636 Appendix

Using Calculators for Financial Analysis

This appendix is designed to help you use either an algebraic calculator (Texas Instruments BA-35 Student 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 below.

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.

	Texas Instruments BA-35	Hewlett-Packard 12C
First clear the calculator	1. ON/C ON/C 2. 0 3. STO Clears memory	1. CLX Clear screen 2. f function 3. REG Clears memory
Set the decimal point The TI BA-35 has two choices: 2 decimal points or variable decimal points. The screen will indicate Dec 2 or the decimal will be variable. The HP 12C allows you to choose the number of decimal points. If you are uncertain, just provide the indicated input exactly as shown on the right.	1. 2^nd 2. STO	1. f 2. 4 (# of decimals)

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. This first occurs on page 641 of the appendix.

637 Appendix

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 that follow, we simply instruct you on how to get the interest factors for Appendixes A, B, C, and D. We have chosen to use examples as our method of instruction.

A

	Texas Instruments BA-35	Hewlett-Packard 12C
Appendix A Future value of $1 I=9%or .09; n=5 years FVIF = (1+I)^n Future value = Present Value x FVIF FV = PV x FVIF Check the answer against the number in Appendix A. Numbers in the appendix are rounded. Try different rates and years.	To find interest factor 1. 1 2. + 3. .09 (interest) 4. = 5. y^x 6. 5 (# of periods) 7. = answer .538624	To find interest factor 1. 1 2. enter 3. .09 (interest) 4. + 5. 5(# or periods) 6. y^x answer 1.5386

B

	Texas Instruments BA-35	Hewlett-Packard 12C
Appendix B Present value of $1 I=9%, or .09; n = 5 PVIF = 1/(1+I)^n Present value = Future value x PVIF PV = FV x PVIF Check the answer against the number in Appendix B. Numbers in the appendix are rounded.	To find interest factor Repeat steps 1 through 7 above. Continue with step 8. 8. 1/x Answer .6499314	To find interest factor Repeat steps 1 through 6 above. Continue with step 7. 7. 1/x Answer .6499

638 Appendix

C

	Texas Instruments BA-35	Hewlett-Packard 12C
Appendix C Future Value of an Annuity of $1 I=9% or .09; n = 5 years FVIFA = (1+I)^n - 1 I Future value = Annuity ^x FVIFA FVA = A ^x FVIFA Check your answer with Appendix C. Repeat example using different numbers and check your results with the number in Appendix C. Numbers in appendix are rounded.	To find interest factor Repeat steps 1 through 7 in part A of this section. Continue with step 8. 8. - Minus 9. 1 10. = Equals 11. / Divided by 12. .09 13. = Answer 5.9847106	To find interest factor Repeat steps 1 through 6 in part A of this section. Continue with step 7. 7. 1 8. - Minus 9. .09 10. / Answer 5.9847

D

	Texas Instruments BA-35	Hewlett-Packard 12C
Appendix D Present Value of an Annuity of $1 I = 9% or .09; n = 5 years PVIFA = 1-[1/(1+I)^n] I Present value = Annuity x PVIFA Check your answer with Appendix D. Repeat example using different numbers and check your results with the number in Appendix D. Numbers in appendix are rounded.	To find interest factor Repeat steps 1 through 8 in parts A & B. Continue with step 9. 9. - Minus 10. 1 11. = Equals 12. +/- plus or minus key 13. / Divided by 14. .09 15. = Answer 3.8896513	To find interest factor Repeat steps 1 through 7 in parts A & B. Continue with step 8. 8. 1 9. - Minus 10. CHS 11. .09 12. / Answer 3.8897

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.

639 Appendix

Bond Valuation Using Both the TI BA-35 and the HP 12C

Solve for P_b = Price of the bond

Given:

It = $80 annual coupon payments or 8% coupon ($40 semiannually)

P_n = $1,000 principal (par value)

n = 10 years to maturity (20 periods semiannually)

Y = 9.0% yield to maturity or required rate of return (4.5% semiannually)

You may choose to refer to Chapter 10 for a complete discussion of bond valuation.

	Texas Instruments BA-35	Hewlett-Packard 12c
BOND VALUATION All steps begin with number 1. Numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed. The Texas Instruments calculator requires that data be adjusted for semiannual compounding, otherwise it assumes annual compounding. The Hewlett-Packard 12C internally assumes that semiannual compounding is used and requires annual data to be entered. The HP 12C is more detailed in that it requires the actual day, month, and year. If you want an answer for a problem that requires a given number of years (e.g., 10 years), simply start on a date of your choice and end on the same date 10 years later, as in the example.	Set finance mode 2^nd FIN Set decimal to 2 places Decimal 2^nd STO 1. 40 (semiannual coupon) 2. PMT 3. 4.5 (yield to maturity) semiannual basis 4. %I 5. 1000 (principal) 6. FV 7. 20 (semiannual periods to maturity) 8. N 9. CPT 10. PV Answer 934.96 Answer is given in dollars, rather than % of par value.	Clear memory f REG Set decimal to 3 places F 3 1. 9.0 (yield to maturity) 2. I 3. 8.0 (coupon in percent) 4. PMT 5. 1.091999 (today's date month-day-year)* 6. enter 7. 1.092009 (maturity date month-day-year)* 8. f 9. Price Answer 93.496 Answer is given as % of par value and equals $934.96. If Error message occurs, clear memory and start over. *See instructions in the third paragraph of the first column.

