Financial calculators for Real Estate Finance …or, everything you wanted to know about financial calculators, but were afraid to ask.

Overview Which calculator should you purchase? Basic arithmetic calculations Mortgages Payments Balances Yields DCF, NPV and IRR Cash flows NPV IRR

Which calculator should you purchase? For applications in real estate, finance and accounting, you want a financial calculator Hewlett-Packard: 10bii, 10bii+, 12c, 17bii The 10bii and 12c support only RPN entry, the 12c Platinum and 17bii allow for a choice between RPN and ALG entry, the 10bii+ supports only ALG The 12c is the only HP calculator approved for CFA exams Texas Instruments: BAII Plus The BAII Plus supports only ALG entry The BAII Plus is the only TI calculator approved for CFA exams

User manuals User manuals for each of these are available online and are invaluable resources – they are full of additional examples similar to what is presented here and provide explanations of calculator functionality beyond what is covered in this tutorial: HP 10bii: http://h10032.www1.hp.com/ctg/Manual/bpia5213.pdf HP 10bii+: http://www.hp.com/ctg/Manual/c02989763.pdf HP 12c: http://www.hp.com/ctg/Manual/c00363319.pdf HP 17bii: http://www.hp.com/ctg/Manual/c00363348.pdf TI BAII Plus: http://library.sait.ca/documents/tibaiiplus.pdf

Basic calculations RPN or ALG? RPN = Reverse Polish Notation To find the solution to 1 + 2, enter “1” then “ENTER” then “2” then “+” – the correct answer, “3”, should be visible in the display. The default (and, sometimes, only) mode for most HP calculators is RPN – RPN usually requires fewer keystrokes to arrive at a given solution and makes more efficient use of “stack” memory. Hint: if there’s no key for “=” on your calculator, entry is based on RPN. ALG = Algebraic notation To find the solution to 1 + 2, enter “1” then “+” then “2” and then, finally, “=”, the correct answer, “3”, should be visible in the display. The default mode for TI calculators is ALG.

Some Preliminaries for HP 10bII+ Make sure you “clear all” to erase any new information Red arrow down key then the “C ALL” button gage Make sure your payments per year is always set correctly! 1 for annual, 2 for semi-annual (bonds), 12 for monthly (mortgages) Mortgage example: 12 then red arrow down key then the “P/YR” button Next time you “clear all” the value for P/YR will display Make sure the number of decimals you want to show is set correctly Assume we want to display 4 decimals Red arrow down key then the “DISP” button then the number of decimals you want to display (4 in this case)

Basic calculations Mortgage calculations are based on the total number of compounding periods and the periodic interest rate. How are these determined using RPN notation? Mortgage payments are made on a monthly basis for 30 years, how many compounding periods are there in a 30-year mortgage? To find the total number of compounding periods, enter “30” then “ENTER” then “12” then “×”. HP12b: Enter 360 for N If the stated annual mortgage interest rate is 5%, what is the periodic interest rate? The periodic interest rate is simply the annual rate divided by the number of compounding periods per year, enter “5” then “ENTER” then “12” then “÷”. HP12b: Note that we enter 5 for I/YR

Mortgages – HP 10 bII+ Main keys used in calculations relating to mortgage loans: N – total number of compounding periods I/YR – annual (quoted) interest rate PV – initial mortgage balance PMT – periodic payment FV – remaining mortgage balance at the end of a given number of compounding periods

Mortgages Conventions and helpful hints: Enter information as if you are the lender – cash outflows, such as PV, should be entered as negative numbers, cash inflows, such as PMT, should be entered as positive numbers. To change the sign of a number, use “CHS” or “+/-” Outcomes are based on payments being made at the end of the month. Information entered into any of the financial function keys remains as entered until either the register is cleared or the information is replaced. To determine the payment associated with a change in the interest rate, just enter the new periodic rate into i and then press PMT to find the new payment – the values for n, PV and FV will remain unchanged To clear the information stored in the financial function keys, enter “f” and then “x><y”

