UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT
Calculator (Hewlett-Packard 10BII) Tutorial
To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key’s primary function is noted in white on the upper portion of the face of the key, while the secondary function is noted in gold on the lower portion of the key. To use the primary (white) function, simply press the key. To use the secondary (gold) function, first press the key with the gold lower face, which we will call the “gold shift” key, and then press the desired function key. (Note that the gold shift key is more orange or brick in color and is the third key from the bottom on the left side of the calculator keyboard.) A third function is written in purple above some keys. We will not be using these functions in this class.
Turning the Calculator On and Off
To turn the calculator on, press
Note that the ON key is in the lower left corner of the keyboard. “ON” is printed in white on the face of the key, while “OFF” (in gold) appears below the word “ON.” Keys are designated throughout this tutorial by the use of small boxes, as shown above. To conserve the battery, the calculator turns itself off about ten minutes after your last keystroke.
To turn the calculator off, press
By pressing the gold shift key first, you activate the gold (lower) function on the lower-left key, which is the off function. Note that pressing the gold shift key places the word “SHIFT” in the lower left corner of the display. Press the gold shift key again and the symbol disappears. The gold shift key is a toggle key that switches back and forth between the white and the gold functions included on most keys. After you press the gold shift key, look only at the gold (lower) functions on the keys.
Clearing the Calculator
Note that the calculator has a continuous memory, so turning it off does not affect data stored in the calculator.
GOLD OFF ON
C ←
calculation. Occasionally, you may purposely want to save data, but in general you will be entering all new data, so starting with a clear memory is the safest approach.
There are three different levels of data you can clear:
clears all memory and the display.
clears the entire display, but not the memory.
clears numbers on the display one at a time if you made a mistake entering data.
Entering Values
To enter values (numbers) into the calculator, press the desired number keys. The values will appear in the display. If you are entering values with decimal places, press the decimal point key as necessary. (It is the middle key in the lower row.)
Changing the Number of Decimal Places Shown in the Display To change the number of decimal places displayed to 4, press When 5555.5555 is entered, 555.5555 is displayed.
To change from 4 places to 2, press
5,555.56 is displayed. (Rounding is automatic.)
We usually set the calculator to display 2 places, which is especially convenient when working with dollars and percentages.
“PEND” in the display means something is pending. Press 4 ÷
The calculator is waiting for the denominator, so “PEND” appears in the display.
Press 6 and = to get 0.67.
Periods per Year Setting
One important setting that can cause problems is the periods per year setting. To check the current setting, press
GOLD C ALL
GOLD DISP 4
GOLD DISP 2
GOLD C ALL
The display briefly shows the setting for periods/year. To keep the display on, hold down the
“C ALL” key. The calculator comes preset at 12 periods per year—that is, it assumes calculations will be done on a monthly basis. However, our illustrations will be done on an annual basis, so we must use 1 period/year. To change the setting:
Press
Now the calculator is set to assume 1 period/year. To confirm this setting, proceed as above. Unless you need to change this setting for other work, leave the calculator setting at 1 period per year.
Time Value of Money (TVM)
The TVM keys are located in the top row of the keyboard.
Although there are five TVM keys, time value analysis generally involves four variables—three are known, and the fourth is unknown.
1 GOLD P/YR
PMT when entering the input data. If you know any three variables, you can find the value of the fourth.
Example 1
What is the FV of $100 after 3 years if the interest rate is 26 percent? First, clear the calculator.
Next, enter the data.
3 N 26 I/YR 100 PV
0 PMT (Optional if the calculator is cleared)
To determine the FV, simply press FV , and the FV of −200.04 appears in the display.
The calculator is programmed so that if the PV is positive, the resulting FV is displayed as negative, and vice versa. In essence, the calculator assumes that one is an inflow and the other is an outflow.
When entering both PV and FV, one must be entered as negative and the other as positive.
Example 2
What is the PV of $500 due in 5 years if the interest rate is 10 percent? Clear first and then enter the following data.
5 N 10 I/YR
0 PMT (Optional if the calculator is cleared) 500 FV
Pressing the PV key reveals that $310.46 will grow to $500 in 5 years at a 10 percent rate.
(Ignore the minus sign for now.)
Example 3
Assume a bond can be purchased today for $200. It will return $1,000 after 14 years. The bond pays no interest during its life. (It is a zero-coupon bond.) What rate of return would you earn if you bought the bond?
