Financial Calculators Using the BA II Plus PDF

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Financial Calculators Using the BA II Plus...

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Financial Calculators Using the BA II Plus¥

The ability to use a financial calculator is an important and useful skill both for business and home finances. With just a little time and effort you will be surprised at how much you can do with a financial or business calculator. While it is always important to understand the concepts and mathematics underlying the calculations, it is also helpful to streamline the practical application of routine financial calculations. The ability to solve problems with the aid of a calculator, however, does not necessarily reflect a conceptual understanding of the material. You are strongly urged to make sure that you understand the basic underlying concepts before relying on the calculator to streamline computations. Most business and financial calculators are designed to offer many more powerful functions. This guide1 provides you with an easy and quick reference guide for some of the most commonly used financial functions, and should be used as a supplement to the Texas Instruments BA II PlusTM Calculator Guidebook. More detailed instructions for the BA II PlusTM can be found in your BA II PlusTM Guidebook.

Getting Started Keys and 2nd Functions The primary function of each key is printed on the key. For example, press ON/OFF to turn the calculator on or off. Some keys provide a secondary function that is printed above the key. When you press the 2nd key the function printed above a key becomes active for the next keystroke. For example, press 2nd [QUIT] to leave a prompted worksheet and return to standard calculator mode. (If you press 2nd by mistake pressing it again will undo it.) Setting the Format for Calculation Method When the calculation method is set to the algebraic operating system (AOS) the calculator solves problems according to the standard rules of algebraic hierarchy, ie it follows BIMDAS. The default setting for the calculator is Chn. It is recommended that you set your calculator to the AOS method as follows: Press 2nd [Format] p p p p . 2nd

[Set]

2nd [QUIT]

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Description The most recently selected calculation method is displayed, either Chn or AOS. Press repeatedly to toggle the two options, leave ‘AOS’ displayed. Return to standard calculator mode.

This quick guide to the Texas Instruments BA II Plus™ is adapted from material published by Texas Instruments supporting the use of their BA II Plus™ Advanced Business Analyst Calculator. It includes brief examples of commonly used BA II Plus calculator settings and financial functions. You should refer to your BA II Plus Guidebook for more detailed BA II Plus instructions.

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Decimal Place Settings The BA II Plus displays two decimal places by default. You can change how many decimal places the calculator displays (up to eight places). For calculating interest rates set the number of decimal places to four as follows: Press 2nd [Format] 4 ENTER 2nd [QUIT]

Display DEC = 4.0000 0.0000

Description Sets the number of decimal places to 4. Return to standard calculator mode.

This four decimal setting continues (even though the calculator is turned off and on) until you change it. Although the calculator displays four decimal places, all calculations are performed with ten digit numbers. If you want to display all the digits after the decimal place follow the steps above replacing ‘4’ with ‘9.’ Obviously where a calculation results in dollars and cents an answer rounded to two decimal places will be sufficient. Payment and Compounding Settings (P/Y, C/Y) The BA II Plus defaults to 12 payments per year (P/Y) and 12 compounding periods per year (C/Y). You can change one or both of the settings to any number. We assume annual compounding at the beginning of the course; ie both the P/Y and C/Y are one. To set both the P/Y and the C/Y to 1: Press 2nd [P/Y] 1 ENTER p 2nd [QUIT]

Display P/Y = 1.0000 C/Y = 1.0000 0.0000

Description Set payment period to annual. Set compounding period to annual. Return to standard calculator mode.

The P/Y and C/Y settings continue (even though the calculator is turned off and on) until you change them. You may need to use different settings later in the course. For example, for monthly payments and quarterly compounding set P/Y to 12 and C/Y to 4: Press 2nd [P/Y] 12 ENTER p.

4 ENTER 2nd [QUIT]

Display P/Y = 12.0000 C/Y = 12.0000 C/Y = 4.0000 0.0000

Description Set payment period to monthly. Display current setting for C/Y Change compounding period to quarterly. Return to standard calculator mode.

Interest Conversion Worksheet Background Information: The nominal interest rate (NOM ) is the interest rate per compounding period multiplied by the number of compounding periods per year. The effective annual interest rate (EAR) is the compound annual interest rate that you actually earn for the period of time stated. In some instances this is also known as the annual percentage rate (APR). The BA II Plus calculator requires the nominal interest rate for input whenever I/Y is used. The calculated I/Y is also a nominal rate. You can convert a nominal rate to an effective rate or vice versa using the interest conversion worksheet.