Mortgage payments – HP 10bII+ What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate? Make sure that P/YR = 12 How much will you borrow from the lender? PV = -225,000 How many payments? N = 360 What is the balance remaining after making the last payment? FV = 0 What is the monthly interest rate? I/YR = 5.00 What is the monthly payment? PMT = ? = 1207.8487

Mortgage payments – HP 10bII+ What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5.5% annual interest rate? Make sure that P/YR = 12 How much will you borrow from the lender? PV = -225,000 How many payments? N = 360 What is the balance remaining after making the last payment? FV = 0 What is the monthly interest rate? I/YR = 5.50 What is the monthly payment? PMT = ? = 1277.5253

Mortgage payments What is the monthly mortgage payment if you finance $335,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a … 4.0% annual interest rate? PMT = ? = 1599.3412 4.5% annual interest rate? PMT = ? = 1697.3958 5.0% annual interest rate? PMT = ? = 1798.3524 5.5% annual interest rate? PMT = ? = 1902.0932 6.0% annual interest rate? PMT = ? = 2008.4943

Mortgage payments – HP 10bII+ What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a fully amortizing 15-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate? How much will you borrow from the lender? PV = -225,000 How many payments? N = 180 What is the balance remaining after making the last payment? FV = 0 What is the monthly interest rate? I/YR = 5.00 What is the monthly payment? PMT = ? = 1779.2857

Mortgage payments What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a fully amortizing 15-year fixed-rate, fixed-payment mortgage with a … 4.0% annual interest rate? PMT = ? = 2625.8921 5.0% annual interest rate? PMT = ? = 2807.3174

Mortgage payments – HP 10bII+ What is the monthly mortgage payment if you finance $225,000 of the purchase price of your new home with a partially amortizing 30-year fixed-rate, fixed-payment mortgage with a $100,000 balloon payment due at maturity and a 5% annual interest rate? How much will you borrow from the lender? PV = -225,000 How many payments? N = 360 What is the balance remaining after making the last payment? FV = 100,000 What is the monthly interest rate? I/YR = 5.00 What is the monthly payment? PMT = ? = 1087.6937

Mortgage payments What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a partially amortizing 30-year fixed-rate, fixed-payment mortgage with a $250,000 balloon payment due at maturity and a 5% annual interest rate? PMT = ? = 1605.3294 What is the monthly mortgage payment if you finance $355,000 of the purchase price of your new home with a non-amortizing 30-year fixed-rate, fixed-payment mortgage with a $355,000 balloon payment due at maturity and a 5% annual interest rate? A non-amortizing mortgage is frequently referred to as an interest-only loan as the payment in any month equals the monthly interest based on the initial loan balance. PMT = ? = 1479.1667

Mortgage balances What is the balance remaining monthly mortgage payment if, three years ago, you borrowed $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate? What is the monthly payment? PMT = ? = 1207.85 What is the balance remaining after making 36 payments? N = 36 FV = ? = 214,523.09

Mortgage balances What is the balance remaining monthly mortgage payment if, five years ago, you borrowed $225,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate? What is the monthly payment? N = 360 I/YR = 5 PV = -225,000 FV = 0 PMT = ? = 1207.8487 What is the balance remaining after making 60 payments? N = 60 FV = ? = 206,614.6472

Mortgage balances If you borrowed $355,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage with a 5% annual interest rate, what is the balance remaining after … four years? N = 360 I/YR = 5 PV = -355,000 FV = 0 PMT = ? = 1,905.7168 N = 48 FV = ? = 332,386.4957 ten years? N = 120 FV = ? = 288,764.3289

Mortgage yield – HP 10bII+ If the monthly payment for the fully amortizing 30-year fixed-rate, fixed-payment mortgage used to finance $225,000 of the purchase price of your new home is $1500, what is the interest rate on your loan? How much will you borrow from the lender? PV = -225,000 How many payments? N = 360 What is the balance remaining after making the last payment? FV = 0 What is the monthly payment? PMT = 1,500.00 What is the interest rate? I/YR = ? = 7.0203

