FCL 345: Computer Applications in Finance
Calculators

Calculator Procedures for Texas Instruments BAII Plus

I. Basics

  II. Single Payment Time Value of Money Problems:

a. FV or Future Value Problem: If $500 investment earned an annual interest rate of 10 percent with annual compounding what would its' value be in five years?

Enter number of years: n = 5
Enter interest rate: i = 10
Enter amount of investment: PV = 500 +/-
Not using payment key: PMT = 0
Calculate unknown: CPT FV, answer is $805.26

b. Pv or Present Value Problem: What amount would have to be invested for five years, earning an annual interest rate of 10 percent, to have $805.26? In other words, what is the present value of 805.26 discounted back five years at an annual rate of 10 percent.

d. Unkown: i. What annual percentage rate must $500 earn to grow to 805.26 at the end of 5 years.

III. Annuities. Time Value of Money Problems using multiple payments of equal value

a. Future Value of a Regular Annuity

What is the Future Value of 10 equal end of period payments of $100 each, invested at an annual interest rate of 10 percent

b. Unkown: Number of years.

c. Unkown: Interest rate needed

Once again, $1,593.74 is needed, and you know ahead of time that you have 10 years to obtain it. What annual interest rate would a $100 annuity have to earn for you to achieve this goal?

Clear time value of money memory: 2^nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1

Enter payment: PMT = 100
Enter Future Value: FV = 1593.74+/-
Enter Present Value: PV = 0
Enter number of years: n = 10
Calculate unknown: CPT i, answer is 9.999 (round to 10)

d. Unknown: Payment.

e. Present Value of a Regular Annuity

What is the present value of a 4 year annuity, with payments of $100 earning 10 percent annually?

Clear time value of money memory: 2^nd CLR TVM   
Compounding should remain at P/Y = 1 and C/Y = 1

        Enter number of years: n = 4
        Enter Interest Rate: i = 10
        Enter Payments: PMT = $100+/-
        Enter Future Value: FV = 0
        Calculate unknown: CPT PV, answer is $316.99

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*** The previous problems all deal with a regular annuities. The next set deals with an annuity due. The difference being that with an annuity due, payments are made at the beginning of the compounding periods.

IV. Annuities Due:  Time Value of Money Problems using equal beginning of period payments.

b. Unknown: Number of years

$1,753.12 is needed sometime in the future. How long, investing $100 per year, earning 10 percent annually, would it take to amass this amount of money?

c. Unkown: Interest rate needed

This time $1,500 is needed, and you know in advance that you have 10 years to obtain it. What annual interest rate would a $100 annuity due have to earn for you to achieve this goal?

d. Unknown: Payment

To obtain an amount of $3000.00 ten years from now, earning 10 percent annually, what amount would have to be invested on a yearly basis in an annuity due form?

 e. Present Value of an Annuity Due

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V.  Loan Amortization

The loan amortization function is used to find the remaining balance, principle, and interest paid, of a loan with equal end of the month payments.  A 36 month loan with an initial balance of $20,000 and an effective monthly interest rate of 2.00% will be used. 

Step 1 will be to find the amount of the 36 equal monthly payments.

Clear time value of money memory: 2^nd CLR TVM
Compounding should remain at P/Y = 1 and C/Y = 1

        Enter Present Value: PV = 20,000+/-
        Enter Future Value: FV = 0
        Enter number of periods: n = 36
        Enter interest rate: i = 2
        Calculate unknown: CPT PMT, answer is $784.657

Step 2 will be to find the amount of the 12th payment allocated to interest and the amount allocated to principle.     

2nd Amort (payment key)
P1 = 12 (enter, down arrow)
P2 = 12 (enter, down arrow)
The screen should now read BAL = -14,840.95, which is the remaining balance of the loan
Press the down arrow again, the screen should now read PRN = 478.27, this is the amount of the payment
assigned to principle.
Press the down arrow again, the screen should now read INT = 306.38, this is the amount of the payment assigned
to pay off interest.

This can be used to find information on any payment in the sequence.   Just repeat the process entering different values for
P1 and P2.

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VI.  Interest Rate Conversion

: The interest conversion function can be used when either the nominal interest rate is given, and the annual effective interest rate is needed, or when the annual effective rate is given and the nominal rate is needed.

To use this function, begin by pressing 2^nd I Conv (#2 key), and then 2^nd CLR Work to erase any old material.

a. A certificate offers a nominal interest rate of 5% with quarterly compounding. What is the annual effective interest rate?

Enter Nominal rate: NOM = 5
Press down arrow twice
Enter quarterly compounding: C/Y = 4
Press up arrow once
Compute unknown EFF: answer is 5.09%

This process can be reversed, for example, to find the Nominal rate when the Effective rate is given.

2. A certificate offers an annual effective interest rate of 6% with quarterly compounding. What is the nominal interest rate?

2^nd CLR Work
Enter effective interest rate: EFF = 6
Press down arrow once
Compounding should still be set at: C/Y = 4
Press down arrow once
Compute unknown NOM: answer is 5.87%

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XII.  NPV and IRR: Using the Cash Flow Register.

3 KEYS:

CF: used to enter even or uneven cashflows. The up and down arrows move between sequential CF and Frequency entries.

