# BUSI 121 Foundations of Real Estate Mathematics

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Real Estate Division BUSI 121 Foundations of Real Estate Mathematics SESSION 2 By Graham McIntosh Sauder School of Business University of British Columbia

2 Outline Introduction Cash Flow Problems Cash Flow Keys Annuities Annuities Due Deferred Annuities Perpetual Annuities 2

3 HP 10BII + Calculator 3

4 Types of Cash Flow Problems Time Present Value Future Value Cash Flows Even Uneven Interval Regular Irregular 4

5 Types of Cash Flow Problems Even cash flows occurring at regular intervals are characteristic of annuity-type of problems Use the annuity formulas and financial calculator keys Examples: solving standard mortgage problems When cash flows are uneven and or irregular it is better to use the cash flow keys 5

6 Types of Cash Flow Problems Time Diagram: Present Value PV = PV 1 + PV 2 + PV 3 + PV PV n-1 + PV n Present Value PV =? CF 1 CF 2 CF 3 CF 4 CF n n-1... CF n n PV 1 = CF 1 (1 + i) -1 PV 2 = CF 2 (1 + i) -2 PV 3 = CF 3 (1 + i) -3 PV 4 = CF 4 (1 + i) -4 PV n-1 = CF n-1 (1 + i) - n-1 PV n = CF n (1 + i) -n 6

7 Types of Cash Flow Problems Time Diagram: Future Value FV = FV 1 + FV 2 + FV 3 + FV FV n-1 + FV n FV =? 0 CF 1 CF 2 CF 3 CF 4 CF n n-1 n... CF n CF n (1 + i) n-n = FV n CF n-1 (1 + i) n-(n-1) = FV n-1 CF 4 (1 + i) n-4 = FV 4 CF 3 (1 + i) n-3 = FV 3 CF 2 (1 + i) n-2 = FV 2 CF 1 (1 + i) n-1 = FV 1 7

8 Types of Cash Flow Problems EXAMPLE: PRESENT VALUE OF UNEVEN CASH FLOWS AT REGULAR INTERVALS An investor has an opportunity to purchase a property. The investor expects to hold the property for 3 years and estimates it to produce the following net cash flows (benefits or revenues costs or expenses ) at the end of each year: End of Year Net Cash Flow 10,000 35, ,000 If the investor desires to earn a yield of j 1 = 11% (compounded annually), how much should the investor pay for the property today (present value)? 8

9 Types of Cash Flow Problems Time Diagram: PV = PV 1 + PV 2 + PV 3 PV = -10,000(1 +.11) ,000(1 +.11) ,000(1+.11) -3 Present Value of uneven Cash Flows PV =? CF 1 -\$10,000 CF 2 \$35,000 CF 3 \$100, PV 1 = CF 1 (1.11) -1 PV 2 = CF 2 (1.11) -2 PV 3 = CF 3 (1.11) -3 9

10 Types of Cash Flow Problems Solution Method 1: Using the Financial Keys Press Display 1 P/YR 1 11 NOM% 11 1 N 1 0 PMT /- FV -10,000 PV 9, M 9, N FV 35,000 PV -28, M+ -28, N 3 100,000 FV 100,000 PV -73, M+ -73,

11 Types of Cash Flow Problems In order for the investor to earn j 1 = 11% on their investment, the maximum amount they would be willing to pay would be \$92, Cumbersome process using the financial keys Much easier using the cash Flow Keys for this type of problem 11

12 Types of Cash Flow Problems Method 2: Using the Cash Flow Keys (highly recommended!) 12

13 Types of Cash Flow Problems NOTATION PV = n -t t t=1 k = discount rate C t = Net Cash Flow in period t n = Last compounding period or cash flow n t=1 [CF x (1 + k) ] = sum of all cash flows at time = 0 SHORTHAND WAY OF WRITING: PV = [CF 1 (1 + k) -1 + CF 2 (1 + k) CF n (1 + k) -n ] or PV = CF1 CF2 CFn + + (1+k) (1+k) (1+k) 1 2 n 13

14 Net Present Value (NPV) Solution Using a HP 10B II+ Financial Calculator: Turn ON and Clear Screen DCF set up Blue Shift Key Access Blue Functions 2. Clear Mem Clear Memory Key 3. 0 Clear Cash Flow Keys (cflo clr) 3

15 Net Present Value (NPV) Solution Using a HP 10B II+ Financial Calculator: 1 P/YR set P/YR = 1 11 I/YR set discount rate = 11% 0 CF j CF 0 0 (cost = 0 we are calculating a PV) /- CF j CF 1 = -10,000 (cash flow group 1) CFj CF 2 = 35,000 (cash flow group 2) CFj CF 3 = 100,000 (cash flow group 3) NPV 92, NPV NPV > 0 Therefore accept the investment Note: 92, is also stored in PV Note: far fewer steps Note: DCF Keys can also be used to solve annuity problems and multi cash flow problems (using N j )

