tick marks designate ends of periods. Time 0 is
the starting point (the beginning of Period 1)
Time 1 is the end of Period 1 (the beginning of
Period 2) and so on.
6
Time Line Illustration 1
1
0
2
5
5
500

• What does this time line show?

7
Time Line Illustration 2
1
0
2
10
10
?
-100

• What does this time line show?

8
What is the FV after 3 years ofa 100 lump sum
invested at 10?
0
1
2
3
10
-100
FV ?

• Finding future values (moving to the right along
  the time line) is called compounding.
• For now, assume interest is paid annually.

9
After 1 year
FV1 PV INT1 PV (PV x i) PV x (1
i) 100 x 1.10 110.00.
After 2 years
FV2 FV1 INT2 FV1 (FV1 x i) FV1
x (1 i) PV x (1 i) x (1
i) PV x (1 i)2 100 x (1.10)2 121.00.
10
After 3 years
FV3 FV2 I3 PV x (1 i)3 100 x
(1.10)3 133.10.
In general,
FVn PV x (1 i)n .
11
Three Primary Methods to Find FVs

• Solve the FV equation using a regular
  (non-financial) calculator.
• Use a financial calculator that is, one with
  financial functions.
• Use a computer with a spreadsheet program such as
  Excel, Lotus 1-2-3, or Quattro Pro.

12
Non-Financial Calculator Solution
0
1
2
3
10
-100
133.10
110.00
121.00
100 x 1.10 x 1.10 x 1.10 133.10.
13
Financial Calculator Solution

• Financial calculators are pre-programmed to solve
  the FV equation
• FVN PV x (1 i)n.
• There are four variables in the equation FV, PV,
  i and n. If any three are known, the calculator
  can solve for the fourth (unknown).

14
Using a calculator to find FV (lump sum)
INPUTS
3 10 -100 0 N I/YR PV PMT
FV 133.10
OUTPUT
(1) For lump sums, the PMT key is not used.
Either clear before the calculation or enter PMT
0.
Notes
(2) Set your calculator on P/YR 1, END.
15
What is the PV of 100 duein 3 years if i 10?
0
1
2
3
10
100
PV ?
Finding present values (moving to the left along
the time line) is called discounting.
16
Solve FVn PV x (1 i)n for PV
PV FVN / (1 i)n.
PV 100 / (1.10)3 100(0.7513) 75.13.
17
Financial Calculator Solution
INPUTS
3 10 0 100
-75.13
N
I/YR
PV
PMT
FV
OUTPUT
Either PV or FV must be negative on most
calculators. Here, PV -75.13. Put in 75.13
today, take out 100 after 3 years.
18
Opportunity Cost Rate

• On the last illustration we needed to apply a
  discount rate. Where did it come from?
• The discount rate is the opportunity cost rate.
• It is the rate that could be earned on
  alternative investments of similar risk.
• It does not depend on the source of the
  investment funds.
• We will apply this concept over and over in this
  course.

19
Opportunity Cost Rate (Cont.)

• The opportunity cost rate is found (at least in
  theory) as follows.
• Assess the riskiness of the cash flow(s) to be
  discounted.
• Identify security investments that have the same
  risk.
• Estimate the expected return that could be earned
  on the security investment.
• When applied, the resulting PV provides a return
  equal to the opportunity cost rate.
• In most capital finance situations, bench-mark
  opportunity cost rates are known.

