TIME VALUE OF MONEY. Hewlett-Packard HP-12C Calculator

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1 SECTION 1, CHAPTER 6 TIME VALUE OF MONEY CHAPTER OUTLINE Clues, Hints, and Tips Present Value Future Value Texas Instruments BA II+ Calculator Hewlett-Packard HP-12C Calculator CLUES, HINTS, AND TIPS Present Value Excel has a very powerful and easy to utilize formula for present value calculations under the title of PV in the financial category. This single formula will handle present value calculations of single sums or annuities as well as adjust them for payment at the beginning or the end of the period. The inserted screen print shows the Present Value dialog box. The chapter 6 data file, chptr6, has numerous examples on the Present Value tab. The basic formula is =PV(Period interest, Number of periods, Amount of each payments, Future value, Payment at the beginning or the end of the period) with payment at the end of the period indicated by a 0 (zero) and payment at the beginning of the period indicated by a 1 (one). Leaving the payment type empty Excel defaults to payment at the end of the period. By omitting the value for payments or by placing a 0 (zero) in the window and providing the formula a future value, the formula will produce the present value of a single sum. By placing the amount of an individual payment in the

2 30 Solving Intermediate Accounting Problems Using Excel For Windows payment window the formula will produce the present value of an annuity. For annuities due place a 1 (one) in the Type window, for an ordinary annuity, place a 0 (zero) in the Type window or leave it blank. Some hints and tips on utilizing the dialog box First, if you establish the data matrix as shown on the Present Value tab in cells A1 through A7 you can have formulas installed that will take the life in years and multiply it by the compounding factor for Nper. You can also divide the interest rate by the compounding factor to get the interest value for the period rate. Remember that as with working with the tables in the textbook, the interest rate and the number of periods must be expressed in comparable values. If the document states that interest is 8% annually and it is compounded quarterly and that the life of the annuity is 10 years, the effective values are 2% interest (8% / 4 quarters) and 40 periods (10 years X 4 quarters per year). The formula will also produce the value of $1, just like the tables by placing the value of 1 (one) in the payment or future value window as appropriate. This value will be carried out to more significant digits than the textbook s tables even if formatted to show the same since Excel keeps the real value in its mind even with trimmed or formatted presentations. Excel works with standard finance and math logic. If the payments are positive, the present value will be negative, if the payments are negative, the present value is positive. This represents cash flows in and out with cash flows out being negatives and cash flows in being positives. Future Value Excel has a similar formula for Future value as it as for Present value under the Financial category. This formula is demonstrated on the Future value tab of the chapter 6 data file, chptr6. The formula is written as =FV(Period Interest, Periods, Payments, Future value, Payment at the beginning or the end of the period). As with the present value formula interest rate and periods must be stated in the same terms. The appearance of the dialog box is very similar. Like the present value formula this single formula with various inputs will provide the future value of a single sum or a series of payments, an annuity. It will accept payments made at the beginning or the end of the period. As with the present value formula the future value formula will produce the future value for the sum of $1. This value will be kept within Excel to a greater number of significant digits than your textbook s tables. This may cause a slight difference between Excel generated present and future values but the differences will not be material. Texas Instruments BA II+ Calculator The BA (Business Analyst) II+ calculator produced by Texas Instruments (TI) is a superb tool for accountants. Within its capabilities is the calculation of the number of periods, the interest rate, the present value, the payment, and the future value of a cash issue. To ensure that the TI BA II+ is set up properly for these calculations follow the following instructions before any calculations are made: The TI BA II Plus calculator for Time Value of Money (TVM) instructions are not real clear. So we will take it simple and one step at a time. I will explain what I think each step means so that you understand it and can utilize it later. 1. Turn your TI BA II+ on with the On/Off button. 2. Press and release the yellow 2nd button on second row, in the first column once. This puts you into the function access to the yellow letter menu above many of the buttons.

3 Section 1, Chapter Press and release the P/Y (I/Y) button on the third row, in the second column. This takes you to a setup menu for the time value of money. You will be presented with a display of P/Y= or C/Y=. 4. Type in the number 1 (one). Then press and release the Enter button on the first row, in the second column. 5. Now press and release either the up arrow button on row one, in the third column or the down arrow on row one, in the fourth column. The display will switch to the remaining factor of P/Y= or C/Y= setup. 6. Type in the number 1 (one) and press and release the Enter button on row one, in the second column. What this does is set up the BA II+ to handle interest rates and periods the same as Excel if the interest rate is 8% annual and compounded quarterly you will need to enter 2% as the interest factor and 4 as the number of periods to find the present or future value of an amount for one year at 8% annual interest compounded quarterly. This setup allows you to compute any value regardless of compounding cycles. 7. Press and release the CE/C button on the bottom, left corner of the calculator to exit the submenu. 8. To set or change your decimal places shown in the display window, press and release the yellow 2nd button on row two, in column one and then the Format /. button on the bottom row, in the center column followed the number of decimal places you want, such as 4. Then press and release the Enter button. Press and release the CE/C button on the bottom, left corner of the calculator to exit the submenu. Now we will calculate the monthly payment of a $15,000 loan for 4 years at 8% with no balance or balloon payment at the end of the loan as a check of the settings. The best method is to always start at the left of the calculator and work right. 1. Since the payments are made monthly and no other data is presented, assume that the interest is compounded monthly as well. You can enter this in in several manners 1) realize that 4 years is 48 months and type that value into the TI BAII+ and then press the N or periods key or 2) type 4 into the TI BAII+ press the multiply key, type in 12 (for months in each year) and press the equal sign key. When 48 is displayed on the TI BAII+, press and release the N key. 2. The next value is interest or I. Since the interest is 8% annually and the compounding periods are monthly, type in the number 8, press and release the division key, type in the number 12, press and release the equal sign key. The result should be (depending on your decimal display). Press and release the I key to enter the value into interest. 3. The principal value is $15,000 so type into the TI BAII+ and press and release the PV or present value key. 4. Since we are solving for payment we can either skip the PMT key or enter 0 (zero) just to make sure. My preference is maintain the flow and enter zero through typing in the value 0 and then pressing and releasing the PMT key. 5. Since there is no balance or balloon payment at the end of the loan, enter 0 (zero) into the TI BAII+ and press the FV or future value key. 6. Now that all the data is entered, press and release the CPT key in the first row, first column and then press and release the PMT or payment key. The result should be a negative (depending on your decimal setting. Now your TI BAII+ is set to handle any compounding factor. Remember that if the initial information is 8% interest for 4 years compounded quarterly, the sum of the 8 and the 4 is 32, when set to its period values of 2% and 16 periods, the sum of 2 and 16 is also 32 a check and they must match.

