Brief Tutorial for the Texas Instruments BAII PLUS Part One By John Stansfield, CFA, Ph D, MBA, and calculator enthusiast.
The Texas Instruments BAII PLUS is the only calculator for the well-dressed finance geek. Seriously it’s the only one for a serious student of finance. Unfortunately the manual runs 142 pages. This document is not meant to replace that book but rather to give you a look around the tool box. Our first chapter this semester (Chapter 4 of the book) is all about the time value of money. After reading this chapter and going to class, you should be able to:
1. Use the Time Value of Money (TVM) keys a. Get into the habit of checking the
payments per year
b. Know what to do with the begin/end mode
2. Use your cash flow keys to solve for a. IRR
b. NPV
c. Realize that you have to specify the correct periodic rate in your cash flow menu
3. Use the interest rate conversion menu 4. Use the amortization menu
This document is intended to give you a “Fast Start” on these functions of your calculator. This tutorial is designed to get you comfortable and familiar with the following:
• The Time Value of Money keys: N , I/Y , PV , PMT, and FV , their associated second functions: [×P/Y], [P/Y], [AMORT], [BGN] and [CLR TVM].
• The cash flow menu: CF , NPV , and IRR .
• The interest rate conversion menu: [ICONV].
• How to clear out the whole calculator 2nd [RESET] ENTER 2nd [QUIT]. • and how to clear out parts: [CLR TVM], [CLR WORK].
We will start with [RESET].
BEFORE YOU CAN DO ANYTHING WITH THIS CALCULATOR YOU MUST LEARN THE RITUAL OF CALCULATOR PURIFICATION.
Press the 2nd button (it’s the second from the top on the left hand side). It’s colored yellow or light green on your calculator. Press the [RESET] key (it’s “behind” the +/– key). Now your calculator will ask you if you’re serious about resetting it: the display will read “RST ?” and the “ENTER”
annunciator will be lighted. Hit the ENTER key and your calculator will display “RST” and 0.00. To get out of this menu (or any menu) press 2nd [QUIT].
What this does is to reset all of your default settings and clear all data. Now your calculator is set the same as the day it came out of the package.
You should get into the habit of resetting or clearing the registers of your calculator on every problem. If you don’t, your calculator might give you the wrong answer because you left some data in there somewhere. “Clearing” just your last entry is done with CE/C , clearing the time value of money keys is [CLR TVM], and clearing the cash flow menu is done with [CLR WORK].
I wrote this tutorial for you to be able to follow along with your calculator out. When you begin a new section please enter 2nd [RESET] ENTER 2nd [QUIT] so that your calculator will look like
mine and (hopefully) you will get the same answers as me.
If you are ever frustrated that you can’t get your calculator to work properly please enter
2nd [RESET] ENTER 2nd [QUIT] and start over.
Flogging you calculator without performing the ritual purification is a waste of time. I The Time Value of Money Keys
Notice the third row of keys. The keys are N , I/Y , PV , PMT, and FV . These keys are related by the following formula:
PV PMT r PMT r r FV r N N = − + + + (1 ) (1 )
That formula is in my study guide on chapter 4 (and 5) and by the way, r = I/Y.
Basically, if you enter values for any four of these variables, the calculator will compute the fifth. The next five examples solve for are N , I/Y , PV , PMT, and FV when the fact pattern of the problem gives the values of the other four variables.
Here’s what the variables mean:
N The number of payments made (e.g. for a 30-year mortgage with monthly payments, N = 360) I/Y The interest rate expressed as an APR (again, this is r in the above formula)
PV The present value PMT The periodic payment
FV The future value
Before we can do these problems we may need to do a little housekeeping. Perform the ritual
calculator purification and enter 2nd I/Y. Your calculator will display either P/Y = 12.00 or P/Y =
1.00. It depends on when your calculator was manufactured. Old, stale, filthy disgusting used calculators have a default of 12 payments per year. New tasty fresh calculators have a default of one payment per year. Seriously one type isn’t better than another—just get into the habit of making the payments per year match the problem at hand. Set it to 12 payments per year for a monthly car loan and two payments per year for a bond that pays interest semiannually. More on this topic later in section 1a Setting the Number of Payments per Year.
For now, just so you can follow along with the first few problems, enter 12 and press ENTER . Your calculator will display P/Y = 12.00; to get out of this menu, hit the [QUIT] key (i.e. 2nd CPT.)
Problem 1
Let’s start with an auto loan with monthly payments. If you borrow $20,000 for 36 months at 5 percent APR, what will be the size of your monthly payment?
Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 36
I/Y 5 (again, this is r in the above formula) PV 20,000
CPT PMT
Now if you hit CPT and PMT the calculator will display PMT = –599.42
What that means is that if the bank gives you $20,000 today, you have to give the bank $599.42 at the end of every month for the next three years. Your calculator has had a bit of economic training, that’s why this answer is negative. You see, money going away from you is negative and money coming at you is positive. Just like in real life.
If you didn’t get a payment of $599.42 your calculator might still be in one payment per year. To fix that enter 2nd I/Y enter 12 and press ENTER . Your calculator will display P/Y = 12.00; to get out of
this menu, hit the [QUIT] key.
Let’s clear out our calculator and try another one. Problem 2
How about saving for retirement? How much money will you have after 30 years if you invest $180 per month into an IRA that earns 8 percent APR?
Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 360 = 30 × 12 I/Y 8
PV Leave blank PMT –180
CPT FV
Now if you hit CPT and FV the calculator will display FV = 268,264.70
By the way, if your calculator displays FV = 49,550.11 it’s not because you’re a bad person. It’s because you did a bad thing—you failed to perform the ritual purification. You should get into the habit of resetting your calculator or clearing your calculator on every problem. If you don’t clear out your calculator it might give you the wrong answer because you left some data in there somewhere. If you see FV = 5,955.99 you did 30 months, not 30 years.
Problem 3
Suppose you charge $5,000 on your credit card and want to make a monthly payment of $150 at the end of each month. If your interest rate is 24% APR, how long will it take you to get out of debt? Please enter 2nd [RESET] ENTER 2nd [QUIT].
CPT N I/Y 24 PV 5,000 PMT –150
FV Leave empty
Now if you hit CPT and N the calculator will display N = 55.48. That means that will take 4 years, 8 months to get out of debt:
55.48 months
4.62 years 12 months per year
12 months
0.62 years = 7.48 months (round up to 8 months) year
=
By the way, if your answer is –25.80 you’re doing this wrong. (You need to have payment be a
negative number.) You probably don’t need Stephen Hawking to tell you that negative time is probably something to worry about. Wide awake and worried.
If N = 237.51 then you didn’t clear out your calculator from the last problem. Try [CLR TVM], this clears out: N , I/Y , PV , PMT , and FV , but leaves [ P/Y] alone.
Problem 4
What would you be willing to pay for a promise to receive $100 per month for five years? The interest rate is 5 percent APR. Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 60 = 5 years × 12 payments per year. Try this: enter 5 then [×P/Y] to get 60 then hit N. I/Y 5
CPT PV
PMT 100
FV Leave empty
Now if you hit CPT and PV the calculator will display PV = –5,299.07. That means that you would have to pay $5,299.07 today to buy this annuity.
Problem 5
You don’t have this month’s rent check of $350, but your roommate offers to loan you the $350 if you agree to pay him $375 in one month. What rate of interest is he charging?
Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 1 CPT I/Y
PV 350 your roommate gives you $350 so this is money coming at you
PMT –375 you have to pay your roommate back, so that makes this cash flow negative FV Leave empty
Now if you hit CPT and I/Y the calculator will display I/Y = 85.71. That means that you should only agree to this loan if your other options have an APR of at least 85.71%.
By the way if you got “Error 5” as an answer it’s because you didn’t have a negative sign on your payment. (There’s no “dude, get a new roomie” message.)
Those five problems pretty much beat to death the time value of money keys as far as monthly loans with end-of-month payments go. Keep in mind that your entries have to make economic sense—you can’t evaluate the interest rate on a “loan” that gives you $350 today and then gives you $375 one month from now. Of the PV , PMT , and FV keys, at least one of them has to be negative.
There are two important details though: setting the number of payments per year and mastering the mysteries of begin mode.
1a Setting the Number of Payments per Year.
What can we do with loans that have annual payments? The answer is to set the number of payments per year to one. The default on your calculator is either 12 payments per year or one payment per year, depending upon when and where your calculator was manufactured. Clear out your calculator and enter 2nd I/Y. Your calculator will display either P/Y = 12.00 or P/Y = 1.00. Enter 1 and ENTER .
Your calculator will display P/Y = 1.00; to get out of this menu, hit the [QUIT] key (i.e. 2nd CPT.)
Now we can use the time value of money keys for annual payment problems instead of monthly payment problems.
If you save $2,000 per year in an IRA that earns 10% per year, how much will you accumulate in 40 years? Your first payment is in one year. Please enter 2nd [RESET] ENTER 2nd [QUIT]. Then get
into 1 payment per year: 2nd I/Y 11 ENTER 2nd [QUIT]
N 40
Now if you hit CPT and FV the calculator will display FV = 885,185.11 Any other type of compounding (monthly, weekly, annual, semiannual whatever) works, as long as you set the number of payments per year. I/Y 10
PV 0 PMT –2,000
FV compute
Mastering the Mysteries of Begin Mode.