20
Solving for i
Assume that a bank offers an account that will
pay 200 after 5 years on each 75 invested.
What is the implied interest rate?
INPUTS
5 -75 0 200 N I/YR PV
PMT FV 21.7
OUTPUT
21
Solving for n
Assume an investment earns 20 percent per
year. How long will it take for the investment
to double?
INPUTS
20 -1 0 2
3.8
N
I/YR
PV
PMT
FV
OUTPUT
22
Types of Annuities
Three Year Ordinary Annuity
0
1
2
3
i
PMT
PMT
PMT
Three Year Annuity Due
0
1
2
3
i
PMT
PMT
PMT
23
What is the FV of a 3-year ordinary annuity of
100 invested at 10?
0
1
2
3
10
100
100
100
110 121 FV 331
24
Financial Calculator Solution
INPUTS
3 10 0 -100 331.00
I/YR
N
PMT
FV
PV
OUTPUT
Here there are payments rather than a lump sum
present value, so enter 0 for PV.
25
What is the PV of the annuity?
0
1
2
3
10
100
100
100
90.91
82.64
75.13
248.68 PV
26
Financial Calculator Solution
INPUTS
3 10 100 0
N
I/YR
PV
PMT
FV
OUTPUT
-248.69
27
What is the FV and PV if theannuity were an
annuity due?
0
1
2
3
10
100
100
100
?
?
28
Switch from End to Begin mode on a financial
calculator. Repeat the annuity calculations.
First find PVA3 273.55.
INPUTS
3 10 100 0 -273.55

N
I/YR
PV
PMT
FV
OUTPUT
Then enter PV 0 and press FV to find FV
364.10.
29
Perpetuities

• A perpetuity is an annuity that lasts forever.
• What is the present value of a perpetuity?
• PV (Perpetuity) .
• What is the future value of a perpetuity?

PMT
Perp fv
i
30
Uneven Cash Flow Streams Setup
4
0
1
2
3
10
100
300
300
-50
90.91
247.93
225.39
-34.15
530.08 PV
31
Uneven Cash Flow StreamsFinancial Calculator
Solution

• Input into the cash flow register
• CF0 0
• CF1 100
• CF2 300
• CF3 300
• CF4 -50
• Enter i 10, then press NPV button to get
  530.09.
• NPV means net present value.

32
Investment Returns

• The financial performance of an investment is
  measured by its return.
• Time value analysis is used to calculate
  investment returns.
• Returns can be measured either in dollar terms or
  in rate of return terms.
• Assume that a hospital is evaluating a new MRI.
  The projects expected cash flows are given on
  the next slide.

33
MRI Investment Expected Cash Flows(in thousands
of dollars)
4
0
1
2
3
310
400
500
750
-1,500

• Where do these numbers come from?

34
Simple Dollar Return
0
1
4
2
3
-1,500
310
400
500
750
310
400
500
750
460 Simple dollar return

• Is this a good measure?

35
Discounted Cash Flow (DCF) Dollar Return
0
1
4
2
3
8
-1,500
310
400
500
750
287
343
397
551
78 net present value (NPV)
Where did the 8 come from?
36
DCF Dollar Return (Cont.)

• The key to the effectiveness of this measure is
  that the discounting process automatically
  recognizes the opportunity cost of capital.
• An NPV of zero means the project just earns its
  opportunity cost rate.
• A positive NPV indicates that the project has
  positive financial value after opportunity costs
  are considered.

37
Rate of (Percentage) Return
0
1
2
3
4
10
-1,500
310
400
500
750
282
331
376
511
0.00 NPV, so rate of return 10.0.
38
Rate of Return (Cont.)

• In capital investment analyses, the rate of
  return often is called internal rate of return
  (IRR).
• In essence, it is the percentage return expected
  on the investment.
• To interpret the rate of return, it must be
  compared to the opportunity cost of capital. In
  this case 10 versus 8.

39
Intra-Year Compounding

• Thus far, all examples have assumed annual
  compounding.
• When compounding occurs intra-year, the following
  occurs.
• Interest is earned on interest more frequently.
• The future value of an investment is larger than
  under annual compounding.
• The present value of an investment is smaller
  than under annual compounding.

40
0
1
2
3
10
-100
133.10
Annual FV3 100 x (1.10)3 133.10.
0
1
2
3
0
1
2
3
4
5
6
5
-100
134.01
Semiannual FV6 100 x (1.05)6 134.01.
41
Effective Annual Rate (EAR)

• EAR is the annual rate which causes the PV to
  grow to the same FV as under intra-year
  compounding.
• What is the EAR for 10, semiannual compounding?
• Consider the FV of 1 invested for one
• year. FV 1 x (1.05)2 1.1025.
• EAR 10.25, because this rate would
• produce the same ending amount
• (1.1025) under annual compounding.

