HP-10BII Tutorial

The Hewlett Packard 10BII is a very easy to use financial calculator which will serve you well in all finance courses. This tutorial will demonstrate how to use the financial functions to handle basic time value of money problems. I will keep the examples rather elementary, we will cover more difficult problems in class.

Setup

Before we get started, we need to correctly configure the calculator. The Hewlett Packard 10BII comes from the factory set to assume monthly compounding (12 periods per year). I prefer that you set the calculator to assume annual compounding and then make manual adjustments when you enter numbers. Why? Because, the compounding assumption is hidden from view and in my experience people tend to forget to set it to the correct period. Of course, most people don't recognize a wrong answer when they get one, so they continue working wondering why they are getting the incorrect answers.

To fix this problem press 1 (once per year) then the shift key (see picture) and finally the PMT key to access P/Yr. To check that it has taken, press shift and then the C key to access C ALL. You should see 1 P_Yr on the screen. Problem solved.

Another issue which sometimes occurs is that the calculator will accidentally get set to "Begin" mode. In the problems I cover in this "quick start," you will need to have your calculator set to "End" mode. If your calculator does accidentally get shifted into "Begin" mode, the calculator's display will say BEGIN below the numerals in the display. If it does not read anything, the calculator is in "End" mode.

One other adjustment is important. By default the 10BII displays only two decimal places. This is not enough. Personally, I like to see four decimal places, but you may prefer some other number. To change the display, press the shift key, then the = key, and finally the numeric key which corresponds to the number of digits you would like to see displayed. I would press shift, =, 4 to display 4 decimal places. That's it, the calculator is ready to go.

Example 1 - Lump Sums

We'll begin with a very simple problem which will provide you with most of the skills to perform financial math on the 10BII:

Suppose that you have $100 to invest for a period of 5 years at an interest rate of 10% per year. How much will you have accumulated at the end of this time period?

In this problem, the $100 is the present value (PV), N is 5, and i is 10%. Before entering the data you need to make sure that the financial registers (each key is nothing more than a memory register) are clear. Otherwise, you may find that numbers left over from previous problems will interfere with the solution to this one. Press shift then C ALL to clear the memory. Now all we need to do is enter the numbers into the appropriate keys: 5 into N, 10 into I/YR, -100 into PV. Now to find the future value simply press the FV key. The answer you get should be 161.05.

A Couple of Notes

Every time value of money problem has either 4 or 5 variables. Of these, you will always be given 3 or 4 and asked to solve for the other. In this case, we have a 4-variable problem and were given 3 of them (N, i, and PV) and had to solve for the 4th (FV). To solve these problems you simply enter the variables that you know in the appropriate keys and then press the other key to get the answer.
The order in which the numbers are entered does not matter.
When we entered the interest rate, we input 10 rather than 0.10. This is because the calculator automatically divides any number entered into the I/YR key by 100. Had you entered 0.10, the future value would have come out to 100.501 -- obviously incorrect.
Notice that we entered the 100 in the PV key as a negative number. This was on purpose. Most financial calculators (and spreadsheets) follow the Cash Flow Sign Convention. This is simply a way of keeping the direction of the cash flow straight. Cash inflows are entered as positive numbers and cash outflows are entered as negative numbers. In this problem, the $100 was an investment (i.e., a cash outflow) and the future value of $161.05 would be a cash inflow in five years. Had you entered the $100 as a positive number no harm would have been done, but the answer would have been returned as a negative number. This would be correct had you borrowed $100 today (cash inflow) and agreed to repay $161.05 (cash outflow) in five years.
We can change any of the variables in this problem without needing to re-enter all of the data. For example, suppose that we wanted to find out the future value if we left the money invested for 10 years instead of 5. Simply enter 10 into the N key and solve for FV. You'll find that the answer is 259.37.

Example 2 - Annuities

Suppose that you are offered an investment which will pay you $1,000 per year for 10 years. If you can earn a rate of 9% per year on similar investments, how much should you be willing to pay for this annuity?