4 32 Solving Intermediate Accounting Problems Using Excel For Windows Because loan payments can be made at the beginning or the end of the period the BAII+ contains a function to switch from one payment scheme to the other. If the payment is made at the beginning of the period, press and release the 2 nd button on row two, in column one followed by the PMT button, followed by the 2 nd button on row two, in column one followed by the Set / Enter button on row 1, in column 2, followed by pressing and releasing the CE/C button on the bottom left corner of the calculator. The BAII+ will announce that will calculate payment values being made at the beginning of the period by displaying BGN in the upper right corner of the display. The value displayed is not accurate and the solution must be regenerated by pressing the CPT button followed by the PMT button. PMT button. The new, and correct, value is $ To switch back to end of period payments, use the same keystrokes press and release the 2 nd button on row two, in column one followed by the PMT button, followed by the 2 nd button on row two, in column one followed by the Set / Enter button on row 1, in column 2, followed by pressing and releasing the CE/C button on the bottom left corner of the calculator. The BGN display will not be visible in the upper portion of the display if payment calculations are made at the end of the period and END will be displayed in the main display until the CE/C button is pressed. To solve for values of N, I/Y, PV, PMT, or FV, simply enter the values known, four required, and compute the last value. Sometimes these values are 0 (zero), they must be entered as such. One tip in using the calculator is to get in the habit of entering the data from left to right, N followed by I/Y, followed by PV, followed by PMT followed by FV where you enter the value to be computed as 0 (zero) during entry to ensure that no other numbers are in the calculator. Remember the interaction of periods and interest discussed earlier. Hewlett-Packard HP-12C Calculator The HP-12C calculator produced by Hewlett-Packard is another accounting and financial profession standard tool. To use the HP-12C effectively you need to appreciate RPN or Reverse Polish Notation keystroke sequences. While the TI BAII+ will take the keystrokes 2+2= and generate the answer 4, the HP-12C requires the keystrokes 2 enter 2 + to get the answer 4. The logic is simple, type in your first number, 2 then enter it into the HP-12C with the enter button, type in your second number, 2 and tell the HP-12C what you want done - + or add and the answer is generated. To calculate the same data in the HP-12C as you did earlier: 1. Turn the calculator on by pressing and releasing the On button on the lower left corner of the calculator. 2. Type in 4 Enter 12 X as see the result of 48 and then press and release the n (Number of periods) button on the first row, in the first column. Or type in the number 4, press and release the blue g button on the fifth row, third column, and press and release the n button, or type in 48 and press and release the n button. The HP-12C will multiply the 4 years by 12 months per year through the blue g button as shown in the blue text in the under face of the n button to get 48 months or periods. 3. Type in 8 Enter 12 as see the result of and then press and release the i (Interest) button on the first row, in the second column. Or type in the number 8, press and release the blue g button on the fifth row, third column, and press and release the i button, or type in 8 and press and release the enter button, type in 12 and press and release the button and then press and release the i button. The HP-12C will divide the 8% by 12 through the blue g button as shown in the blue text in the under face of the i button to get monthly or period interest of %. 4. Type in and press and release the PV (Present value) button.

5 Section 1, Chapter Type in 0 (zero) and press and release the PMT (Payment) button. 6. Type in 0 (zero) and press and release the FV (Future value) button. 7. Press and hold the PMT button for several seconds. The HP-12C will display running to indicate it is working on the solution and then display $ if your display is set to 4 places. Since the present value was entered as a positive number, the payment is a negative number. If the payment were being made at the beginning of the period, press and release the blue g button on row five, in column three followed by pressing and releasing the 7/BEG button on row one, in column seven. The display will show BEGIN in the center bottom. The value displayed is not accurate and the solution must be regenerated by pressing and holding the PMT button for several seconds. The new, and correct, value is $ To change the HP- 12C back to a payment at the end of the period, press and release the blue g button on row five, in column three followed by pressing and releasing the 8/END button on row one, in column eight. The displayed BEGIN will vanish. The value displayed is not accurate and the solution must be regenerated by pressing and holding the PMT button for several seconds. The new, and correct, value is $ To change the decimals displayed in the HP-12C, press and release the orange f button followed by the number button for the amount of decimals you want displayed 4 for four decimal places.