Do you want to master your Texas Instruments BA II Plus calculator and unlock the power of present value calculations? You're in the right place! Understanding present value (PV) is a cornerstone of finance, allowing you to compare investments, analyze cash flows, and make informed decisions. This comprehensive guide will walk you through every step of calculating present value on your BA II Plus, engaging you from the very beginning.
Let's dive in and transform you into a PV pro!
Step 1: Familiarizing Yourself with Your Texas Instruments BA II Plus
Before we jump into calculations, let's make sure you're comfortable with your calculator. Pick up your BA II Plus. Feel its buttons. Notice the different sections. The more familiar you are, the smoother your calculations will be.
Key Financial TVM (Time Value of Money) Buttons:
N: Number of periods (often years or months)
I/Y: Interest rate per year (or period)
PV: Present Value (this is what we're solving for!)
PMT: Payment (for annuities or recurring payments)
FV: Future Value (the value of an investment at a future date)
CPT: Compute (used to calculate the unknown variable)
Clearing Memory: It's crucial to clear any previous calculations from your calculator's memory before starting a new problem. This prevents errors.
Press 2ND then CLR TVM (which is above the FV button). You should see "0.00" or similar on the display.
Alternatively, you can press 2ND then CLR WORK (above the CPT button) to clear specific work registers, but CLR TVM is generally sufficient for TVM problems.
Step 2: Understanding Present Value (PV) – The Core Concept
What is Present Value? Present value is the current worth of a future sum of money or stream of cash flows, given a specified rate of return. In simpler terms, it answers the question: "How much would I need to invest today to have a certain amount of money in the future?" It's the opposite of future value.
Why is PV Important?
Investment Decisions: Helps compare different investment opportunities with varying future payoffs.
Loan Analysis: Used to determine the principal amount of a loan based on future payments.
Valuation: Essential for valuing assets, businesses, and projects.
Financial Planning: Assists in planning for retirement, education, or other future financial goals.
Step 3: Setting Up Your Calculator for PV Calculations
The BA II Plus has two main modes for calculating payments: END mode and BGN mode.
END Mode vs. BGN Mode:
END Mode (Default): Payments are assumed to occur at the end of each period. This is the most common setting for loans, bonds, and many investments.
BGN Mode: Payments are assumed to occur at the beginning of each period. This is used for annuities due, like lease payments or rent, where payments are made upfront.
Checking and Changing the Payment Mode:
Look at your calculator's display. If you see "BGN" in the top right corner, you are in BGN mode. If you don't see anything, you are in END mode.
To switch modes: Press 2ND then BGN (above the PMT button).
Then press 2ND then SET (above the ENTER button).
The display will toggle between "END" and "BGN". Press 2ND then QUIT (above the CPT button) to exit. For most present value calculations where we're finding the present value of a single future sum, the payment mode doesn't matter, as PMT will be zero. However, it's good practice to be aware of it.
Step 4: Calculating Present Value of a Single Future Sum (Lump Sum)
This is the most fundamental PV calculation. You know a future amount and want to find its worth today.
Scenario: You want to have $10,000 in 5 years. Your investment earns an annual interest rate of 7%. How much do you need to invest today?
Step-by-Step Input:
Clear TVM: Press 2ND then CLR TVM.
Enter N (Number of Periods):
Type 5
Press N
Enter I/Y (Interest Rate per Year):
Type 7 (enter as a whole number, not a decimal)
Press I/Y
Enter FV (Future Value):
Type 10000
Press FV
Enter PMT (Payment): For a single lump sum, there are no recurring payments.
Type 0
Press PMT
Compute PV (Present Value):
Press CPT
Press PV
Result: You should see a negative value, approximately -7,129.86. The negative sign indicates an outflow of cash (an investment) to receive a future inflow. So, you would need to invest $7,129.86 today.
Step 5: Calculating Present Value of an Ordinary Annuity
An ordinary annuity involves a series of equal payments made at the end of each period.
Scenario: You will receive $500 at the end of each year for the next 4 years. The discount rate is 6% per year. What is the present value of this annuity?
Step-by-Step Input:
Clear TVM: Press 2ND then CLR TVM.
Ensure END Mode: If you're not sure, refer back to Step 3 to confirm your calculator is in END mode.
Enter N:
Type 4
Press N
Enter I/Y:
Type 6
Press I/Y
Enter PMT (Payment): This is the recurring payment.
Type 500
Press PMT
Enter FV (Future Value): Since these are the only payments and there's no additional lump sum at the end, FV is 0.
Type 0
Press FV
Compute PV:
Press CPT
Press PV
Result: You should get approximately -1,732.55. This means the right to receive these future payments is worth $1,732.55 today.
Step 6: Calculating Present Value of an Annuity Due
An annuity due involves a series of equal payments made at the beginning of each period.
Scenario: You will receive $500 at the beginning of each year for the next 4 years. The discount rate is 6% per year. What is the present value of this annuity due?
Step-by-Step Input:
Clear TVM: Press 2ND then CLR TVM.
Set to BGN Mode:
Press 2ND then BGN
Press 2ND then SET (the display should show "BGN")
Press 2ND then QUIT
Enter N:
Type 4
Press N
Enter I/Y:
Type 6
Press I/Y
Enter PMT:
Type 500
Press PMT
Enter FV:
Type 0
Press FV
Compute PV:
Press CPT
Press PV
Result: You should get approximately -1,836.50. Notice it's higher than the ordinary annuity because you receive the payments sooner.
Important Note: After completing an annuity due calculation, always remember to switch your calculator back to END mode unless you specifically need BGN mode for your next calculation. This prevents errors in subsequent problems.