In this case we need to solve for the present value of this annuity since that is the amount that you would be willing to pay today. Press shift C ALL to clear the financial keys. Enter the numbers into the appropriate keys: 10 into N, 9 into I/YR, and 1000 (cash inflow) into PMT. Now press the PV key to solve for the present value. The answer is -6,417.6577. Again, this is negative because it represents the amount you would have to pay (cash outflow) to purchase this annuity.

Now, suppose that you will be borrowing $1000 each year for 10 years at a rate of 9%, and then paying back the loan immediate after receiving the last payment. How much would you have to repay? All we need to do is to put a 0 into PV to clear it out, and then press FV to find that the answer is -15,192.92972 ( a cash outflow).

Example 3 - Uneven Cash Flows

In addition to the previously mentioned financial keys, the 10B also has a key labeled CF_j to handle a series of uneven cash flows.

Suppose that you are offered an investment which will pay the following cash flows at the end of each of the next five years:

Period	Cash Flow
0	0
1	100
2	200
3	300
4	400
5	500

How much would you be willing to pay for this investment if your required rate of return is 12% per year?

We could solve this problem by finding the present value of each of these cash flows individually and then summing the results. However, that is the hard way. Instead, we'll use the cash flow key (CF_j). All we need to do is enter the cash flows exactly as shown in the table. Again, clear the financial keys first. Now, press 0 then CF_j, 100 CF_j, 200 CF_j, 300 CF_j, 400 CF_j, and finally 500 CF_j. Now, enter 12 into the I/YR key and then press the shift key and then the key labeled NPV. We find that the present value is $1,000.17922.

Now suppose that we wanted to find the future value of these cash flows instead of the present value. There is no key to do this so we need to use a little ingenuity. Realize that one way to find the future value of any set of cash flows is to first find the present value. Next, find the future value of that present value and you have your solution. In this case, we've already determined that the present value is $1,000.17922. Clear the financial keys (shift C ALL) then enter 1000.17922 into the PV key. N is 5 and I/YR is 12. Now press the FV key and you'll see that the future value is $1,762.65753. Pretty easy, huh? (Ok, at least its easier than adding up the future values of each of the individual cash flows.)

A Couple of Notes

The HP10BII is fairly notorious for having things saved in the calculator's memory registers and the user not being aware of it. So, before starting any problem, be sure to clear all the memory registers using shift C ALL.
When setting up a cash flow problem, you will need to adjust the calculator's compounding periods to reflect those of the problem you are analyzing. Example: For the problem above, you would start by setting the calculator's compound period to once per year. For a problem involving monthly compounding, you should enter 12 shift P/YR.
When you are inputting a series of identical cash flows into the cash flows, you can take advantage of a time saving technique and use the N_j function. If that in the above problem we needed to enter the last CF_j of 500 for 20 times we can enter the CF_j as above and then 20 shift N_j. This will enter that year 5 cash flow for 20 periods without the need to enter it manually. This can be a big time saver.
A final note about a quirk with the HP10BII. This calculator will run out of memory if you try to enter more than 99 cash flows into a single memory register using the N_j function. If you need to enter more than 99 cash flows, you will need to enter them in a series which adds up to the number of cash flows you wish to obtain.

Example 4 - NPV and IRR

Calculating the net present value (NPV) and/or internal rate of return (IRR) is virtually identical to finding the present value of an uneven cash flow stream as we did in Example 3.

Suppose that you were offered the investment in Example 3 at a cost of $800. What is the NPV? IRR?

To solve this problem we must not only tell the calculator about the annual cash flows, but also the cost. Generally speaking, you'll pay for an investment before you can receive its benefits so the cost (initial outlay) is said to occur at time period 0 (i.e., today). To find the NPV or IRR, first clear the financial keys and then enter -800 into CF_j, then enter the remaining cash flows exactly as before. For the NPV we must supply a discount rate, so enter 12 into I/YR and the press Shift PRC (note that above the PRC key says NPV in yellow). You'll find that the NPV is $200.17922. Solving for the IRR is done exactly the same way, except that the discount rate is not necessary. This time, you'll press Shift CST and find that the IRR is 19.53820%.