640 Appendix

Yield to Maturity on both the TI BA-35 and HP 12C

Solve for Y = yield to maturity

Given:

Pb = $895.50 price of bond

It = $80 annual coupon payments or 8% coupon ($40 semiannually)

PN = $1,000 principal (par value)

N = 10 years to maturity (20 periods semiannually)

	Texas Instruments BA-35	Hewlett-Packard 12C
YIELD TO MATURITY All steps begin with number 1. Numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed. The TI BA-35 does not internally compute a semiannual rate, so the data must be adjusted to reflect semiannual payments and periods. The answer received in step 10 is a semiannual rate, which must be multiplied by 2 to reflect an annual yield. The HP 12C internally assumes that semiannual payments are made and, therefore, the answer in step 9 is the annual yield to maturity based on semiannual coupons. If you want an answer on the HP for a given number of years (e.g., 10 years), simply start on a date of your choice and end on the same date 10 years later, as in the example.	Set finance mode 2^nd FIN Set decimal to 2 places Decimal 2^nd STO 1. 20 (semiannual periods) 2. N 3. 1000 (par value) 4. FV 5. 40 (semiannual coupon) 6. PMT 7. 895.50 (bond price) 8. PV 9. CPT 10. %I Answer 4.83% 11. X 12. 2 13. = Answer 9.65% (annual rate)	Clear memory f REG Set decimal f 2 1. 89.55 (bond price as a percent of par 2. PV 3. 8.0 (annual coupon in %) 4. PMT 5. 1.091999 (today's date month-day-year)* 6. enter 7. 1.092009 (maturity date month-day-year) 8. f 9. YTM In case you receive an Error message, you have probably made a keystroke error. Clear the memory f REG and start over. *See instructions in the third paragraph of the first column.

641 Appendix

Net Present Value of an Annuity on both the TI BA-35 and the HP 12C

Solve for PV = present value of annuity

N = 10 years (number of years cash flow will continue)

PMT = $5,000 per year (amount of the annuity)

I = 12% (cost of capital K_a)

Cost = $20,000

You may choose to refer to Chapter 12 for a complete discussion of net present value.

	Texas Instruments BA-35	Hewlett-Packard 12C
NET PRESENT VALUE OF AN ANNUITY All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. The calculation for the present vale of an annuity on the TI BA-35 requires that the project cost be subtracted from the present value of the cash inflows. The HP 12C could solve the problem exactly with the same keystrokes as the TI. However, since the HP uses a similar method to solve uneven cash flows, we elected to use the method that requires more keystrokes but includes a negative cash outflow for the cost of the capital budgeting project To conserve space, several keystrokes have been put into one step..	Set finance mode 2^nd FIN Set decimal to 2 places Decimal 2^nd STO 1. 10 (years of cash flow) 2. N 3. 5000 (annual payments) 4. PMT 5. 12 (cost of capital) 6. %I 7. CPT 8. PV 9. - 10. 20,000 11. = Answer $8,251.12	Set decimal to 2 places F 2 F REG 1. 20000 (cash outflow) 2. CHS changes sign 3. G 4. Cfo 5. 5000 (annual payments) 6. g CFj 7. 10 g Nj (years) 8. 12 I (cost of capital) 9. f NPV Answer $8251.12 If Error message appears, start over by clearing the memory with f REG.

642 Appendix

Net Present Value of an Uneven Cash Flow on Both the TI BA-35 and the HP 12C

Solve for NPV = Net present value

N = 5 years (number of years cash flow will continue)

PMT = $5,000 (yr.1); 6000 (yr.2); 7000 (yr.3); 8000 (yr.4); 9000 (yr.5)

I = 12% (cost of capital K_a)