To switch back to END mode: Press 2ND then BGN, then 2ND then SET, then 2ND then QUIT.
Step 7: Handling Compounding Periods Other Than Annual
Often, interest is compounded more frequently than once a year (e.g., semi-annually, quarterly, monthly). You need to adjust N and I/Y accordingly.
Key Adjustments:
N: Multiply the number of years by the number of compounding periods per year.
I/Y: Divide the annual interest rate by the number of compounding periods per year.
Scenario: You want to have $10,000 in 5 years, and your investment earns an annual interest rate of 6% compounded monthly. How much do you need to invest today?
Step-by-Step Input:
Clear TVM: Press 2ND then CLR TVM.
Calculate N (Monthly): 5 years * 12 months/year = 60 months
Type 60
Press N
Calculate I/Y (Monthly): 6% annual / 12 months/year = 0.5% per month
Type 0.5
Press I/Y
Enter FV:
Type 10000
Press FV
Enter PMT:
Type 0
Press PMT
Compute PV:
Press CPT
Press PV
Result: You should get approximately -7,413.72. Compounding more frequently leads to a slightly higher present value (you need to invest less today) because your money earns interest more often.
Step 8: Understanding the Cash Flow (CF) Worksheet for Uneven Cash Flows
Sometimes, you'll encounter situations where cash flows are not equal. The CF worksheet is your best friend here.
Scenario: You expect to receive the following cash flows:
Year 1: $1,000
Year 2: $1,500
Year 3: $800 The discount rate is 8%. What is the present value of this uneven cash flow stream?
Step-by-Step Input:
Clear Memory: Press 2ND then CLR WORK (above CPT). It's good practice to clear the work registers when using the CF worksheet.
Enter CF0 (Initial Cash Flow): For this problem, there's no initial cash flow.
Type 0
Press CFo (above the CE/C button)
Press ENTER
Press the down arrow key
Enter C01 (Cash Flow 1):
Type 1000
Press C01
Press ENTER
Press the down arrow key
Enter F01 (Frequency of Cash Flow 1): Since it occurs only once, the frequency is 1 (this is the default).
Press down arrow key (no need to change if it's 1)
Enter C02 (Cash Flow 2):
Type 1500
Press C02
Press ENTER
Press the down arrow key
Enter F02 (Frequency of Cash Flow 2):
Press down arrow key
Enter C03 (Cash Flow 3):
Type 800
Press C03
Press ENTER
Press the down arrow key
Enter F03 (Frequency of Cash Flow 3):
Press down arrow key
Compute NPV (Net Present Value):
Press NPV (above the CPT button)
Enter I (Interest Rate):
Type 8 (enter as a whole number)
Press ENTER
Press the down arrow key
Press CPT
Result: You should get approximately 2,836.06. This is the present value of the uneven cash flow stream.
Step 9: Practicing and Troubleshooting
The key to mastering your BA II Plus is practice! Work through various examples from textbooks, online resources, or real-life scenarios.
Common Errors and Troubleshooting:
Not Clearing Memory: Always start with 2ND CLR TVM or 2ND CLR WORK.
Incorrect Mode (END vs. BGN): Double-check your payment mode, especially for annuity problems.
Incorrectly Entering I/Y: Remember to enter the interest rate as a whole number (e.g., 7 for 7%).
Sign Conventions: Present Value (PV) and Future Value (FV) often have opposite signs. If you invest money (outflow), PV will be negative. If you receive money (inflow), FV will be positive. The calculator adheres to this cash flow convention.
Compounding Periods: Don't forget to adjust N and I/Y for non-annual compounding.
Misplacing PMT and FV: Understand when a value is a recurring payment (PMT) versus a single future amount (FV).
By consistently practicing and paying attention to these details, you'll become incredibly proficient with your BA II Plus.
Frequently Asked Questions (FAQs)
How to clear the TVM memory on the BA II Plus?
To clear the TVM memory, press 2ND then CLR TVM (located above the FV button).
How to switch between END and BGN payment modes on the BA II Plus?
Press 2ND then BGN, then 2ND then SET. The display will toggle between "END" and "BGN." Press 2ND then QUIT to exit.
How to enter an interest rate (I/Y) on the BA II Plus?
Enter the interest rate as a whole number (e.g., type 5 for 5%, not 0.05).
How to handle semi-annual compounding for present value on the BA II Plus?
Divide the annual interest rate by 2 for I/Y, and multiply the number of years by 2 for N.
How to calculate the present value of a perpetuity on the BA II Plus?
The BA II Plus doesn't have a direct perpetuity function. You can approximate it by using a very large N (e.g., 9999) or calculate it manually using the formula: PV = Payment / Interest Rate.
How to use the cash flow (CF) worksheet for uneven cash flows on the BA II Plus?
Press CF, enter CF0, C01, F01, etc., using the ENTER and arrow keys. Then press NPV, enter I, and press CPT.
How to interpret a negative present value result on the BA II Plus?
A negative present value typically indicates an initial cash outflow or investment required to achieve a future positive cash flow.
How to fix "ERROR 5" on the BA II Plus during present value calculations?
"Error 5" often means you're trying to compute a variable without enough other variables entered, or an impossible scenario (e.g., all values are zero). Ensure at least three of the TVM variables (N, I/Y, PMT, FV) are entered before computing PV.
How to reset the BA II Plus to factory settings?
Press 2ND then RESET (above the ENTER button). Then press ENTER. This will clear all memory and reset settings to default.
How to find the exact present value without rounding on the BA II Plus?
The BA II Plus displays rounded values, but it stores full precision. To see more decimal places, you can adjust the decimal settings (2ND then FORMAT), but for calculations, the internal precision is always used.