Reconsider the preceding example: If you save $2,000 per year in an IRA that earns 10% per year, how much will you accumulate in 40 years? Your first payment is not in one year, but rather today. If we really thought about the time line, we’re just shifting all the payments back one year. So our FV will just be FV = $885,185.11 × 1.10 = $973,703.62
Our calculator will save us a bit of thinking if we just set it for begin mode. The keystrokes are
2nd [BGN] (look under PMT ) the display shows END and in tiny letters SET. Hit 2nd [SET] the display
will show BGN and in tiny letters “SET” and “BGN”. Enter 2nd [QUIT] and you’re out of there. Now your
calculator will show just the begin annunciator (BGN) to remind you that you’re in begin mode. Kind of
like the check engine light on your car, it’s not much of a warning, but it is there. N 40
I/Y 10 PV 0 PMT –2,000 CPT FV
Now if you hit CPT and FV the calculator will display FV = 973,703.62
How cool is that? Anyway, lots of situations are begin mode problems. Two examples are car leases and apartment leases. Suppose you decide to lease a Mini Cooper. The car is worth $25,000 and interest rates are 9% APR. If the lease lasts for 60 months, what is the amount of the lease payment? The first payment is due at lease signing.
Stay in begin mode. Make sure that you’re in 12 payments per year.
N 60 Now if you hit CPT and PMT the calculator will display PMT = –515.10. If you got 515.96 you’re in end mode. If you got 2,076.01 you’re in 1 payment per year.
Be sure to clear out your calculator before each problem. I/Y 9
PV 25,000 CPT PMT
2 Using the Cash Flow Keys
Not all investments have nice even cash flows. Consider a proposal to open a gold mine. The size and timing of the cash flows are shown below:
Year 0 Year 1 Year 2 Year 3
–$800,000 $500,000 $1,000,000 –$500,000
Opening the mine costs $800,000. In one year we make $500,000, the year after that we make a million dollars and in year three we have to shut down the mine and pay reclamation costs of half a million dollars.
If we undertake this investment, what is our rate of return? We could algebrate our way solving this for r:
3 2 (1 ) 000 , 500 $ ) 1 ( 000 , 000 , 1 $ ) 1 ( 000 , 500 $ 000 , 800 $ r r r + + − + + =
That looks like work, being a third degree polynomial and all. Instead let’s use the cash flow keys. Please enter 2nd [RESET] ENTER 2nd [QUIT].
Find the CF key next to the 2nd key.
The calculator display shows CF0 = 0.00. Type 800,000 +/– and push ENTER. Use the down arrow key, ↓ , (next to ON/OFF) to enter the next three cash flows. 500,000 ENTER C01 = 500,000 ↓ ,
F01 = 1.00 ↓ , (by the way, this means the frequency of the first cash flow is just once) 1,000,000 ENTER C02 = 1,000,000 ↓ ,
F02 = 1.00 ↓ ,
+/– 500,000 ENTER C03 = –500,000 ↓ , F03 = 1.00 ↓ ,
To find the rate of return, hit the IRR key then CPT
The display should read IRR = 22.84. If you don’t believe me, evaluate the right hand side of this equation: 3 2 (1.2284) 000 , 500 $ ) 2284 . 1 ( 000 , 000 , 1 $ ) 2284 . 1 ( 000 , 500 $ 000 , 800 $ = + −
The great thing about this calculator is that when you’re in the cash flow menu you can use the ↓. .↑. keys to navigate up and down through the cash flows to double check your data entry.
Suppose on the same problem, your interest rate is 15 percent. What is the Net Present Value of the project? Find the NPV key. Enter 15 for the interest rate. 15 ENTER The display should show I = 15.00 Hit the ↓. key. The display should show NPV = 0.00. Hit the CPT key to compute net present value.
The display should show NPV = 62,168.16. To convince yourself, you could check the following:
3 2 (1.15) 000 , 500 $ ) 15 . 1 ( 000 , 000 , 1 $ ) 15 . 1 ( 000 , 500 $ 000 , 800 $ 16 . 168 , 62 $ =− + + −
By the way, one more thing about the cash flow menu. It is not on the same payments per year plan as the time value of money keys. That is you did not have to set P/Y = 1 to get the results on the last page. That’s fine if the cash flows are annual, but what if the cash flows are monthly? We just have to use the right discount rate. The right discount rate is the monthly rate.
Suppose your friendly furniture dealer offers to sell you a $5,000 bedroom suite on the following terms: Make no payment for six months, then pay $450 per month for 12 months. What rate of interest (APR) is being extended? Please enter 2nd [RESET] ENTER 2nd [QUIT].