42
The EAR Formula
q
iStated
EAR 1 - 1.0
q
2
0.10
1 - 1.0

2
(1.05)2 - 1.0 0.1025 10.25.
Or, use the EFF key on a financial calculator.
43
EAR of 10 at Various Compounding
EARAnnual 10. EARQ (1 0.10/4)4 -
1.0 10.38. EARM (1 0.10/12)12 - 1.0
10.47. EARD(360) (1 0.10/360)360 - 1.0
10.52.
44
Using the EAR
4
0
1
2
3
5
6 6-month periods
5
100
100
100
Here, payments occur annually, but compounding
occurs semiannually, so we cannot use normal
annuity valuation techniques.
45
First Method Compound Each CF
5
6
4
2
0
1
3
5
100
100.00
100
110.25
121.55
331.80
46
Second Method Treat as an Annuity

• Find the EAR for the stated rate

EAR (1 ) - 1 10.25.
2
0.10 2

• Then use standard annuity techniques

3 10.25 0 -100
INPUTS
N
I/YR
PV
FV
PMT
331.80
OUTPUT
47
Amortization
Construct an amortization schedule for a 1,000,
10 annual rate loan with 3 equal payments.
48
Step 1 Find the required payments.
0
1
2
3
10
PMT
PMT
PMT
-1,000
3 10 -1000 0

402.11
INPUTS
N
I/YR
PV
FV
PMT
OUTPUT
49
Step 2 Find interest charge for Year 1.
INTt Beginning balance x i. INT1 1,000 x
0.10 100.
Step 3 Find repayment of principal in Year 1.
Repmt PMT - INT 402.11 - 100
302.11.
50
Step 4 Find ending balance at end of
Year 1.
End bal Beg balance - Repayment 1,000 -
302.11 697.89.
Repeat these steps for Years 2 and 3 to complete
the amortization table.
51
BEG PRIN END YR BAL PMT INT PMT BAL
1 1,000 402 100 302 698 2 698 402 70 332 36
6 3 366 402 37 366 0 TOTAL 1,206.34 206.34 1,
000
Note that annual interest declines over time
while the principal payment increases.
52

402.11
Interest
302.11
Principal Payments
0
1
2
3
Level payments. Interest declines because
outstanding balance declines. Lender earns 10
on loan outstanding, which is falling.
53
Context in MS Office

• Word processing (text-oriented)
• MS Word
• Database (data storage-oriented)
• MS Access
• Presentation (slide-oriented)
• MS PowerPoint
• Web Development (web-page-oriented)
• MS FrontPage
• Numerical Analysis (processing-oriented)
• MS Excel

54
Context in MS Office (cont.)

• Oriented is key since all perform similar tasks
  but to different degrees
• Integration across applications important
• Need should drive choice among apps
• In business setting, planning and setup are
  important
• Training is costly, so cost/benefit prevails

55
Purposes of Excel

• Data entry/storage
• Access to data by
• File Import
• Database Query
• Data entry
• Data analysis
• What if analysis
• Functions/Wizards/Macros (Programming)
• Presentation/Reports/Graphics

56
Grid/Cells

• Referencing the grid columns/row intersect
• Fundamental unit is the cell
• A1, B3, etc. relative referencing is default
• in front of either is absolute reference
• Affects what happens when you copy formulas
• Formulas
• A1B1
• , /, , -,
• Typical precedence
• Functions
• E.g. Sum(cell reference to range affected)

57
Data Entry

• Cells contain
• Text
• Numbers
• Formulas, referencing other cells
• Functions, referencing other cells
• Divide work (and spreadsheet)
• Data
• Analysis
• Presentation

58
Objects

• Workbook (corresponds to .xls file)
• Worksheet (many per Workbook)
• Special ones for Graphical and statistical output
• Cells (many per Worksheet)