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Example 1:2 A bank is offering a fixed deposit that pays a nominal interest rate of 7% with quarterly compounding. What is the effective annual interest rate? Press 2nd [I Conv] 2nd [CLR Work]

7 ENTER p p 4 ENTER

Display NOM (old contents) NOM = 0.0000 NOM = 7.0000 C/Y = 4.0000

n CPT EFF = * Indicates computed value.

7.1859*

Description Select interest conversion worksheet Clear worksheet Enter nominal interest rate of 7 percent Enter number of compounding periods per year Compute annual effective interest rate

Example 2: The effective interest rate offered by a competitor is 5.25%. What nominal interest rate compounded monthly should you offer to a customer to match your competitor’s effective rate? Press 2nd [I Conv] 2nd [CLR Work]

p 5.25 ENTER p 12 ENTER n n CPT

Display NOM (old contents) NOM = 0.0000 EFF = 5.2500 C/Y = 12.0000 NOM =

5.1278*

Description Select interest conversion worksheet Clear worksheet Enter effective interest rate of 5.25 percent Enter number of compounding periods per year Compute nominal interest rate

Time Value of Money (TVM) The TVM worksheet is used for time value of money calculations. To compute TVM values or clear the TVM worksheet you must be in the standard calculator mode. To return to the standard calculator mode press 2nd [QUIT]. TVM Variables There are five TVM variables, which you can enter in any sequence by keying in a value and pressing the appropriate TVM keys below. You can check the value of any variable during the calculation by pressing RCL and the variable key. Variable Key N I/Y PV PMT FV

Meaning Total number of payment periods Annual (nominal) Interest Rate** Present Value Payment Amount Future Value

** If the effective interest rate is provided simply ensure that the C/Y is set to 1. See Interest Conversion Worksheet notes if effective interest rate conversion to nominal interest rate is required for your final solution. You will usually enter three variables and calculate the fourth. In some FV calculations you will enter four variables and calculate the fifth. Changing one variable does not affect either entered or calculated values in the other variables.

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Related self-test examples with solutions are provided at the end of this appendix.

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Positive and Negative Cash Flows In general, each TVM problem will have at least two cash flows: one outflow which is entered or computed as a negative value; the other an inflow which is entered or computed as a positive number. To Clear the TVM Worksheet: Press CE/C 2nd [CLR TVM]

Display

Description Clears all values (N, I/Y, PV, PMT, and FV) in the TVM worksheet.

0.0000 0.0000

It is important to realise that previous values may affect your next calculation if they are not cleared. For example, calculator instructions for simple TVM calculations assume that PMT is set to zero and this may not be so if the TVM Worksheet is not cleared. Beginning and End of Period Settings (BGN and END) The BA II Plus can assume that payments occur either at the beginning (BGN) of a period or at the end (END) of a period. The default setting is END. (In this course we assume that cash flows occur at the end of the period, unless otherwise stated.) To set the calculator to beginning of period: Press 2nd [BGN] 2nd [SET] CE/C

Display END BGN 0.0000

Description Displays current setting. Change setting to beginning of period. Return to standard calculator mode.

A small BGN appears above the number display, indicating the mode is beginning of period. The BGN setting continues indefinitely (even though the calculator is turned off and on) until you change it. To set the calculator back to end of period: Press 2nd [BGN] 2nd [SET]

Display Description BGN Displays current setting. END Change setting to end of period. CE/C 0.0000 Return to standard calculator mode. Once you press 2nd [BGN], the 2nd [SET] keys act as a toggle switch between BGN and END.

Calculating the Future Value of a Lump Sum Amount Example 3: If Peter invests $1,500 today in an asset earning a 10% rate of return (compounded annually), how much will he have after 3 years? For this example, the BA II Plus should be set to: x annual C/Y (and P/Y) x two decimal places, and x end of period payment

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Enter three variables (PV, N and I/Y) and calculate the fourth (FV). Press CE/C 2nd [CLR TVM] 1500 +/- PV

3N 10 I/Y CPT FV

Display 0.00 PV = -1,500.00 N= 3.00 I/Y = 10.00 FV = 1,996.50*

Description Set time value of money variables to zero. Enter present cash outflow of $1,500. Enter the number of time periods as 3. Enter interest per year as 10%. Calculate the future (cash inflow) value.