Then enter the cash flows CF0 5,000
CF1 0
F01 5 (see the time line) CF2 –450
F02 12
When you compute the IRR the result is 0.67 the correct interpretation is that this is a loan with a MONTHLY interest rate of 0.67. The APR = 0.67 × 12 = 8.09%
0 1 2 3 4 5 $5,000 0 0 0 0 0 6 7 8 9 10 11 –$450 –$450 –$450 –$450 –$450 –$450 12 13 14 15 16 17 –$450 –$450 –$450 –$450 –$450 –$450 18 19 … 0 0
3. Interest Rate Conversion Menu [ICONV] First some background:
Suppose you are offered an investment that costs $1,000 today and promises to pay $2,000 in 5 years. What rate of return are you earning?
Please enter 2nd [RESET] ENTER 2nd [QUIT].
If your calculator is in 12 payments per year you would enter N 60
CPT I/Y
PV –1,000 PMT 0
FV 2,000
Now if you hit CPT and I/Y the calculator will display I/Y = 13.94 But if you were in 1 payment per year your results would be different:
N 5 CPT I/Y
PV –1,000 PMT 0
FV 2,000
Now if you hit CPT and I/Y the calculator will display I/Y = 14.87
What’s going on here? Well 13.94 percent and 14.87 percent are both the right answers …
… the right answers to different questions, that is. 13.94 percent is the Annual Percentage Rate (APR) of this loan (if the loan has monthly
compounding). 14.87 percent is the Effective Annual Rate (EAR). The Effective Annual Rate has economic significance, the APR has legal significance. In the U.S., lenders are required by law to disclose the APR of any loan. APRs are handy and easy. That’s why you see them in TV commercials. As financial economists, we should be interested in economic significance.
If you know the number of compounding periods you can easily go back and forth between APR and EAR. In fact, your calculator has a special menu to convert between these interest rates—it’s called the Interest Rate Conversion Menu [ICONV].
Open up the [ICONV] menu (it’s hiding out under the number 2).
The display shows NOM = 0.00. Enter 13.94. Now use the down arrow key, ↓ , (next to the ON/OFF
key). The display now shows EFF = 0.00. Hit the CPT key to see EFF = 14.87
Consider a loan with monthly compounding and an APR of 12%. This is really a loan with a monthly rate of 1%. If you borrowed $1,000 in one year you would owe $1,126.83
N 12 I/Y 12 PV 1,000 PMT 0
If this was an economically identical loan with annual compounding, the interest rate would obviously be 12.683% since r = 12.683% solves the equation:
$1,126.83 = $1,000 × (1 + r) Another way of finding r = 12.683% is to solve the following:
(1.01)12 = 1 + r
An APR of 12% with monthly compounding is another way of saying a 12-month loan with interest charged at 1% per month.
Open up the [ICONV] menu.
The display shows NOM = 0.00. Enter 12. Now use the down arrow key, ↓ . The display now shows EFF=0.00. Hit CPT to see EFF = 12.68
Hit ↓ again. The display shows C/Y = 12.00. That is the default setting for the number of
compounding periods per year. Since most loans in the U.S. have monthly payments the engineers at Texas Instruments must have decided to make all the defaults work with the type of loan that we see a lot of. We can change to C/Y = 2 if we had a loan with semi-annual payments or C/Y = 52 if we had a loan with weekly payments
When do you use APR and EAR? Well if you’re comparing two loans that are identical in terms of the number of payments per year, you can use either. But if you’re comparing loans with different
numbers of payments per year, you really have to go with EAR.
Which loan is the better deal? Borrow $1,000,000 for one year at 10% APR with monthly compounding or borrow $1,000,000 at 9.98% APR with weekly compounding?