59
Practice (d-click table)
60
Microsoft Office Excel 2003

• Tutorial 2 Working With Formulas and Functions

61
Use Excels functions

• You can easily calculate the sum of a large
  number of cells by using a function.
• A function is a predefined, or built-in, formula
  for a commonly used calculation.
• Each Excel function has a name and syntax.
• The syntax specifies the order in which you must
  enter the different parts of the function and the
  location in which you must insert commas,
  parentheses, and other punctuation
• Arguments are numbers, text, or cell references
  used by the function to calculate a value
• Some arguments are optional

62
Work with the Insert Function button

• Excel supplies more than 350 functions organized
  into 10 categories
• Database, Date and Time, Engineering, Financial,
  Information, Logical, Lookup, Math, Text and
  Data, and Statistical functions
• You can use the Insert Function button on the
  Formula bar to select from a list of functions.
• A series of dialog boxes will assist you in
  filling in the arguments of the function and this
  process also enforces the use of proper syntax.

63
Math and Statistical functions
64
Define functions, and functions within functions

• The SUM function is a very commonly used math
  function in Excel.
• A basic formula example to add up a small number
  of cells is A1A2A3A4, but that method would
  be cumbersome if there were 100 cells to add up.
• Use Excel's SUM function to total the values in a
  range of cells like this SUM(A1A100).
• You can also use functions within functions.
  Consider the expression ROUND(AVERAGE(A1A100),1)
  .
• This expression would first compute the average
  of all the values from cell A1 through A100 and
  then round that result to 1 digit to the right of
  the decimal point

65
Copy and paste formulas and functions

• Copying and pasting a cell or range of cells is a
  simple, but highly effective means for quickly
  filling out a large worksheet.
• To copy and paste a cell or range
• Select the cell or range to be copied and then
  click the Copy button on the standard toolbar
• Select the cell or range into which you want to
  copy the selection and then click the Paste
  button on the standard toolbar
• Once you are finished pasting, press the Esc key
  to deselect the selection

66
Copy and paste effects on cell references

• Copied formulas or functions that have cell
  references are adjusted for the target cell or
  range of cells.
• For example, if cell G5 contains the formula
  F5B5/B7, and you copy and paste this formula to
  cell G6, the formula in cell G6 will be
  F6B6/B8.
• This may or may not be correct for your
  worksheet, depending upon what you are trying to
  do.
• You can control this automatic adjusting of cell
  references through the use of relative and
  absolute references.

67
Problems using copy and paste with formulas

• When Excel does not have enough room to display
  an entire value in a cell, it uses a string of
  these symbols to represent that value.
• For example, the formula in cell J5 is
  F5-(H5I5) and this was pasted into cell J6 by
  updating the cell references there to
  F6-(H6I6).
• Cell G5 has the formula F5B5/B7 and cell G6
  contains F6B6/B8. This is where things went
  wrong. Sometimes this automatic update is very
  useful and other times it does not give you the
  desired result for your worksheet.
• In this case, cells B5 and B7 should be
  referenced in the formula in column G in all 240
  payment period rows, but in column J, you want
  the cell references to be automatically updated.
  You can control this result using relative and
  absolute references.

68
Use relative references

• A relative reference is a cell reference that
  shifts when you copy it to a new location on a
  worksheet.
• A relative reference changes in relation to the
  change of location.
• If you copy a formula to a cell three rows down
  and five columns to the right, a relative
  reference to cell B5 in the source cell would
  become G8 in the destination cell.

69
Use absolute references

• An absolute reference is a cell reference that
  does not change when you copy the formula to a
  new location.
• To create an absolute reference, you preface the
  column and row designations with a dollar sign
  ().
• For example, the absolute reference for B5 would
  be B5.
• This cell reference would stay the same no matter
  where you copied the formula.

70
Use mixed references

• A mixed reference combines both relative and
  absolute cell references.
• You can effectively lock either the row or the
  column in a mixed reference.
• For example, in the case of B5, the row
  reference would shift, but the column reference
  would not
• In the case of B5, the column reference would
  shift, but the row reference would not
• You can switch between absolute, relative and
  mixed references in the formula easily in the
  edit mode or on the formula bar by selecting the
  cell reference in your formula and then pressing
  the F4 key repeatedly to toggle through the
  reference options.