Calculating the Present Value of a Lump Sum Amount Example 4: How much should you invest today, at an interest rate of 9% (compounded monthly) to be able to afford to buy a car that will cost $65,000 in one and a half year’s time? For this example, the BA II Plus should be set to: x monthly (12) C/Y (and P/Y) x two decimal places, and x end of period payment Enter three variables (FV, N and I/Y) and calculate the fourth (PV). Press

Display

CE/C 2nd [CLR TVM]

0.00 FV = 65,000.00 N= 18.00 I/Y = 9.00 PV = -56,820.15*

65000 FV 18 N 9 I/Y CPT PV

Description Set time value of money variables to zero. Enter future cash flow of $65,000. Enter the number of time periods ie1.5x12=18. Enter nominal interest per year of 9%. Calculate the present value (cash outflow).

Calculating the Future Value or Present Value of an Annuity Example 5: You have recently won a lottery prize of $10,000. Your winnings will come in five annual payments of $2,000 each, starting today. If the annual compound interest rate is 5.8% how much is the lottery prize worth at the end of five years? How much is the lottery prize worth now? For this example, the BA II Plus should be set to: x annual C/Y and P/Y x two decimal places, and x beginning of period payment (a small BGN should be above the number display).

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Enter three variables (PMT, N and I/Y) and calculate the fourth (PV or FV). Press

Display

CE/C 2nd [CLR TVM] 2000 PMT

0.00 PMT = 2,000.00 N= 5.00 I/Y = 5.80 FV = -11,880.55* FV = 0.00 PV = -8,962.07*

5N 5.8 I/Y CPT FV

0 FV CPT PV

Description Set time value of money variables to zero. Enter the amount of the periodic cash inflow Enter the number of time periods ie 5. Enter annual interest rate per year of 5.8%. Calculate the future value. Clear FV result prior to calculation of PV. Calculate the present value.

Calculating the Number of Payments or Receipts Example 6: If you wish to retire with $500,000 saved, and you can afford maximum savings of $500 each month, starting in one month, how long will you have to continue working if you can earn a 10% annual return (compounded monthly) on your savings? For this example, the BA II Plus should be set to: x monthly (12) C/Y and P/Y x two decimal places, and x end of period payment. Enter three variables (FV, PMT and I/Y) and calculate the fourth (N). Press

Display

CE/C 2nd [CLR TVM] 500 +/- PMT

0.00 PMT = -500.00 FV = 500,000.00 I/Y = 10.00 N= 269.15*

500 000 FV 10 I/Y CPT N

Description Set time value of money variables to zero. Enter the amount of the periodic savings Enter the future savings total. Enter annual interest rate per year of 10%. Calculate savings period (ie months).

Calculating the Payment Amount Example 7: If you wish to retire with $750,000 saved and you are currently 25 years old and plan to retire at age 65, how much will you have to contribute each fortnightly pay period if you can earn 6% per year on your savings (compounded monthly)? You will start contributing a fortnight from today. For this example, the BA II Plus should be set to: x fortnightly (ie 365.25 days y14) = 26.0893 for P/Y x monthly C/Y x four decimal places, and x end of period payment.

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Enter three variables (FV, N and I/Y) and calculate the fourth (PMT). Press

Display

CE/C 2nd [CLR TVM] 40 2nd xP/Y N

0.0000 N = 1043.5714 FV = 750,000.0000 I/Y = 6.0000 PMT = -172.9883*

750 000 FV 6 I/Y CPT PMT

Description Set time value of money variables to zero. Enter the number of fortnights in 40 years Enter the future savings total. Enter interest rate per year of 6%. Calculate savings required per fortnight.

Calculating the Interest Rate Example 8: If you invest $300 at the end of each month for six years, for a promised return of $30,000 at the end, what interest rate are you earning on your investment? For this example, the BA II Plus should be set to: x monthly C/Y and P/Y x four decimal places, and x end of period payment. Enter three variables (FV, N and PMT) and calculate the fourth (I/Y). Press

Display

CE/C 2nd [CLR TVM] 72 N 30000 FV 300 +/- PMT CPT

I/Y

N FV PMT I/Y

0.0000 = 72.0000 = 30,000.0000 = -300.0000 = 10.5892*

Description Set time value of money variables to zero. Enter the number of months in six years Enter the future savings total. Enter investment amount per month of $300 Calculate I/Y (nominal rate compounded monthly)

Bond Valuation using the TVM Worksheet The BA II Plus financial calculator has more advanced bond functions available in the bond worksheet that we will not be using. We will use the calculator to compute values from the bond valuation formula that assumes the number of coupon payments is an integer (ie no fractional periods). Example 9: Assume the date is January 1, 2003 and you want to know the value of a bond that matures in 15 years (on January 1, 2018). The bond has a par value of $1,000 and a coupon rate of 8%, which is paid semi-annually. Your required rate of return is 10%. (NB The question is simply interpreted as finding the PV of a series of cash flows.) For this example, set the BA II Plus to: x semi-annual for P/Y and C/Y x two decimal places, and x end of period payment