NPV: The NPV key is used to compute the net present value of a stream of cashflows. After the stream has been inputed, an interest rate must be entered to discount the cashflow. Once all the factors are present, the NPV can be computed.

IRR: The IRR button is used to compute the internal rate of return. This being the rate at which the NPV equals zero.

Finding the NPV and the IRR of a stream of uneven cashflows.

Beginning with a cash outflow (investment) of $400, a project will result in 4 inflows of unequal amounts, spaced evenly, of 100, 200, 200, and 300 dollars.

CF, 2^nd CLR Work
CF0 = 400+/-
CO1 = 100
FO1 = 1 (default)
CO2 = 200
FO2 = 2, sets frequency of cashflow #2 at 2
CO3 = 300

Press the NPV button and enter 10 for the rate the CF’s will be discounted at.   Press the down arrow and then compute.  The screen shoulc display NPV = 211.365.  Press the IRR key and the calculator will auto-compute displaying a figure of 28.9.  At a discount rate of 28.9% the net present value of the cash flows will equal 0.

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The Bond Worksheet can be used to find either the yield or the price of a bond. The Worksheet can be opened by pressing 2^nd Bond (key #5). The up and down arrows will move between entries.

Information needed:

SDT: Settlement date – this is the date at the time of purchase

CPN: Annual coupon rate in percent form

RDT: Redemption date – the date the bond matures

RV: Redemtion value

ACT: The default setting on the calculator is actual, which is actual/actual and is commonly used. The other option is to use a 30/360 setting which assumes 30 days in a month and 360 days in a year. It can be changed by pressing 2^nd  SET.

2/Y: Since a majority of bonds in the U.S. pay a biannual coupon, this is the default setting on the calculator. It can be changed to 1/Y by pressing 2^nd SET.

YLD: Yield to redemption

PRI: Dollar price of the bond

To calculate the Yield To Maturity

What is the yield of a bond with a coupon rate of 8 that matures in November of the year 2021, with a current price of $127.594, and a redemtion value of $100?

The two date entries should be made in a MM.DDYY format. February 24, 1998 should be entered as 2.2498. For this example, 2-24-98 will be used.

SDT = 2 – 24 – 1998 (2.2498 enter)

CPN = 8

RDT = 11 – 15 – 2021 (11.1521 enter)

RV = 100

ACT, 2/Y – should be at the default settings

PRI = 127.594

YLD = Calculate unknown, answer is 5.836

If the yield is given and the current price unknown, simply enter the yield first and then calculate the price.

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XI.  Data Entry

To enter statistical data:

Begin by pressing 2nd Data.  X01 = should appear on the screen.  The calculator allows for two variables, X and Y, to be entered for the regression function, but only the X variable will be used for this data entry example. 

The yearly return on the Market over a period of five years is given:

            Year                 Market Return
                1                          23.8%
                2                           (7.2)
                3                            6.6
                4                          20.5
                5                          30.6
               
Using the up and down arrows, enter the data as follows:
(Press the enter key after each entry)

X01 = 23.8
Y01 = 1
X02 = 7.2+/-
Y02 = 1
X03 = 6.6
Y03 = 1
X04 = 20.5
Y04 = 1
X05 = 30.6

Now that the single variable data has been entered, the next step is to perform the statistical calculations.

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X.  Statistics

Begin by pressing 2nd Stat to retrieve the statistics worksheet.  The BAII Plus has Five different types of analysis it can perform.  2nd SET will scroll through them.

LIN:  Standard Linear Regression
Ln:  Logarithmic Regression
EXP:  Exponential Regression
PWR:  Power Regression
1 - V:  One-Variable statistics

Since we have only entered figures for the x variable at this point, choose the one-variable statistics setting, 1- V.  The calculator will auto-compute the figures as you scroll through using the up and down arrows.

Number of observations: n = 5
Sample Mean: Xbar = 14.86
Sample standard deviation: Sx = 15.11

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XI.  Regression

To perform a Linear Regression analysis, a second  variable needs to be added.   In this case, the yearly return on Stock J.  Leave the X variables, but change each of the Y variables from 1 to the following( 2nd Data. . .):

     Year                        Return on Stock J
       1 (Y01)                          38.6%
       2 (Y02)                         (24.7)
       3 (Y03)                          12.3
       4 (Y04)                            8.2
       5 (Y05)                          40.1

To perform the regression, press 2nd Stat followed by 2nd SET, scrolling through and selecting LIN for linear regression.
Also press 2nd CLR Work to erase any old data.  Scrolling throught using the down arrow, the calculator should compute the following figures:

     n   = 5     
Xbar  = 14.86
   Sx   = 15.119
Ybar  = 14.9
  Sy    = 26.535
     a   = -8.922
     b   = 1.603
     r    = 0.913

Plugging these figures into the linear equation Y = a + bX we get Y = -8.922 + 1.603X, which can be used to predict a Y variable given the X variable and an X variable given a Y variable.  This can be done manually or the BAII Plus will compute for you. Continue scrolling down until the screen displays X = 0. 

Suppose the market is predicted to have a 10% return the following year.  Enter this as the X variable then press the down arrow  and compute.  The screen should display Y = 7.1089.  This would be the return on stock J if the predicted market return was correct. 

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Created by Roger Severance (Undergraduate Independent Study Project, 1998)
Last Updated on 4 June 1999
Email any comments to: robert.balik@wmich.edu