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Calculator Handout Your calculator is a small computer that has been programmed to answer various financial questions based upon particular assumptions or initial settings. All of the information in this handout, and all of the answers to the problems in the back of the chapters, are based on certain initial settings or parameters; if your calculator is not set up correctly with these initial settings, all of your answers may be wrong. The calculator must be set up as follows before using it to solve any financial problems. All of the answers are based on the assumption that your display is set to show decimals to 4 places. To accomplish this: 1) Press the 2nd key 2) press the format key - it should read DEC = 3) press the 4 key 4) press the 2nd key 5) press the set key (above enter) 6) press the enter key - the display should read DEC = 4.0000 7) press the 2nd key 8) press the quit key (above the CPT key). 4) press the enter key 5) press the 2nd key 6) press the quit key All of the instructions are based on the assumption that the calculator is set up for ordinary annuities where the payments occur at the end of the period. To check that this is the setting: 1) press the 2nd key 2) press the BGN key (above the PMT key) 3) If the display reads END, you're all set - hit the 2nd key then the quit key 4) if the display reads BGN 5) press the 2nd key 6) press the set key so the display reads END. 7) press the 2nd key 8) press the quit key. If the problem involves multiple cash flows you have to tell the calculator the number of cash flows per year. In addition, the interest you pay or receive may be compounded more than once per year - you must tell the calculator how many times per year the interest is compounded. We will initially assume one payment per year and that interest is compounded once a year - the appropriate commands are: 1) Press the 2nd key 2) Press the P/Y (payments per year) key - the screen should read P/Y = 3) press the 1 key 4) press enter 5) hit the down arrow key the screen should read C/Y (compounding per year) = 6) press the 1 key 7) press the enter key 8) press the 2nd key 9) press the enter key Chapter 5 - Time Value of Money Problems You can solve almost all of the problems in chapter 5 using the time value of money keys, which are the light brown keys in the third row down, on your calculator. Note: Almost all of the problems in Chapter 5 are lump sum problems that do not involve multiple payments over time. In solving these problems you must assign a value of 0 to the PMT variable. Just press 0, then PMT to do this. If you fail to do this you may get an incorrect answer since the calculator will assign the last value entered for PMT when solving the problem. In addition, if you are given a value for PV enter the amount as a negative number by pressing the +/- key after you enter the amount. 1) You deposit $1,000 into a retirement that pays 8% interest. How much will you have in 40 years? PMT = 0, PV = -1,000, N = 40, I/Y = 8.0. Hit FV then CPT to get 21,724.52. 2) answer (1) assuming that the interest is compounded monthly. There are two ways to do this: (1) Enter the monthly interest rate and the number of months in 40 years: PMT = 0, PV = -1,000, I/Y = 8/12, N = 40 x 12 then hit FV and CPT to get 24,273.3855. (2) Instruct your calculator to change the frequency of compounding: hit 2nd, then I/Y. Hit 1, then enter, then hit the down arrow key - it should read C/Y = ?. If you want monthly compounding, enter 12, then enter, then 2nd, then enter. Now solve as follows: PMT = 0, PV = -1,000, I/Y = 8, n = 12, then hit Fv and CPT to get 24,273.85. 3) You receive $50,000 today and invest it at 7.5% interest. How long will you have to wait until you have 1,000,000? Fv = 1,000,000, PMT = 0, PV = -50,000, I/Y = 7.5. Hit N then CPT to get N = 41.4225 years. 4) Your grandparents give you $50,000 to use as a down payment on a house in 10 years. What return must you earn if you need 100,000 for the down payment? FV = 100,000, PMT = 0, PV = -50,000, N = 10. Hit I/Y then CPT to get I/Y = 7.1773%. 5) I offer you a winning lottery ticket that will pay $3,000,000 in 20 years. If the discount rate is 8.25%, how much should you pay for the ticket? FV = 3,000,000, N = 20, PMT = 0, I/Y = 8.25. Hit PV then CPT to get -614,558.393. Chapters 5 & 6: Nominal Rates, Compounding, and the Effective Annual Rate Your calculator has a set of routines to compute EAR given the nominal interest rate, r, and the frequency of compounding, m. Define: NOM: the nominal interest rate or the APR C/Y the frequency of compounding per year EFF: the effective annual rate or EAR. To bring up the spreadsheet used for interest rate conversions hit the 2nd key, then the ICONV key (the 2 key). You move between the NOM, C/Y, and EFF keys by hitting the up or down arrow keys. 1) Given a nominal rate of 10% and monthly compounding, compute EAR. a) Hit the 2nd key, then the ICONV key. b) type in 10.0, then hit enter. c) hit the down arrow key - after the first time you will see EFF, hit the down arrow key a second time until you see C/Y d) type in 12, then hit enter e) hit the down arrow key twice until you see EFF - hit the CPT key - the EFF = EAR = 10.4713. 