71
Open the Insert Function dialog box

• To get help from Excel to insert a function,
  first click the cell in which you wish to insert
  the function.
• Click the Insert Function button. This action
  will open the Insert Function dialog box.
• If you do not see the Insert Function button, you
  may need to select the appropriate toolbar or add
  the button to an existing toolbar.

72
The Average Function

• The average function is necessary to calculate
  the average of a range of cells.
• Like any other formula, the average function may
  be copied across cells.

73
Date Functions
74
Excel's date functions

• Excel stores dates as integers, where the integer
  value represents the number of days since January
  1, 1900.
• For example, the integer value for the date
  January 1, 2008 is 39448 because that date is
  39,448 days after January 1, 1900
• You typically do not see these numbers, because
  Excel automatically formats them to appear in a
  date format.
• This method of storing dates allows you to work
  with dates the same way you work with numbers.
• Excel's commonly used date functions are DATE,
  DAY, MONTH, NOW, TODAY, WEEKDAY and YEAR.

75
The TODAY and Now functions

• The TODAY and NOW functions always display the
  current date and time.
• You will not normally see the time portion unless
  you have formatted the cell to display it.
• If you use the TODAY or NOW function in a cell,
  the date in the cell is updated to reflect the
  current date and time of your computer each time
  you open the workbook.

76
Use a formula to enter the date
77
Excel's financial functions

• Financial functions are very useful to calculate
  information about loans.
• Common functions are FV, IPMT, PMT, PPMT and PV.
• All these financial functions will use similar
  arguments that differ based upon which function
  you are using.
• Think of the arguments as members of an equation
• The arguments represent the values of the
  equation that are known and the function provides
  the solution for a single variable, or unknown,
  value

78
Use the financial functions

• The FV function calculates the future value of an
  investment based on periodic, constant payments
  and a constant interest rate per period.
• The IPMT function provides the interest payment
  portion of the overall periodic loan payment.
• The PMT function calculates the entire periodic
  payment of the loan.
• The PPMT function calculates just the principal
  payment portion of the overall periodic payment.
• The PV function calculates the present value of
  an investment.

79
Financial Function descriptions
80
Recognize optional arguments

• In the preceding figure, note how rate and nper
  are arguments for each function.
• For some of the functions, the final two
  arguments of each function are in brackets. These
  represent optional arguments, meaning if you do
  not enter anything, the default values for these
  arguments will be used.
• For example, note the PMT function has fv and
  type as its final two arguments, which are
  optional. The assumed values, if no others are
  supplied, are 0 for both
• Arguments without brackets do not have default
  values, so you must supply values or cell
  references in order for the function to be able
  to return a value.

81
Use the Insert Function dialog box to enter
function arguments
82
Create logical functions

• A function that determines whether a condition is
  true or false is called a logical function.
• Excel supports several logical functions such as
  AND, FALSE, IF, NOT, OR and TRUE.
• A very common function is the IF function, which
  uses a logical test to determine whether an
  expression is true or false, and then returns one
  value if true or another value if false.
• The logical test is constructed using a
  comparison operator that compares two expressions
  to determine if they are equal, not equal, if one
  is greater than the other, and so forth.
• The comparison operators are , gt, gt, lt, lt, and
  ltgt
• You can also make comparisons with text strings.
  You must enclose text strings within quotation
  marks.

83
Using the If function

• The arguments for the IF function are
• IF(logical_test,value_if_true,value_if_false)
• For example, the function IF(A110,20,30) tests
  whether the value in cell A1 is equal to 10
• If it is, the function returns the value 20,
  otherwise the function returns the value 30
• Cell A1 could be empty or contain anything else
  besides the value 10 and the logical test would
  be false therefore, the function returns the
  value 30
• To insert an IF function, click the Insert
  Function button and search for the IF function,
  then click OK.
• When the Function Arguments dialog box appears,
  simply fill in the arguments.

84
Case 11

• Review
• Questions