The 9.98% APR is actually the more expensive:
[ICONV] since the default is 12 payments per year, let’s do this one first. NOM = 10.00 ↓ ,
EFF = 10.47
To evaluate the effective annual rate on the second loan
[ICONV] First, change to 52 payments per year by hitting the up arrow, ↑ . C/Y = 52 ↓ ,
NOM = 9.98 ↓ , EFF = 10.48
The payment at the end of the year is only $1,104,713.07 with the 10 percent loan with monthly compounding but is $1,104,844.23 with the 9.98 percent APR loan with weekly compounding:
N 12 I/Y 10 PV 1,000,000 PMT 0 FV –1,104,713.07 N 52 I/Y 9.98 PV 1,000,000 PMT 0 FV –1,104,844.23
4. AMORT menu
Most consumer loans in the U.S. are amortizing. The level payment that you commit yourself to has an interesting feature: while the size of the payment is constant, the amount of each payment that is interest and principal varies with each payment. Consider the following loan: You borrow $1,000 and agree to repay $87.92 at the end of each of the next 12 months. Your interest rate is 10% APR. Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 12 I/Y 10 PV 1,000 PMT 0 CPT FV –87.92
Month Payment Interest Principal Loan Balance
1 $87.92 = $8.33 + $79.59 $920.41 = $1,000.00 – $79.59 2 $87.92 = $7.67 + $80.25 $840.16 = $920.41 – $80.25 3 $87.92 = $7.00 + $80.92 $759.24 = $840.16 – $80.92 4 $87.92 = $6.33 + $81.59 $677.65 = $759.24 – $81.59 5 $87.92 = $5.65 + $82.27 $595.38 = $677.65 – $82.27 6 $87.92 = $4.96 + $82.96 $512.42 = $595.38 – $82.96 7 $87.92 = $4.27 + $83.65 $428.77 = $512.42 – $83.65 8 $87.92 = $3.57 + $84.35 $344.42 = $428.77 – $84.35 9 $87.92 = $2.87 + $85.05 $259.37 = $344.42 – $85.05 10 $87.92 = $2.16 + $85.76 $173.62 = $259.37 – $85.76 11 $87.92 = $1.45 + $86.47 $87.14 = $173.62 – $86.47 12 $87.87 = $0.73 + $87.14 $0.00 = $87.14 – $87.14
The calculations are straightforward applications of our earlier work. Consider the first payment. The interest expense is $8.33 = $1,000 × 0.10
12
This result can also be found using the time value of money menu:
N 1 I/Y 10 PV 1,000 PMT 0
CPT FV –1,008.33 Now if our payment is $87.92 and $8.33 of that first payment is interest, then the difference is the amount of the principal repaid in the first payment:
$79.59 = $87.92 – $8.33
Since we retired $79.59 in principal with the first payment, our outstanding balance is now only $920.41 = $1,000 – $79.59
And so on for 12 months. Notice that our last payment is a nickel lower than others. That’s because we truncate the payments at pennies in the U.S. (since the smallest decimal division of money in the U.S. is the cent). If we had something smaller than a penny then our payment would be something like $87.915887 and we would have perfect amortization. By the way we can truncate numbers on our calculator with the [ROUND] key. Try it on the loan payment to see that the total sum of payments in the real world is $1,055.04 and not $1,054.991.
For a lot of reasons, we often need to amortize loans. Here’s how to do it with the BAII PLUS First, please enter 2nd [RESET] ENTER 2nd [QUIT]. Then get in 12 payments per year and enter:
N 12 Then find the [AMORT] menu hiding behind the PV key.
2nd [AMORT] your display reads P1 = 1.00.
Hit the down arrow ↓ , P2 = 1.00. Hit the down arrow ↓ , I/Y 10 PV 1,000 CPT PMT –87.92 FV 0 BAL = 920.41 ↓ , PRN = –79.59 ↓ , INT = –8.33 ↓ .
The real value of this menu is the way it can easily find the balance on the loan at any point in time. Suppose after month 6 you get a big bonus and want to pay off the balance on the loan. The table above shows the balance as $512.42 and we can verify that easily by changing P2 = 6
P1 = 1.00 ↓ , P2 = 6.00 ↓ , BAL = 512.42
We can also find total interest expense at any point in the loan. Suppose that we made our first payment on this loan in May. We will have made eight payments in that tax year: May, June, July, August, September, October, November, and December. When we do our taxes the next year we could claim a deduction on the interest paid in that year. This is easily found as
P1 = 1.00 ↓ , P2 = 8.00 ↓ , BAL = 344.42 ↓ , PRN = –655.58 ↓ ,
INT = –47.78
Notice that it would be a real pain to do this by hand:
May June July August September October November December $47.78 = $8.33 + $7.67 + $7.00 + $6.33 + $5.65 + $4.96 + $4.27 + $3.57
Closing thoughts on the Introductory Section
With regard to knowing what numbers to put in your calculator, you should be able to read a problem and identify the size and timing of the known cash flows, know how many payments are made in a year, know how long the project or investment lasts, and what the relevant interest rates are. Then you should be able to identify what the problem is asking for. Solving for what the problem is asking for can be a simple matter of entering values for N , I/Y , PV , PMT , and then solving for FV .
On harder problems you might have to do additional steps to solve for what the problem is asking for. By the way, there’s other fun menus like [DEPR], [BOND], and [BRKEVN] that we’ll cover in later chapters. For now we have a good start—more than enough on our plate.
You can just imagine R. Lee Ermey shouting “This is my calculator this is my friend! There are many like it but this one is mine!”
Other Menus: Bond Pricing (chapter 5 material)
Pricing a bond is a straightforward application of our earlier work.
