HP 12C Calculations. 2. If you are given the following set of cash flows and discount rates, can you calculate the PV? (pg.

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1 HP 12C Calculations This handout has examples for calculations on the HP12C: 1. Present Value (PV) 2. Present Value with cash flows and discount rate constant over time 3. Present Value with uneven cash flows but constant discount rate 4. Annuity 5. Loan 6. Bond 7. Yield to Maturity (YTM) 8. YTM with semi-annual coupons 9. Internal Rate of Return (IRR) 10. IRR with uneven cash flows Examples 1, 3, and 6 show the exact order of how to enter the numbers into the calculator. Use these as a guide to the rest of the problems and practice figuring out how to enter numbers and ask for an answer given various forms of questions. At the end of this handout you will find answers to common questions. If you are having trouble or have any other questions, please send an to me or to Jen. 1. Problems on HP 12C (p.27 of class #2) n number of periods i interest rate (or discount rate) in % (so you don t need to enter it as a decimal) PV present value PMT periodic payment (repeats every period, as in an annuity or perpetuity) FV future value (i.e. one-time payment at end, as in a bond) 2. If you are given the following set of cash flows and discount rates, can you calculate the PV? (pg. 28 of class #2) C1 = 50.0 r1 = 0.06 C2 = 60.0 r2 = 0.06 step 1: clear all registers: {f} REG step 2: enter data: {50} [g] [CFj] ( enter period 1 cf ) {60} [g] [CFj] ( enter period 2 cf ) {6} [i] ( enter int. rate ) [f] [NPV] ( ask for answer ) =

2 3. If you are given the following set of cash-flows (same every year) and discount rates, can you calculate the PV? (notice the discount rate is constant over time) (p.35 of class #2). C1 = 15.0 r1 = 7.50% C2 = 15.0 r2 = 7.50% C3 = 15.0 r3 = 7.50% {3} [g] [Nj] ( enter number of periods ) {7.5} [i] ( enter int. rate ) {15} [g] [CFj] (enter cf, which is constant over all periods ) [f] [NPV] ( ask for answer ) = Uneven cash flows. {g} CF0 = 0 {g} CF1 = 20,000 {g} CF2 = 22,000 {g} CF3 = 24,200 i = 8 Then click {f} NPV = $56, For CF1 through CF3 use the CFj button. 5. Annuities and the calculator (p.14 of class #3). You can afford to pay $632 per month toward the purchase of a new car. Your bank tells you that you can borrow money at 1% per month for 48 months. How much can you borrow? Calculator: N = 48 i = 1 PMT = -632 Then click PV = $23, For an annuity, you need four variables--the periodic payment (C), the interest rate (i), the number of periods (t) and the PV of the borrowing. Given any 3 variables, you can calculate the 4 th. Pgs of class #3 go over these different scenarios. 6. Loan calculations (pg 26 of Class #3). Pages go over an auto loan in detail. {10000}[CHS][PV] Loan amount. {908.33}[PMT] Payments. {12}[n] Number of payments. [i] Calculate 1 mo. rate. (Note that the 1.35 is a percentage). Again, given any 3 variables out of 4 (PV, C, N, i) you can calculate the 4 th.

3 7. Bond Valuation (pg. 25 of Class #5). Consider a bond with a 10% annual coupon rate, 5 years to maturity and assume the market interest rate r is 12%. What is the current price of the bond? With a calculator: N = 5 i = 12 PMT = 100 FV = 1000 Then click PV = -$ Remember the sign convention: this is what you pay for that stream of cash flows. So whenever you enter the price of a bond, hit {CHS} PV. 8. Computing the Yield to Maturity (YTM) (pg. 34 of Class #5) Finding the YTM is similar to finding r for an annuity Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. The current price is $ Calculator: N = 15 PV = Crucial the sign convention!! FV = 1,000 PMT = 100 Then click i = 11% There is no formula to find the YTM of a bond! 9. Computing the yield to maturity with semi-annual coupons (pg 36. of Class #5). Same problem to midterm question just different numbers. Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $ What is the semiannual coupon payment? PMT = 1,000 * 0.10 / 2 = 50 How many periods are there? N = 20 * 2 = 40 What is the YTM of this bond? PV = -1, FV = 1,000 Then click i = 4% This is the Period Rate!! YTM = APR = 4%*2 = 8%