Example 5 - Mortgages

Calculating the payment on a mortgage is very similar to the process previously learned in order to find the present value of a lump sum and for valuing annuities. We will be using some of the same financial keys including PV, N, and i, but now we will be solving for the payment (PMT) to determine the loan payment which would fully amortize the mortgage loan.

Before starting the problem, you need to set your calculator to 12 monthly payments to adjust the compounding to monthly as the problem specifies. So you will enter the numeral 12 and then press shift and then the P/YR key to set your calculator's compounding to 12. Next, make sure that the financial registers are clear by pressing the shift key and then input. Your calculator should flash "12 P_Yr" which confirms that the calculator's compounding is set to 12 payments per year.

Now, we can begin entering our data. In this problem, the bank is giving us $100,000 at T₀ which is the present value (PV), the i is 10% and finally the term (N) is 30. However, since the problem specifies monthly payments, when you enter the term (N), you will need to adjust the term to allow for the monthly compounding. An easy way to do this on an HP is to take advantage of the xP/YR function on your calculator by entering the numeral 30 and then shift N. The calculator will then display 360 for the term. Now all that remains is to solve for the payment by pressing the PMT key. The answer you will get is $-877.57157.

Example 6 - Amortization

Frequently, we will want to solve for the amount of interest, principle, or outstanding balance on a loan for a particular point in time or a set of periods in time. Now, our calculators can easily accomplish these calculation but first we have to solve for the payment on the loan which will fully amortize the loan. To demonstrate, lets continue our previous example where we solved for the fully amortizing payment on the $100,000 home loan at 10% interest for 30 year with monthly payments. The first thing you need to do is to solve for the monthly payment which will amortize the loan fully. The answer, of course, is -877.57157 just as before. You will need to solve for this payment amount before proceeding to use the amortization function.

Suppose that you want to purchase a $100,000 home with no down payment at a 10% interest rate for a 30 year term with monthly payments from a bank. What will be the monthly payments on this fully amortizing loan? (NOTE: You have to solve for this first before the amortization function will work properly)

Now, what is the total amount of interest paid in the first year? (Months 1-12) How much principle is paid? Finally, what is the outstanding balance at the end of the first year? What about solving for this same information for the second year? (Months 13-24)

To start, first we calculate the payment on this fully amortizing loan and get -$877.571517. Now we can answer all of the above questions with ease. But, to start, we need to understand how our calculator has solved for the fully amortizing payment on the loan. Specifically, it was solved for with monthly compounding and so when we enter the set of periods for amortizing, it needs to be in monthly terms as well.

For this loan, to amortize the first years payments, you should enter 1, input, 12, shift and then AMORT. The calculator will display 1-12 telling you it is amortizing the set of monthly payments for the first year. Now then you can simply press the equal key to scroll through the amount of interest paid, principle paid, and finally the outstanding balance at the end of the first year. The answers are -$9,974.98026 for interest $-555.87858 for principle and an outstanding balance of $99,444.12142. If you wanted to amortize the next series of payments, you could either press the shift and amortization key to see the next set of periods (13-24 shown in the display) or press 13 input 24 shift AMORT to see 13-24 shown in your calculators display. You do not need to clear your calculator to amortize a new set of periods. Now you can scroll through the amount of interest paid, principle paid, and finally the outstanding balance at the end of the second year. The answers are -$9,913.77253 for interest $-614.08631 for principle and an outstanding balance of $98,830.03511.

A Couple of Notes

Every time you are faced with an amortization problem, you must first solve for the payment which fully amortizes the loan. You can then solve for any period's interest, principle, or outstanding balance based on the compounding period used to solve for the fully amortizing payment.
You can amortize any set of periods without the need to solve for the fully amortizing payment again. Simply change the periods being amortized.
Pay close attention to the compounding periods used to solve for the payment which fully amortizes the loan. When you input the range of periods to be amortized using the amortization function it will be in those terms. Example: If you solve for the yearly payment on the example above (100,000 PV, 30 N, 10 i) then the appropriate way to amortize the first year would be 1 input 1 shift AMORT which will give you -$10,100 for interest $-607.92483 for principle and an outstanding balance of $99,392.075