2) Given an effective rate of 13.5% and weekly compounding, compute the APR or the nominal rate. a) Hit the 2nd key then the ICONV key b) hit the down arrow key once - type in 13.5 for EFF - hit enter. c) hit the down arrow key once - you will see C/Y - type in 52 and then hit enter. d) hit the down arrow key once - you will see NOM = - hit the CPT key - the nominal rate = 12.6787%. Chapter 6 - Annuity Problems In this chapter we add multiple payments to the problems, using the PMT key; otherwise the FV, PV, I/Y, and N key uses remain the same. It is important that you keep two things straight in working these problems: 1) the frequency of the payments, P/Y 2) the frequency of the compounding, C/Y In most problems these two variables will be the same, as in most cases the frequency of compounding matches the frequency of the payments. In some cases, however, the two may differ. To set the frequency of payments: hit the second key, then the I/Y key - the screen reads P/Y = ?. If you want annual payments, hit 1, then enter - the screen now reads P/Y = 1.0000. If you also want annual compounding, hit the down arrow key, then C/Y =1, then enter, then the 2nd key, then the enter key again. If you wanted monthly payments with monthly compounding, enter 12 instead of 1 in each case. If you want annual payments with monthly compounding, set P/Y = 1 and C/Y = 12. 1) How much will you have if you in 30 years if you deposit $2400 per year into an account that pays 10% interest (assuming annual compounding)? PMT = 2,400, PV = 0, I/Y = 10, N = 30, hit FV then CPT to get 394,785.65 2) Redo (1) assuming you deposit $200/ month. Set P/Y = C/Y = 12, and PMT = 200, PV = 0, I/Y = 10. Then enter 30, 2nd, N, then N again to get N = 360. Hit FV then CPT to get 452,097.59. 3) What return must you earn if you want 500,000 in 30 years and deposit 200/month into a savings account for 30 years? Set P/Y = I/Y = 12. FV = 500,000, PMT = -200, PV = 0. Enter 30, 2nd, N, N again to get N = 360. Hit I/Y then CPT to get 10.4696, which is the required annual return. 4) How much must you save each month if invest a fixed amount monthly for 30 years at 10% and want a total of 1,000,000? Set P/Y = C/Y = 12. FV = 1,000,000, I/Y = 10, enter 30, 2nd N, N again to get N = 360, and PV = 0. Hit PMT then CPT to get 442.38. 5) You buy a new car for $25,000. You finance the entire amount for 5 years at 8% interest. What is your monthly payment? Set P/Y = C/Y = 12. PV = 25,000, I/Y = 8, FV = 0. Enter 5, 2nd N, N again to get N = 60. Hit PMT then CPT to get 506.91. 6) Using the information from (5) assume your monthly payments are 625. What interest rate are you paying? FV = 0, PMT = -625, PV = 25,000, then enter 5, 2nd N, N again to get N = 360. Hit I/Y then CPT to get 17.2737. 7) You will deposit $5,000 per year for 25 years on an annual basis. The bank pays 8% annual interest, but compounds it monthly. How much will you have in 25 years? Set P/Y = 1 and C/Y = 12. Set PMT = -$5,000, I/Y = 8, FV = 0, and then enter N = 25, 2nd N, N again to get 300. Hit FV then CPT to get FV = 381,940.58. Chapter 7 - Bond Valuation Your calculator has a separate spread sheet for bond calculations, but it's fairly complicated and is really more than you need for this chapter. You can do all of the bond calculations just using the cash flow keys from chapters 5 and 6. The first step is to translate the bond terminology into the variables used in the time value of money problems: 1) Face Value = FV; the face or par value is a lump sum you receive at some point in the future, so you can call it the FV. 2) PMT = coupon payments. The coupon payments are nothing more than an annuity, so you can represent them using the PMT keys. 3) PV = price or value of the bond. The value of a bond is simply the PV of all of the future payments. 4) I/Y = YTM = discount rate. 5) N = the number of coupon payments. Examples: 1) Calculate the value of a 10% coupon bond with a face of 1,000, 10 years to maturity, and a YTM = 8%, assuming annual coupon payments. Enter FV = 1,000, PMT = 100, N = 10, I/Y = 8, then CPT PV to get the PV of 1,134.20 2) Same bond with semi-annual coupon payments. Set C/Y = P/Y = 2. Enter FV = 1,000, PMT = 100/2 = 50, I/Y = 8, then enter 10, 2nd N, N to get 120. Finally, CPT PV to get 1,135.90. 