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HP 17bII+ Financial Calculator  The Solver  Business Finance Applications
The HP Solver
One of the most powerful tools contained in the HP 17bII+ calculator is the HP Solver. This tool allows you to key in an equation in algebraic format, enter values for the variables you know, and then automatically solve for the unknown variable. For example, you could key in the equation A = B + C, and if you know the value of A and C, automatically solve for the unknown variable B – without any programming. Very complicated equations can be entered and solved in this manner.
The HP solver allows the user to customize the HP 17bII+ calculator to suit their own personal needs and circumstances. It is unique to HP and demonstrates HP’s continuing commitment to give users flexibility to find their own solutions.
More information is found in the learning module that introduces the solver.
Accessing the solver
The HP Solver is accessed from the main menu, as shown below.
Figure : Displaying the main menu options
Pressing will do one of two things. If there are no existing equations in the HP 17bII+ calculator, then the screen in Figure 2 is displayed. This indicates that you must press to enter an equation.
Figure : Entering an equation
If the HP 17bII+ already has some equations in the equation catalog, a screen similar to the one shown in Figure 3 would be displayed. The equation is shown on the top line of the screen.
Figure : Displaying the equation
The key allows you to edit the currently displayed equation. The key allows you to remove the currently displayed equation from the catalog. The key will enter the equation calculation environment for the currently displayed equation where you can solve for variables within the equation.
Entering an equation
When you are in the equation catalog and the menu key is displayed, pressing it allows you to enter a new equation into the catalog. Pressing displays the screen as shown in Figure 4.
Figure : Entering a new equation
The prompt is displayed indicating that you should use the displayed alpha menu keys to enter the equation and press when you are finished. Each of the displayed alpha menu keys will access a second screen that allows the entry of the individual letters shown. For example, the key allows you to enter , , , , or . If you press, the second screen is shown as below. To exit this screen, press one of the letter menu keys or .
Suppose you wish to enter A = B + C into the solver. If the screen from Figure 4 is still displayed, you would press the following keys: . If you pressed the keys correctly, the screen should look like Figure 5 below.
Figure : Displaying the equation entered
If your equation is too long to fit in the display, it may look like the screen in Figure 6 below with an ellipsis at the end of the equation indicating that the text continues off the display. The example in Figure 6 also shows that you can use long variable names if you wish.
Figure : Using long variable names
Solving an equation
When an equation is displayed in the equation catalog, pressing the key will enter the equation calculation environment you can solve for variables within the equation. What the HP 17bII+ does at this point is scan through the equation to verify that it is valid. If the equation is valid, the HP 17bII+ will scan through the equation for variable names and create a custom menu key screen for the variables in the equation. If the equation A = D + C were the one chosen, then the solver screen would appear as shown in Figure 7 below after was pressed.
note:
Although you can use long variable names in equations, names longer than 4 or 5 characters long may not be displayable in a menu key location in the display.
Figure : Displaying the solver screen
At this point, you can enter values for any two variables that you know and solve for the unknown variable. If A = 6, you press . The display appears as shown in Figure 8.
Figure : Displaying the value for A entered
If D = 2, press . The display appears as shown in Figure 9.
Figure : Displaying the value for D entered
To solve for C, just press . Figure 10 shows the result.
Figure : Displaying the result
Solver applications – Return on equity
The return on equity (ROE) ratio measures the profitability of a company relative to the amount of equity (ownership) capital invested. The measure is usually calculated each year, over a period of five or more years, to identify trends in this measure. Return on equity is also used to compare companies or industries.
Example 1
Enter the formula to compute the Return on Equity Ratio, ROE = INCOME ÷ CAPITAL x 100.
Solution
Keystroke

Display


Figure : Displaying the formula

Answer
The formula should appear as shown above in Figure 11.
note:
Since the formula is wider than the display, an ellipsis is present at the right side of the screen.
Example 2
Use the formula entered in Example 1. Your company has after tax earnings of $2,500,000 and a net worth of $18,000,000. What is the return on equity?
Solution
Keystroke

Display


Figure : Displaying the return on equity

Answer
The ROE is 13.89%.
note:
Since two of the variable names used in the formula are somewhat long, the screen cannot display the entire name as a menu key.
Example 3
Your industry averages 14.76% ROE. Given the capital investment in Example 2, what would your after tax income need to be to match that return on equity?
Solution
Keystroke