Mortgage yield – HP 10bII+ If the monthly payment for the fully amortizing 30-year fixed-rate, fixed-payment mortgage used to finance $225,000 of the purchase price of your new home is $1250, what is the interest rate on your loan? How much will you borrow from the lender? PV = -225,000 How many payments? N = 360 What is the balance remaining after making the last payment? FV = 0 What is the monthly payment? PMT = 1,250.00 What is the interest rate? I/YR = ? = 5.3040

Mortgage yield If you borrowed $355,000 of the purchase price of your new home with a fully amortizing 30-year fixed-rate, fixed-payment mortgage, what is the annual interest rate associated with the loan if the monthly payment is … $1,750? i = .3556, y = 4.27% HP 10bII+ I/YR = 4.2674% $2,500? i = .6311, y = 7.57% HP 10bII+ I/YR = 7.5731%

Discounted cash flows – HP 10bII+ Main keys used in calculations relating to cash flows: CFj – the cash flow received in period j CF0 – amount paid up front CF1 – 1st cash flow received CF2 – 2nd cash flow received (and so on) Nj – the number of payments equal to CFj, default value is 1 Enter cash flow, then . If this cash flow is received 3 times, for example, then hit 3 then then NPV – net present value IRR/YR – internal rate of return C ALL to clear cash flow register

Discounted cash flows – HP 10bII+ Suppose that an initial investment of $1,000 results in the following sequence of annual cash flows: What is the internal rate of return associated with this investment? Make sure P/YR = 1 Enter the initial cash flow, -1000, into CF0 Enter the first cash flow, 25, into CFj Enter the second cash flow, 35, into CFj Enter the third and final cash flow, 1300, into CFj Solve for the IRR, 11.0560% Period 1 2 3 Cash flow 25 35 1300

Discounted cash flows – HP 10bII+ Suppose that an initial investment of $1,000 results in the following sequence of annual cash flows: What is the net present value associated with this investment if your required return is 10%? Make sure P/YR = 1 Enter the initial cash flow, -1000, into CF0 Enter the first cash flow, 25, into CFj Enter the second cash flow, 35, into CFj Enter the third and final cash flow, 1300, into CFj Enter 10.00 into I/YR Solve for the NPV, 28.3621 Period 1 2 3 Cash flow 25 35 1300

Discounted cash flows – HP 10bII+ Suppose that an initial investment of $5,000 results in a payment $750 a year for 25 years. Make sure P/YR = 1. What is the IRR of this investment? Enter the initial cash flow, -5000, into CF0 Enter the cash flow, 750, into CFj Enter the number of payments, 25, into Nj Solve for IRR/YR, 14.4909 What is the net present value associated with this investment if your required return is 12%? Enter 12.00 into I/YR Solve for the NPV, 882.3543 What is the net present value associated with this investment if your required return is 15%? Enter 15.00 into I/YR Solve for the NPV, -151.8882

Discounted cash flows – HP 10bII+ Suppose that an initial investment of $10,000 results in a payment $750 a year for 100 years. Make sure P/YR = 1. What is the IRR of this investment? Enter the initial cash flow, -5000, into CF0 Enter the cash flow, 750, into CFj Enter the number of payments, 90, into Nj Enter the number of payments, 10, into Nj Solve for the IRR, 7.4945 What is the net present value associated with this investment if your required return is 10%? Enter 10.00 into I/YR Solve for the NPV, -2500.5442

Discounted cash flows Suppose that an initial investment of $2,500 results in the following sequence of annual cash flows: What is the internal rate of return associated with this investment? IRR = 6.2350% What is the net present value associated with this investment if your required return is 10%? -242.2239 What is the net present value associated with this investment if your required return is 5%? 87.1072 Period 1 2 3 Cash flow 60 75 2850

Discounted cash flows Suppose that an initial investment of $7,000 results in a payment $825 a year for 120 years What is the IRR of this investment? IRR =11.7857 What is the net present value associated with this investment if your required return is 10%? NPV = 1249.9110 What is the net present value associated with this investment if your required return is 12%? NPV = -125.0085