Consider a Treasury bond that pays a $45 coupon payment twice a year on January 1 and July 1. The bond has a remaining maturity of exactly 5 years (today is January 2 of 2008). If the par value is $1,000 and the yield to maturity is 6 percent APR (effective rate of 6.09%--use the ICONV menu) we can value the bond as the present value of the coupons and principal discounted back at 6 percent:
$45 $45 $45 $45 $45 $45 $45 $45 $45 $1,045 0 ½ ↓ 1 ↓ ↓ ↓ 1½ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 2 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 2½ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 3 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 3½ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 4 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 4½ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ 5 ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ ↓ $43.69= 0.5 $45 (1.0609) $42.42←←←← 1 $45 (1.0609) $41.18←←←←←←←← 1.5 $45 (1.0609) $39.98←←←←←←←←←←←← 2 $45 (1.0609) $38.82←←←←←←←←←←←←←←←← 2.5 $45 (1.0609) $37.69←←←←←←←←←←←←←←←←←←←← 3 $45 (1.0609) $36.59←←←←←←←←←←←←←←←←←←←←←←←← 3.5 $45 (1.0609) $35.52←←←←←←←←←←←←←←←←←←←←←←←←←←←← 4 $45 (1.0609) $34.49←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←← 4.5 $45 (1.0609) $777.58←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←←← 5 $1,045 (1.0609) $1,127.95
Consider how much work that would be to manually price a 30-year bond with semiannual coupon payments.
While it’s tempting to use the cash flow menu here, the caution is that you have to be sure to correctly specify the periodic rate, which is easy to forget.
Here’s how: 2nd [RESET] ENTER
CF0 0 CF1 45
F01 9 (see the time line) CF2 1,045
F02 1
I 3 (the periodic rate (6 month period) is ½ the stated APR) CPT NPV $1,127.95
There’s a much easier way to find $1,127.95 using the time value of money keys.
–Price
Par Value
Yield to Maturity
Remaining Years to Maturity × Payments per Year
[Coupon Rate × Par Value] Payments per Year N [×P/Y] I/Y [P/Y] PV [AMORT] PMT [BGN] FV [CLR TVM]
←2 times per year for Treasury Bonds, 1 or 2 times per year for corporate bonds
Please enter 2nd [RESET] ENTER 2nd [QUIT].
N 10 = 5 years × 2 payments per year. Try this: enter 5 then [×P/Y] to get 10 then hit N. I/Y 6
CPT PV –1,127.95 PMT 45
FV 1,000 (a common mistake is 1,045 but your calculator is programmed to expect 1,000) The other advantage of using the time value of money menu is that we could solve for a coupon rate if we were given a price and a yield to maturity, but we could never do that with the cash flow menu. Why show you those two hard ways at all? In my experience of teaching this material to over 4,000 students over the years, there’s always somebody every semester who doesn’t want to buy a financial calculator. He has his calculator from high school and wants to save $30 by doing every problem by hand. There is also the student who is infatuated with the cash flow menu and who then misses almost all of the bond pricing questions. Don’t be those guys this semester.
We’re not done with bond pricing quite yet. In the real world we need to be able to price bonds at dates between coupon payment dates. Over the years bond market participants came up with the idea of accrued interest to be fair about how much interest a seller of a bond is entitled to when he sells between coupon dates. It’s a pretty simple idea easiest seen in the form of an example. Suppose we are negotiating the purchase of that Treasury bond in the last example that pays a $45 coupon every
January 1 and July 1. If settlement of the trade is September 9th then there will have been 70 days since the last coupon payment. In a way the seller is entitled to keep $17.12 $45 70
184
= × this represents the interest that he earned by holding on to the bond from July 2nd until September 9th. (There are 184 days between July 1 and January 1 going forward.) This does ignore compounding, but it’s the way that bond traders have been doing it for literally hundreds of years so it’s not going to change anytime soon. It can be a hassle finding the number of days between dates (your calculator does it with the DATE menu which is shown later). There is a wonderful menu that shows you how to price bonds any day of the year. It’s called the bond menu and it gives us the “dirty price” of a bond.
Finding the “Dirty Price” and Accrued Interest
Settlement is 2 business days following the trade date.2nd [BOND]
SDT= 12-31-1990 ENTER
0.0 Enter the annual coupon in dollars here
CPN= ENTER
12-31-1990
RDT= m.ddyy ENTER m-dd-yyyy
RV= ENTER RV= PAR
Yield to Maturity
ACT 2/Y YLD= ENTER
PRI= 100 CPT
AI=
Enter dates as m.dd.yy they are displayed in mm-dd-yyyy format here we will deal with the semiannual / annual issue down here
Redemption date is the maturity date. Enter par value in dollars here
Actual for Treasury Bonds 360 for corporate bonds
2nd ENTER To change settings Price and AI calculated only if you CPT
Price
m.ddyy m-dd-yyyy
Please enter 2nd [RESET] ENTER 2nd [QUIT].
