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

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

 For applications in real estate, finance and accounting, you want a financial calculator Hewlett-Packard: 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 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 Which calculator should you purchase?

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 not covered in this tutorial:  HP 10bii  HP 12c  HP 17bii  TI BAII Plus pdf pdf User manuals

 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 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. 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 “×”.  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 “÷”. Basic calculations

Main keys used in calculations relating to mortgage loans:  n – total number of compounding periods  i – periodic 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 and To clear the information stored in the financial function keys, enter “f” and then “x><y” Mortgages

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?  How much will you borrow from the lender? PV = -225,000  How many payments? n = 12 x 30 = 360  What is the balance remaining after making the last payment? FV = 0  What is the monthly interest rate? i = 5.00/12 =.4167  What is the monthly payment? PMT = ? = Mortgage payments

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?  How much will you borrow from the lender? PV = -225,000  How many payments? n = 12 x 30 = 360  What is the balance remaining after making the last payment? FV = 0  What is the monthly interest rate? i = 5.50/12 =.4583  What is the monthly payment? PMT = ? = 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 30-year fixed-rate, fixed-payment mortgage with a …  4.0% annual interest rate? PMT = ? =  4.5% annual interest rate? PMT = ? =  5.0% annual interest rate? PMT = ? =  5.5% annual interest rate? PMT = ? =  6.0% annual interest rate? PMT = ? = Mortgage payments

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 = 12 x 15 = 180  What is the balance remaining after making the last payment? FV = 0  What is the monthly interest rate? i = 5.00/12 =.4167  What is the monthly payment? PMT = ? = 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 = ? =  5.0% annual interest rate? PMT = ? = Mortgage payments

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 = 12 x 30 = 360  What is the balance remaining after making the last payment? FV = 100,000  What is the monthly interest rate? i = 5.00/12 =.4167  What is the monthly payment? PMT = ? = 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 = ? = 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 = ? = Mortgage payments

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 = ? =  What is the balance remaining after making 36 payments? n = 36 FV = ? = 214, 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? PMT = ? =  What is the balance remaining after making 60 payments? n = 60 FV = ? = 206, 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? FV = ? = 332,  ten years? FV = ? = 288, Mortgage balances

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 = 12 x 30 = 360  What is the balance remaining after making the last payment? FV = 0  What is the monthly payment? PMT =  What is the interest rate? i = ? =.5850 y = 12 x i = 7.02% Mortgage yield

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 = 12 x 30 = 360  What is the balance remaining after making the last payment? FV = 0  What is the monthly payment? PMT =  What is the interest rate? i = ? =.4420 y = 12 x i = 5.30% 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 …  $1750? i =.3556, y = 4.27%  $2500? i =.6311, y = 7.57% Mortgage yield

Main keys used in calculations relating to cash flows:  CF0 – the required investment  CFj – the cash flow received in period j j <= 19, if cash flows are entered for 20 periods, the 20 th cash flow is stored in FV  Nj – the number of payments equal to CFj the default value of Nj is 1 Nj <= 99  NPV – net present value  IRR – internal rate of return To solve for the IRR, at least one entry into the cash flow register must be negative  REG – clears the cash flow register Discounted cash flows

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? 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, % Discounted cash flows Period123 Cash flow

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%? 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 into i Solve for the NPV, Discounted cash flows Period123 Cash flow

Suppose that an initial investment of $5,000 results in a payment $750 a year for 25 years  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 the IRR,  What is the net present value associated with this investment if your required return is 12%? Enter into i Solve for the NPV,  What is the net present value associated with this investment if your required return is 15%? Enter into i Solve for the NPV, Discounted cash flows

Suppose that an initial investment of $10,000 results in a payment $750 a year for 100 years  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 cash flow, 750, into CFj Enter the number of payments, 10, into Nj Solve for the IRR, 7.49  What is the net present value associated with this investment if your required return is 10%? Enter into i Solve for the NPV, 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 = %  What is the net present value associated with this investment if your required return is 10%?  What is the net present value associated with this investment if your required return is 5%? Discounted cash flows Period123 Cash flow

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 =  What is the net present value associated with this investment if your required return is 10%? NPV =  What is the net present value associated with this investment if your required return is 12%? NPV = Discounted cash flows