4 10. Computing the Internal Rate of Return (IRR) There is no formula for the IRR: You need: i) a spreadsheet, ii) a financial calculator, or iii) the ability to solve 3rd degree equations by hand Using the calculator, as for the NPV rule: {g} {CHS} CF0 = -165,000 {g} CF1 = 63,120 {g} CF2 = 70,800 {g} CF3 = 91,080 Then click IRR = 16.13% (pg. 21, Class #6) 11. Calculating the IRR with uneven cash flows. (pg.20 of Class #6) NPV = K (1 ) 1 (1 ) 2 (1 ) 3 (1 ) 4 + r + r + r + r (1 + r ) 20 If we want to make NPV=0, then r =??? (i) {CHS} {g} CF0= 2.7, (ii) {g} CF1 = 0.1, {g} Nj=1 (iii) {g} CF2 =0.3, {g} Nj =1, (iv) {g} CF4 = 0.5, {g} Nj =1 (v) {g} CF5=1.2, {g} Nj = 17 (vi) Click {f} IRR IRR = 26.6%

5 HP-12C Questions 1. Question Why does my calculator only show two decimal places? The default precision is two decimal places, but that can be changed. If you want 4 decimal places, type [f] 4. For maximum precision, type [f] 9 2. Question I press the same buttons as you do, but get a different answer! Do you have the word "BEGIN" showing in your display? This is a bad thing. It means that when you do calculations using the [PV], [PMT], [n] etc. buttons, the calculator will assume that the periodic payments occur at the beginning of each period (so the first payment is right now), rather than at the end of each period (i.e. first payment is one period from today), which is the usual assumption. This will change all your results. If you have the word "BEGIN" displayed, you should get rid of it by pressing [g] [END] (under the "8" key). 3. Question I tried that, and I still get different answers If you cleared the calculator before starting by pressing the clear button, [CLX], this only clears the display. The last values you used for [PV], [PMT], etc. are still there, and can affect your calculations. The safest thing is to press [f] [REG] (above the [CLX] button), which clears everything. You can probably get away with [f] [FIN] (above the [x<->y] button), which (I think) clears the financial registers, but not all the numbers you've put into, for example, memory location Question HELP! My calculator has switched "," and ".", so, for example, 1, appears as "1.000,23" First turn off the calculator. Now press the "." button, and while keeping it pressed turn the calculator back on. You'll be back to normal. 5. Question 5a. How do I do calculations using the [PV] etc. buttons and fractional periods? 5b. What's that letter "C" in my display? By default, the HP-12C will use the interest of the fractional period. For example, suppose you invest $100 for 1.5 years at 10%. Try: 100 [CHS][PV] 10 [i] 1.5 [n] [FV] You will (probably) get the answer $ This is equal to 100 x 1.10 x 1.05

6 In the extra 6 month period, you earn 5% (= 10% / 2), rather than the true 6 month rate of (1.1)^0.5-1 = 4.88% You were probably hoping for the answer $ (= 100 x 1.1^1.5). You can get the calculator to do this. Press [STO] [EEX] (obvious, huh?), and you'll see the letter "C" appear in your display. Now redo the calculation, and you'll get the behavior you want. 6. Question How do I get every bit of the display to switch on simultaneously? (This is not all that useful, but I discovered it by accident and thought you ought to know.) Switch off the calculator, press the "+" key, and while keeping it pressed turn the calculator back on. The calculator will do something (I've no idea what...) for a very long time, with "Running" flashing in the display. I'm not sure what it's doing, or if it will ever stop of its own accord, but if you press lots of keys it will eventually stop flashing, and every possible line and symbol in the display will be switched on.