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Press

Display 0.00

CE/C 2nd [CLR TVM] 30 N

N=

30.00

10 I/Y 40 PMT

I/Y = PMT =

10.00 40.00

1000 FV

FV = 1,000.00 PV = -846.28*

CPT PV

Description Set time value of money variables to zero. Enter 2 x15=30 the number of semi annual interest payments Enter annual nominal interest rate Enter the value ($40) of semi-annual coupon interest payments (cash inflows) ie (0.08x1,000)/2=40 Enter future par value as cash inflow Compute present value.

Computing the Yield to Maturity (YTM) on a Bond Example 10: What yield will you earn if you pay $1,100 for a bond that matures in 8 years with a par value of $1,000 and pays half-yearly coupon interest at a rate of 12% per year. For this example, check that the BA II Plus is set to: x semi-annual for P/Y and C/Y x four decimal places, and x end of period payment Press CE/C 2nd [CLR TVM] 1100 +/- PV 16 N

Display 0.0000

1000 FV 60 PMT

PV = -1,100.0000 N= 16.0000 FV = 1,000.0000 PMT = 60.0000

CPT I/Y

I/Y =

Description Set time value of money variables to zero.

Enter present cost (cash outflow) of bond Enter 2x8=16 number of semi annual periods Enter future par value as cash inflow Enter the value ($60) of semi-annual coupon interest (cash inflows) ie (0.12u1,000)/2 = 60 10.1451* Calculate YTM (nominal with semi-annual compounding)

Calculating Net Present Value (NPV) and Internal Rate of Return (IRR) Where cash flows are equal amounts each period (ie an annuity) the method used for bond valuation may be used to find the PV of cash flows and then the NPV is simply the (PV – Initial Cost). The IRR calculation is then done in the same way as the YTM calculation (using annual payment and compounding periods). Example 11: The firm is considering a capital project that would cost $80,000. The firm’s cost of capital is 12%. The project life is 10 years, during which time the firm expects to receive $15,000 per year. Calculate the NPV and IRR. For this example, check that the BA II Plus is set to: x annual P/Y and C/Y x four decimal places, and x end of period payment

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Press CE/C 2nd [CLR TVM] 10 N

12 I/Y 15,000 PMT CPT PV

80000 =. 80000 +/- PV

+/- -

CPT I/Y

Display 0.0000 N= 10.0000 I/Y = 12.0000 PMT = 15,000.0000 PV = -84,753.3454 4,753.3454* PV = -80,000.0000 I/Y= 13.4344*

Description Set time value of money variables to zero. Enter the number of payments received Enter annual interest rate Enter value of annual cash inflows ie $15,000 Compute present value. Compute NPV by comparing with initial cost. Set PV to cost for IRR calculation** Calculate IRR

** Recall that IRR is the rate that equates the PV of future cash flows with the initial outlay or cost. Where cash flows are unequal the Cash Flow worksheet is used to calculate the NPV and the IRR. While using this worksheet remember to look for small words and symbols that appear in the top line of the display. These help you to remember what you can and can’t do within the worksheet. More detailed instructions can be found in Chapter 4 of your BA II PlusTM guidebook. Example 12: The firm is considering a capital project that would cost $110,000. The firm’s cost of capital is 15%. The project life is 5 years with the following cash flows: -$25,000, $50,000, $60,000, $60,000, and $70,000. In addition you expect to receive $30,000 from salvage of the equipment. Calculate the NPV and IRR. To do this example you need to access and clear the Cash Flow worksheet, enter the data, compute the IRR, and compute the NPV using an interest rate per period (I) of 15%. Note that the calculator allows successive cash flows that are identical in amount to be input as one group using the frequency option. Press CF 2nd [CLR Work]

110000 +/- ENTER p 25000 +/- ENTER p. p 50000 ENTER p. p 60000 ENTER p 2 ENTER p

100000 ENTER

p. IRR CPT NPV

15 ENTER p

CPT

Display CFo = 0.0000 CFo = -110,000.0000 C01 = -25,000.0000 F01 = 1.0000 C02 = 50,000.0000 F02 = 1.0000 C03 = 60,000.0000 F03 = 2.0000

Description Access the worksheet and clear it Enter initial outlay ...