If we wanted to price our treasury bond on Friday September 5 2008 we would enter
2nd [BOND] ↓ Settlement is of course in 2 business days so the trade date was Friday September 5 2008.
SDT ↓ 09-09-2008
CPN ↓ 90 enter annual coupon rate × par value
RDT ↓ 1-01-2013 Redemption date (enter as 1.01.13 m.dd.yy) RV ↓ 1000 Redemption value = par value
YLD ↓ 6 yield to maturity
ACT ↓ Use ACT for Treasuries and a 360-day year for corporate bonds 2/Y ↓ Since the bond pays semiannually we leave this alone
CPT PRI ↓ $1,112.30 A bit less that our earlier result, but we’ve missed a coupon AI $17.12 (we will owe the seller of the bond the accrued interest)
One other odd thing: corporate bonds are traded with accrued interest figured with 30-day months and 360-day years while treasury bond’s accrued interest is calculated based on the actual number of days between specific dates and of course a 365-day year (except during leap years when there are 366 days).
The accrued interest due if that last bond had been an other-wise identical corporate would be$17.00 $45 68
180
= × .
It’s easiest to use the bond menu to find accrued interest. If you think that I’m wrong on the last accrued interest, try it on your bond menu setting ACT to 360.
The Date Menu
No this menu won’t get you a companion for Friday night, but it does do two useful things. The first useful thing: calculating the days between any two dates in the past or future. Please enter 2nd [RESET] ENTER 2nd [QUIT].
Open up the [DATE] menu.
The display shows DT1 = 12-31-1990. Enter 7.0108 The display shows DT1 = 7-01-2008 Now use the down arrow key, ↓ .
The display now shows DT2 = 12-31-1990. Enter 9.0908 The display shows DT1 = 9-09-2008 Hit the down arrow key, ↓ . The display now shows DBD= 0.00
Hit CPT to see DBD = 70
Hit ↓ again. The display shows ACT. Using the 2nd button and ENTER you can toggle between calculating days between dates using a 360-day year and the actual number of days between dates on the real calendar for any given year. Corporate bonds use a 360-day year and Treasuries use the actual days between dates and usually a 365-day year but of course a 366 day year every leap year.
The second useful thing: calculating the day of the week for any date in the past or future. It’s a surprisingly sophisticated bit of programming. Go up ↑ to date two and try to change it from September 9 2007 to February 29 2007. You will get an error message since 2007 wasn’t a leap year. But if you change the date to February 29, 2008 you calculator will accept it. Go ahead and calculate the days between dates ( ↓ . The display now shows DBD= 70.00 Hit CPT to see DBD = 243) now go back up to up ↑ to date two and Hit CPT to see that leap day 2008 will be on a Friday.
If you didn’t calculate the days between dates as 243 then it changes date two and tells you what day of the week is 70 days away from the first of July 2007. By the way you can toggle up ↑ to date one and see that July 1 2007 was on a Sunday. How cool is that?
Why is this in a financial calculator? Settlement on a bond occurs two business days after the trade date and Saturdays and Sundays don’t count. What else is this menu useful for? Long engagements. If you want to figure out what days in June three years from now are Saturdays it will do it for you. If you want to know how many days you have been alive it will do it for you.
The FORMAT Menu
This is arguably the menu that I get the most questions about during exams when I am typically disinclined to teach students how to use their calculator. You calculator does not round. The display can be adjusted to you preferences.
Please enter 2nd [RESET] ENTER 2nd [QUIT].
Using the 2nd button we see DEC= 2.00 this is where I prefer to leave well enough alone, since in the
field we like to see answers in dollars and cents and interest rates out to basis points. But if that’s not good enough for you, type in the number 8 and hit the ENTER key. Now the display looks like DEC= 8.00000000
What that does for you is just to change the display that you see. It does not change the accuracy of any internal calculation. Do us both a favor and change it back to DEC= 2.00 before you put an eye out. Now use the down arrow key, ↓ .
The display now shows DEG. You could change from degrees to radians. Use the 2nd button and the
ENTER key. Remember that from analytic geometry? Let’s leave well enough alone and use the down arrow key, ↓ .
The display now shows US 12-31-1990. We could change the way our calculator displays dates to the way the Europeans (and the U.S. military) does it to EUR 31-12-1990. Use the 2nd button and the ENTER key. This is a preference issue generally but the depreciation menu changes based on your choices here. For now if you’re in U.S. and not in the Army, Air Force, Navy or Marine Corps leave it alone. If you’re in ROTC go ahead and choose EUR 31-12-1990 you might as well get used to it. Now use the down arrow key, ↓ .