Cost = $25,000

	Texas Instruments BA-35	Hewlett-Packard 12C
NET PRESENT VALUE OF AN UNEVEN CASH FLOW All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. Because we are dealing with uneven cash flows, each number must be entered. The TI BA-35 requires that you make sure of the memory. In step 2, you enter the future cash inflow in year 1 and, in step 3, you determine its present value, which is stored in memory. After the first 1-year calculation, following year present values are calculated in the same way and added to the stored value using the SUM key. Finally, the recall key RCL is used to recall the present value of the total cash inflows. The HP 12C requires each cash flow to be entered in order. The Cfo key represents the cash flow in time period 0. The CFj key automatically counts the year of the cash flow in the order entered and so no years need be entered. Finally, the cost of capital of 12% is entered and the f key and NPV key are used to complete the problem.	Clear memory ON/C 0 STO Set decimal to 2 places Decimal 2^nd STO Set finance mode 2^nd FIN 1. 12 %I 2. 5000 FV 3. 1 N CPT PV SUM 4. 6000 FV 5. 2 N CPT PV SUM 6. 7000 FV 7. 3 N CPT PV SUM 8. 8000 FV 9. 4 N CPT PV SUM 10. 9000 FV 11. 5 N CPT PV SUM 12. RCL (answer 24420.90) 13. - 14. 25000 (Cash flow) 15. = answer -$597.10 Negative net present value.	Set decimal to 2 places F 2 F REG clears memory 1. 25000 (cash outflow) 2. CHS changes sign 3. g CFo 4. 5000 g CFj 5. 6000 g CFj 6. 7000 g CFj 7. 8000 g CFj 8. 9000 g CFj 9. 12 I 10. f NPV Answer -579.10 Negative net present value. If you receive an Error Message, you have probably made a keystroke error. Clear memory with: f REG and start over with step 1.

643 Appendix

Internal Rate of Return for an Annuity on Both the TI BA-35 and the HP 12C

Solve for IRR = Internal rate of return

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)

	Texas Instruments BA-35	Hewlett-Packard 12C
INTERNAL RATE OF RETURN ON AN ANNUITY All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. The calculation for the internal rate of return on an annuity on the TI BA-35 requires relatively few keystrokes. The HP 12C requires more key-strokes than the TI BA-35, because it needs to use the function keys f and g to enter data into the internal programs. The HP method requires that the cash outflow be expressed as a negative, while the TI BA-35 uses a positive number for the cash outflow. To conserve space, several keystrokes have been put into one step.	Clear memory ON/C 0 ON/C Set finance mode 2^nd FIN Set decimal to 2 places Decimal 2^nd STO 1. 10 (years of cash flow) 2. N 3. 10000 (annual payments) 4. PMT 5. 50000 (present value) 6. PV 7. CPT 8. %I Answer is 15.10% At an internal rate of return of 15.10%, the present value of the $50,000 outflow is equal to the present value of $10,000 cash inflows over the next 10 years.	Set decimal to 2 places F 2 F REG clears memory 1. 50000 (cash outflow) 2. CHS changes sign 3. G 4. CFo 5. 10000 (annual payments) 6. g CFj 7. 10 g Nj (years) 8. f IRR Answer is 15.10% If an Error message appears, start over by clearing the memory with f REG.

644 Appendix

Internal rate of Return with an Uneven Cash Flow on Both the TI BA-35 and the HP 12C

Solve for IRR = internal rate of return (return which causes present value of outflows to equal

Present value of the inflows.)

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

	Texas Instruments BA-35	Hewlett-Packard 12C
INTERNAL RATE OF RETURN ON UNEVEN CASH FLOW All steps are numbered and some steps include several keystrokes. All numbers following each step are keystrokes followed by a box . Each box represents a keystroke and indicates which calculator function is performed on that number. Because we are dealing with uneven cash flows, the mathematics of solving this problem with the TI BA-35 is not possible. A more advanced algebraic calculator would be required. However, for the student willing to use trial and error, the student can use the NPV method and try different discount rates until the NPV equals zero. The HP 12C requires each cash flow to be entered in order. The CFo key represents the cash flow at time period 0. The CFj key automatically counts the year of the cash flow in the order entered and so no years need to be entered. To find the internal rate of return, use the f IRR keys and complete the problem.	Clear memory ON/C 0 STO Set decimal to 2 places Decimal 2^nd STO Set finance mode 2^nd FIN 1. 12 %I 2. 5000 FV 3. 1 N CPT PV SUM 4. 6000 FV 5. 2 N CPT PV SUM 6. 7000 FV 7. 3 N CPT PV SUM 8. 8000 FV 9. 4 N CPT PV SUM 10. 9000 FV 11. 5 N CPT PV SUM 12. RCL (answer 24420.90) 13. - 14. 25000 (Cash flow) 15. = answer -$597.10 Negative NPV Start over with a lower discount rate (try ll.15). Answer is 24999.75. With a cash outflow of $25000, the IRR would be 11.15%	Set decimal to 2 places F 2 F REG clears memory 1. 25000 (cash outflow) 2. CHS changes sign 3. g CFo 4. 5000 g CFj 5. 6000 g CFj 6. 7000 g CFj 7. 8000 g CFj 8. 9000 g CFj 9. f IRR Answer 11.15% If you receive an Error Message, you have probably made a keystroke error. Clear memory with: f REG and start over with step 1.