14 N
200 +/− PV (The first key changes the sign.) 0 PMT (Optional if the calculator is cleared) 1000 FV
Simply press the I/YR key, and the rate of return (12.18) appears in the display.
Remember that the calculator is programmed so that if the PV is positive, the FV is displayed as negative, and vice versa. When entering both PV and FV values, one must be entered as a negative and one as a positive. The +/− key changes the sign of the value being entered.
Now suppose you learn that the bond will actually cost $300. What rate of return will you earn?
Override the −200 by entering 300 +/− PV , and then press I/YR to get 8.98 percent. If you pay more for the bond, you earn less on it. The important thing, though, is that you can do “what if”
analyses with the calculator.
Ordinary Annuities Example 1
What is the FV of an annuity of $100 paid at the end of each year for 5 years if the interest rate equals 6 percent?
0 6%
5 N
1 2 3 4 5 ├────────┼────────┼────────┼────────┼────────┤
−$100 −$100 −$100 −$100 −$100
6 I/YR
Example 2
What is the PV of the same annuity?
Leave the data in the calculator, but enter 0 FV to override; then press PV to get 421.24. The FV must be changed to zero because the calculator “recorded” 563.71 as the FV in the previous operation.
Annuities Due
Each payment of an annuity due occurs at the beginning of the period instead of at the end as with a regular annuity. In essence, each payment is shifted one period to the left in an annuity due. To analyze annuities due, press
The word “BEGIN” appears on the screen. Then proceed as above. To change back to the end of period mode, press again.
Interest Conversion
The effective annual rate (EAR) equation can be used to convert a stated rate to an EAR. However, it is much easier to use the calculator.
Given: IStated = 10% and M = 12 payments/year:
Then, 10.47 (percent) appears in the display.
Be sure to switch back to 1 payment per year:
GOLD BEG/END
GOLD BEG/END
GOLD NOM
GOLD P/YR GOLD EFF%
1 GOLD P/YR 10
12
Uneven Cash Flow Streams Example 1: Finding Present Values
Assume the following cash flows:
0 10%
0 CF
1 2 3 4
├────────┼────────┼────────┼────────┤
$0 $50 $100 $150 $200 What is the PV of these CFs?
First clear the calculator and make sure that periods/year is set equal to 1.
j Sets CF0 50 CF
equal to 0.
j Sets CF1 100 CF
equal to 50.
j
150 CF
And so on.
j
200 CF
10 I/YR This function enters the interest (discount) rate.
At this point, all of the relevant information has been entered into the calculator. To find the PV,
j
press , and the value $377.40 will appear in the display. Note that NPV stands for net present value, or the sum of the present values of two or more cash flows.
Example 2: Rate of Return (IRR)
Assume that we invest $1,000 now (t = 0) and then expect to receive the following cash inflows:
0 1 2 3 4
├────────┼────────┼────────┼────────┤
−$1,000 $300 $400 $200 $600
What rate of return is expected on this investment? Clear the calculator, and then enter the following:
GOLD NPV
200 CFj
600 CF
j
Then press
The answer 16.71 (percent) appears in the display.
You can also determine the NPV of the investment. Leave data entered, and then enter the opportunity cost (discount) rate, say 8 percent:
8 I/YR
The NPV of 220.50 appears in the display. Thus, the PV of the cash inflows exceeds the cost of the investment by $220.50.
Amortization
The calculator can be used to create amortization schedules.
Example
Determine the interest and principal paid each year and the balance at the end of each year on a three- year $1,000 amortized loan that carries an interest rate of 10 percent. The payments are due annually.
First check payments/year and make sure it is 1. Also clear the calculator. Then perform the following steps:
3 N 10 I/YR 1000 PV
PMT
The value −402.11 appears in the display, which is the amount of each annual payment.
Here is the amortization schedule corresponding to the loan:
GOLD IRR/YR
GOLD NPV
Year Beginning Balance Payment Interest Principal Repayment
1 INPUT
Ending Balance
1 1,000.00 402.11 100.00 302.11 697.89
2 697.89 402.11 69.79 332.32 365.57 3 365.57 402.11 36.56 365.55 .02 With the data still entered in the calculator, do the following to calculate the values in the above table:
(“1-1” appears in the display.)
= “PRIN” and −302.11 appear in the display.
= “INT” and −100 appear in the display.
= 697.89 appears in the display.
Repeat the steps, starting with two more times to complete the table.
GOLD AMORT
GOLD AMORT