The display now shows US 1,000.00 We use commas for separators and periods for the decimal but in Europe they use periods where we use commas and commas where we use periods. I’ve worked in Italy and Spain for the last three summers and when I’m over there I make this switch because those guys just can’t wrap their heads around how backwards we are on this. When in Rome, do as the Romans do.
Now use the down arrow key, ↓ .
The Depreciation Menu DEPR :
We will need this in chapter 8. If you’ve had an accounting class you know that there are a lot of different types of depreciation choices out there: Straight-line, Sum-of-Years-Digits, Declining Balance, Double-Declining-Balance-with crossover. There’s even more (e.g. the French do straight-line depreciation differently that we do and your calculator will do that if you first change your formatting to the European way—then your last choice in this menu is SLF straight line French) but for now in this class let’s stay in straight-line depreciation (SL).
To understand how to use this menu, let’s depreciate a $60,000 piece of equipment straight-line to a salvage value of $6,000 over 3 years. From our accounting prerequisites we know that the depreciation charge in each year will be $18,000 $60,000 $6,000
3
− =
And if this were an accounting class we could come up the following worksheet YEAR 0 YEAR 1 YEAR 2 YEAR 3
Book Value $60,000
Depreciation Charge $18,000 $18,000 $18,000
Remaining Book Value $60,000 –$18,000 $42,000 $42,000 – $18,000 $24,000 $24,000 – $18,000 $6,000 Remaining Depreciable Value $36,000 $18,000 $0
Let’s do this with our calculator: please enter 2nd [RESET] ENTER 2nd [QUIT] 2nd DEPR . The display shows SL leave that alone and use the down arrow key, ↓ .
The display now shows LIF= 1.00 Enter 3. The display shows LIF = 3.00 Now use the down arrow key, ↓ .
The display now shows M01= 1.00 leave that alone and use the down arrow key, ↓ .
(In the real world, if we had put an asset into service on Valentine’s Day we would only be entitled to a partial depreciation charge in the first year, entering M01 =2.5 means February 14.)
The display now shows CST= 0.00 Enter 60,000 The display shows CST= 60,000.00 Use the down arrow key: ↓ .
The display now shows SAL= 0.00 Enter 6,000 The display shows SAL = 6,000.00 Use the down arrow key: ↓ .
The display now shows YR= 1.00 leave that alone and ↓ to view our results: DEP = 18,000.00 ↓ RBV = 42,000.00 ↓ RDV = 36,000.00 ↓ 2 ENTER YR = 2 ↓ DEP = 18,000.00 ↓ RBV = 24,000.00 ↓ RDV = 18,000.00 ↓ 3 ENTER YR = 3 ↓ DEP = 18,000.00 ↓ RBV = 6,000.00 ↓ RDV = 0.00
The Profit Menu
2nd PROFIT
CST = The cost of an item SEL = The selling price MAR = The profit margin
Enter values for any two variables and the calculator will solve for the third. The Break Even Menu
This menu calculates accounting break even price or quantity.
2nd BRKEVN
FC = Fixed cost VC = Variable cost
P = The selling price per unit PFT = Total profit
Q = The accounting break-even quantity
Enter values for any four variables and the calculator will solve for the remaining one.
Most often we set profit equal to zero and either solve for break-even quantity or break-even price. The Percentage Change Menu
This menu is kind of embarrassing.
2nd Δ%
OLD = The original value NEW = The new value
%CH = The percentage change per period #PD = Number of periods
The Memory Menu
This menu shows the values that we have entered into our calculator’s memory.
We can have our calculator remember any number that we like and it will remember as many as ten different numbers for us. Our ten memory registers are the numbers 0 through 9. We store a number in a memory register by entering STO and we can recall a number by using the RCL key and then the number of the register.
So for example, let’s store the number 105 in memory register 5:
2nd [RESET] ENTER 2nd [QUIT]
Enter 105 STO 5
Now clear the display with the CE/C key.
We can recall our stored data by using the RCL key: enter RCL 5 and our display shows 105.00 To see all of the stored values
2nd MEM M0 = 0.00 ↓ M1 = 0.00 ↓ M2 = 0.00 ↓ M3 = 0.00 ↓ M4 = 0.00 ↓ M5 = 105.00 ↓ M6 = 0.00 ↓ M7 = 0.00 ↓ M8 = 0.00 ↓ M9 = 0.00 ↓
You will really save yourself a lot of existential angst if you get in the habit of using your calculator’s memories. Your calculator saves the number out to 24 decimal places (even if the display only shows you two). Your calculator also doesn’t have “fat fingers” that thinks it’s entering 105 but is really entering 150 by mistake.
That’s about it for the kinds of menus that you will need in a finance class. There’s a lot of other menus: trigonometry, statistics, transcendental functions, factorials, combinations and permutations, the thing even can do five different kinds of regression, but we’re just not about that kind of fun in this course.