Display


Figure : Displaying the income

Answer
Your income would need to be $2,656,800.
Solver applications – Bond interest coverage ratio
The bond interest coverage ratio is a measure of a bond’s quality and financial safety. It is a ratio of the funds available to pay interest during a given year to the interest requirements associated with a bond issue. The calculation can be made several ways, depending on the legal status of different issues of bonds, interest costs on other than bond debt, and whether the company has issued preferred stock. All other things being equal, the higher the coverage ratio, the higher the quality of the bond.
Example 4
Enter the formula to compute the bond interest coverage ratio, COVER = (EARN + INT) ÷ INT.
Solution
Keystroke

Display


Figure : Displaying the formula

Answer
The formula should appear as shown above in Figure 14.
Example 5
Use the formula entered in Example 4. What is the interest coverage ratio of a bond with annual interest payments of $2,000,000 and corporate earnings of $8,000,000?
Solution
Keystroke

Display


Figure : Displaying the result

Answer
Five dollars of funds are available to pay each dollar of bond interest.
Example 6
Use the formula entered in Example 4. Suppose the average bond interest coverage ratio in your industry is 4.85. Calculate how much you could pay in annual interest payments if you borrowed additional funds so that your bond interest ratio matched that of the industry. Assume this example is worked immediately after Example 5.
Solution
Keystroke

Display


Figure : Displaying the result

Answer
You could pay approximately $78,000 more in interest payments.
note:
The solver searches for a numerical solution and displays intermediate answers.
Solver applications – Pricetoearnings ratio
The pricetoearnings ratio is used by investors to indicate how much they are investing to obtain one dollar of earnings. Individual securities are often compared to the ratios of the stock market indices or averages.
Example 7
Enter the formula to compute the pricetoearnings ratio, PE = PRICE ÷ EARN.
Solution
Keystroke

Display


Figure : Displaying the formula

Answer
The formula should appear as shown above in Figure 17.
Example 8
Use the formula entered in Example 7. Your company stock is selling for $75 a share and has earnings of $6 per share. What is the pricetoearnings ratio?
Solution
Keystroke

Display


Figure : Displaying the pricetoearnings ratio

Answer
The PE ratio is 12.5.
Example 9
Use the formula entered in Example 7. A major stock index is at a price of $4,510 and the earnings of the index are at $409.50. Is your company stock doing better or worse than this market index in terms of pricetoearnings ratio? Assume this example is worked immediately after Example 8.
Solution
Keystroke

Display


Figure : Displaying the pricetoearnings ratio

Answer
The price to earnings ratio for your stock is higher than the market index, indicating that your stock is more attractive as an owner of the stock when compared to the index.
Solver applications – Return on investment
One way of evaluating a new investment is through a simple return on investment (ROI) analysis. Return on investment is the ratio of net profit after taxes to the assets used to make the profit.
Example 10
Enter the formula to compute return on investment, ROI = ( REV x PROF ÷ 100 ) ÷ INV x 100, where ROI is the return on investment, REV are the total revenues, PROF is the net profit as a percent of revenues, and INV is the capital investment in the project.
Solution
Keystroke

Display


Figure : Displaying the formula

Answer
The formula should appear as shown above in Figure 20.
Example 11
Use the formula entered in Example 10. A new store requires $480,000 in new assets. The anticipated revenues the first year are $1,000,000. Your net profit goal is 10%. Assuming the net profit goal is met, calculate the return on investment.
Solution
Keystroke

Display


Figure : Displaying the return on investment

Answer
The 'ROI' is 20.83%.
Example 12
Use the formula entered in Example 10. The store’s sales are actually $750,000 the first year. Calculate the ROI. Assume this example is worked immediately after Example 11.
Solution
Keystroke

Display


Figure : Displaying the actual return on investment

Answer
The actual ROI was 15.63%.
Example 13
Use the formula entered in Example 10. At the level of revenues from Example 12, what total investment in the store can you sustain to achieve an ROI of 18%? Assume this example is worked immediately after Example 12.
Solution
Keystroke

Display


Figure : Displaying the total investment

Answer
You can sustain an investment of $416,666.67 at an ROI of 18%.
Example 14
Use the formula entered in Example 10. Suppose you realize a 5% net profit on revenues of $750,000 with $480,000 of investments. What is the ROI? Assume this example is worked immediately after Example 13.
Solution
Keystroke

Display


Figure : Displaying the investment amount

Answer
You can sustain an investment of $416,666.67 at an ROI of 18%.
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