3) A bond currently sells for 1,150, has a 10% coupon, a YTM of 7% and pays interest annually You want to know when the bond matures, so you are solving for N. FV = 1,000, PMT = 100, I/Y = 7, and PV = - 1,150. Hit CPT then N to get N = 6.3670 (it should be a round number but you get the idea.) 4) A bond currently sells for 875, has 9 years to maturity, a discount rate of 10%, a face value of 1,000, and pays interest annually. What coupon rate does it carry? Fv = 10,000, PV = -875, N = 9, and I/Y = 10, so hit CPT PMT to get PMT = 78.2949. Divide this by 1,000 to get the coupon rate of 7.83%. 5) You purchased a bond for 1,050; the bond has a coupon rate of 8.5%, 10 years to maturity, and a face of 1,000. What return do you expect to earn if you hold the bond to maturity and it pays interest semi-annually? Set P/Y = C/Y = 2. You want the YTM or I/Y. Enter FV = 10,000, PMT = 42.5, PV = -1,050, enter 10, 2nd N, N. Then hit CPT I/Y to get 7.7716%. Chapter 9: Net Present Value and other Investment Criteria You can compute the NPV of a project as follows: Assume you have the following problem: Year Cash Flow discount rate = 10% 0 -50,000 1 10,000 2 15,000 3 20,000 4 25,000 1) Hit the CF key 2) Hit the 2nd key 3) Hit the CLR Work key - this clears all of the previous entries 4) The screen now reads CF0 - this is where you enter the cost of the project - Hit -50000, then the enter key - the screen should read CF0 = -50,000 5) Hit the down arrow key once - the screen should read C01 Hit 10,000, then the enter key - the screen should read C01 = 10,000 6) Hit the down arrow key once - the screen should read F01 = 1 the F's represent the frequency of the cash flows. If the cash flows were constant over say 5 years, you could simply enter 5 without entering the rest of the cash flows. In most problems the cash flows will vary each period, so hit the down arrow key again - the screen should read C02 7) Hit 15,000, then enter - the screen should read C02 = 15,000 8) Hit the down arrow key twice until you see C03 - hit 20,000, then enter. The screen should read C03 = 20,000. 9) Hit the down arrow key twice until you see C04 - hit 25,000, then enter. The screen should read C04 = 25,000. 10) Hit the down arrow key twice - the screen should read C05. Hit the NPV key - the screen should read I = 0.000. Enter the discount rate by typing 10.0, then enter. 11) Hit the down arrow key once - the screen should read NPV = 0.000. Hit CPT to compute the NPV of the cash flows at a discount rate of 10%. NPV = 3,589.24. Computing the IRR for the project: Repeat steps 1-9 above; you have now cleared the worksheet and entered all of the cash flows: 1) Hit the down arrow key twice - the screen should read C05 = 0.0000. Hit the IRR key - the screen should read IRR = 0.0000. Hit CPT - the screen should read IRR = 12.8257. Assume you have the following problem Year Cash Flow Discount rate = 10% 0 -50,000 1 20,000 2 20,000 3 20,000 4 20,000 5 -10,000 1) Hit CF, then the 2nd key, then CLR WORK to clear the calculator. 2) Hit -50,000, then enter - the screen should read CF0 = -50,000 3) Hit the down arrow key once - hit 20,000, then enter - the screen should read C01 = 20,000 4) Hit the down arrow key once - the screen should read F01 = 1.000. Hit 4, then enter - the screen should now read F01 = 4.000. You have now told the calculator that you have 4 consecutive cash flows of 20,000. 5) Hit the down arrow key once - the screen reads C02 0.000. Hit -10,000, then enter - the screen should read C02 = -10,000. 6) Hit the down arrow key twice - the screen should read C03 0.000. Hit the NPV key - the screen should read I = 0.000. Hit 10.0, then enter - the screen should read I = 10.0000. 7) Hit the down arrow key once - then CPT - the NPV = 7,188.0957. Chapter 12 Capital Market History You can use the statistical functions in your calculator to compute the mean and standard deviation for a sample of data. Assume you have the following returns: 5%, 12%, -7%, 21%, -5%. To compute the mean and standard deviation you do the following: 1) hit the 2nd key, then the data key (the 1 key) 2) hit the 2nd key, then the CLR WORK key 3) the screen should now read X01 - type in 5, then enter 4) hit the down arrow key twice - the screen should now read X02 - hit 12, then enter 5) hit the down arrow key twice - the screen should no read X03 - hit -7, then enter 6) hit the down arrow key twice - the screen should now read X04 - hit 21, then enter 7) hit the down arrow key twice - the screen should now read X05 - hit -5, then enter 8) hit the down arrow key twice - the screen should now read X06 9) hit the 2nd key, then the STAT key 10) hit the 2nd key, then CLR WORK 11) hit the down arrow key once n = 5 is the sample size 12) hit the down arrow key once xbar is the mean of 5.2% 13) hit the down arrow key once - Sx is the sample standard deviation = 11.7132%. if you square this you get the variance.