Using Calculators for Financial Analysis
Using Calculators for Financial Analysis
This appendix is designed to help you use either an algebraic calculator (Texas Instruments BAII Plus Business Analyst) or the Hewlett-Packard 12C Financial Calculator. We realize that most calculators come with comprehensive instructions, and this appendix is meant only to provide basic instructions for commonly used financial calculations.
There are always two things to do before starting your calculations as indicated in the first table: Clear the calculator and set the decimal point. If you do not want to lose data stored in memory, do not perform steps 2 and 3 in the first box on the next page.
Each step is listed vertically as a number followed by a decimal point. After each step you will find either a number or a calculator function denoted by a box . Entering the number on your calculator is one step and entering the function is another. Notice that the HP 12C is color coded. When two boxes are found one after another, you may have an f or a g in the first box. An f is orange coded and refers to the orange functions above the keys. After typing the f function, you will automatically look for an orange-coded key to punch. For example, after f in the first Hewlett-Packard box (right-hand panel), you will punch in the orange-color-coded REG. If the f function is not followed by another box, you merely type in f and the value indicated.
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The g is coded blue and refers to the functions on the bottom of the function keys. After the g function key, you will automatically look for blue-coded keys. The TI BAII Plus is also color coded. The gold 2nd key, located near the top left corner of the calculator, refers to the gold functions above the keys. Upon pressing the 2nd key, the word “2nd” appears in the top left corner, indicating the gold function keys are active.
Familiarize yourself with the keyboard before you start. In the more complicated calculations, keystrokes will be combined into one step.
In the first four calculations, we solve for the future value (FV), present value (PV), future value of an ordinary annuity (FVA), and present value of an ordinary annuity (PVA), each for $100.
On the following pages, you can determine bond valuation, yield to maturity, net present value of an annuity, net present value of an uneven cash flow, internal rate of return for an annuity, and internal rate of return for an uneven cash flow.
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Bond Valuation Using Both the TI BAII Plus and the HP 12C
Solve for V = Price of the bond
Given:
| Ct = | $80 annual coupon payments or 8% coupon ($40 semiannually) |
| Pn = | $1,000 principal (par value) |
| n = | 10 years to maturity (20 periods semiannually) |
| i = | 9.0% rate in the market (4.5% semiannually) |
You may choose to refer to Chapter 10 for a complete discussion of bond valuation.
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Yield to Maturity on Both the TI BAII Plus and HP 12C
Solve for Y = Yield to maturity
Given:
| V = | $895.50 price of bond |
| Ct = | $80 annual coupon payments or 8% coupon ($40 semiannually) |
| Pn = | $1,000 principal (par value) |
| n = | 10 years to maturity (20 periods semiannually) |
You may choose to refer to Chapter 10 for a complete discussion of yield to maturity.
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Net Present Value of an Annuity on Both the TI BAII Plus and the HP 12C
Solve for A = Present value of annuity
Given:
| n = | 10 years (number of years cash flow will continue) |
| PMT = | $5,000 per year (amount of the annuity) |
| i = | 12% (cost of capital Ka) |
| Cost = | $20,000 |
You may choose to refer to Chapter 12 for a complete discussion of net present value.
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Net Present Value of an Uneven Cash Flow on Both the TI BAII Plus and the HP 12C
Solve for NPV = Net present value
Given:
| n = | 5 years (number of years cash flow will continue) |
| PMT = | $5,000 (yr. 1); $6,000 (yr. 2); $7,000 (yr. 3); $8,000 (yr. 4); $9,000 (yr. 5) |
| i = | 12% (cost of capital Ka) |
| Cost = | $25,000 |
You may choose to refer to Chapter 12 for a complete discussion of net present value concepts.
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Internal Rate of Return for an Annuity on Both the TI BAII Plus and the HP 12C
Solve for IRR = Internal rate of return
Given:
| n = | 10 years (number of years cash flow will continue) |
| PMT = | $10,000 per year (amount of the annuity) |
| Cost = | $50,000 (this is the present value of the annuity) |
You may choose to refer to Chapter 12 for a complete discussion of internal rate of return.
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Internal Rate of Return with an Uneven Cash Flow on Both the TI BAII Plus and the HP 12C
Solve for IRR = Internal rate of return (return that causes present value of outflows to equal present value of the inflows)
Given:
| n = | 5 years (number of years cash flow will continue) |
| PMT = | $5,000 (yr. 1); $6,000 (yr. 2); $7,000 (yr. 3); $8,000 (yr. 4); $9,000 (yr. 5) |
| Cost = | $25,000 |
You may choose to refer to Chapter 12 for a complete discussion of internal rate of return.
1The assumption is that the bond has a $1,000 par value. If the par value is higher or lower, then this value would be discounted to the present from the maturity date.
2For now, we are using annual interest payments for simplicity. Later in the discussion, we will shift to semiannual payments, and more appropriately determine the value of a bond.
3Actually a slightly more accurate representation would be this: Risk-free rate = (1 + Real rate of return)(1 + Inflation premium) − 1. We would show: (1.03)(1.04) − 1 = 1.0712 − 1 = .0712 = 7.12 percent.
4On the other hand, common stock carries the potential for very high returns when the corporation is quite profitable.
5Of course the required rate of return on all other financial assets will also go up proportionally.
6Since this is a no-growth stock, D1 equals D0. Formula 10-6 uses D1 to emphasize that the first dividend payment comes at the end of year 1.
7This EPS value for the past 12 months is different from the value in the table for the latest year, which represents a calendar year.