16 Types of Cash Flow Problems Problems that involve irregular or uneven cash flows, solve with the cash flow keys This topic will be revisited in Chapter 9 16

17 What is a mortgage? Financial Definition: A mortgage is a loan secured by real estate Legal Definition: mort = dead gage = pledge The borrower pledges their real estate to the lender as security (collateral) for the loan The pledge (mortgage) is registered on the certificate of title Once the loan is repaid, the mortgage is removed from the title

18 Mortgage Terminology The borrower is referred to as the mortgagor The lender is referred to as the mortgagee Their relationship is subject to a mortgage contract 18

19 Mortgage Terminology Fully Amortized Loan: when the amortization period equals the term Partially Amortized Loan: when the term is less than the amortization period 19

20 Classification of Mortgage Loans Type of property (residential vs non residential) Use of Mortgage Default Insurance conventional < 80% L/V high ratio >80% L/V Sources of Mortgage Funds Institutional Lenders: banks, credit unions, trust co, mortgage loan companies, life insurance co, pension funds Private Lenders Priority of mortgage on title (first, second, etc.)

21 Constant Blended Payments Equal payments occurring at equal intervals of time (an annuity) Payments are a blend of principal and interest The blend of principal changes as the loan is repaid, gradually more principal and less interest constitutes each payment 21

22 Periodic Payment on a Constant Mortgage Principal and Interest Split Constant Payment Mortgage Monthly Payments (\$) Interest Principal Amortization Period Outstanding Balance on a Constant Payment Mortgage Outstanding Balance (\$) Amortization Period

23 Standard Mortgage Calculations General Steps: 1. Read the Question Carefully. 2. Read it again! 3. Summarize the Facts. 4. Calculator Steps 5. Record the Answer 23

24 Standard Canadian Mortgages This is an application of the general annuity Characteristics 1. Equal payments occurring at regular intervals of time. 2. Payment frequency usually does not match the interest rate compounding frequency. 24

25 Standard Canadian Mortgages 3. The term does not match the amortization period, called a partially amortized loan. Solution Before calculating the payment on this type of mortgage, an interest rate conversion must be conducted. 25

26 EXAMPLE 1: Standard Canadian Mortgages Interest rate conversion and mortgage payment calculation. A \$300,000 mortgage is negotiated with the following terms: interest rate j 2 = 9% 25 year amortization monthly payments not in advance What is the size of the required monthly payments? 26

27 EXAMPLE 1: Standard Canadian Mortgages Equations for Annuities PV = PMT 1 (1 + i) i n Solve for PV OR PMT = PV 1 (1 + i) i n Solve for PMT NOTE: These equations can only be used if the payment and compounding frequencies match. 27

28 EXAMPLE 1: Standard Canadian Mortgages Solution STEP 1: Convert j 2 = 9% to the equivalent nominal rate (i.e., j 12 ) to match the payment frequency. STEP 2: Calculate the required monthly payment. 28

29 EXAMPLE 1: Standard Canadian Mortgages Step 1: Interest Rate Conversion (using the interest rate conversion keys) Press Display Comments 9 NOM% 9 stated nominal rate 2 P/YR 2 stated compounding frequency EFF% effective rate 12 P/YR 12 desired compounding frequency NOM% j 12 equivalent rate (automatically stored in I/YR ) 29

30 EXAMPLE 1: Standard Canadian Mortgages Step 2: Payment Calculation Press Display Comments = 300 N 300 number of payment period 300,000 PV 300,000 loan amount 0 FV 0 PMT -2, monthly payment NOTE: Always round payments to the next highest cent. PMT = 2,

31 Recall Function RCL Key Use in conjunction with other TVM keys to check data entered RCL N RCL I/YR RCL PV RCL PMT RCL FV - check number of periods - check nominal interest rate - check present value - check payment - check future value RCL P/YR - check compounding frequency per year 31

32 Recall Function RCL Key Last example: RCL N 300 (months) RCL I/YR (j 12 rate) RCL PV 300,000 (loan amount) RCL PMT -2, (pmt) RCL FV 0 RCL P/YR 12 (compounding frequency per year) 32

33 Standard Mortgage Questions Table Complete the following table Mortgage Interest Amortization Payment Payment Amount Rate (years) Frequency \$500,000 j 4 = 8% 15 Monthly?? j 2 = 5% 20 Monthly \$2500 \$100,000 j 2 = 7%? Monthly \$ \$200,000 j 2 =? 25 Monthly \$

34 Step 1: Interest Rate Conversion Question 1 Solving for the Payment Convert j 4 = 8% j 12 Rate Press Display Comments 8 NOM% 8 4 P/YR 4 EFF% P/YR 12 NOM% j 12 Rate j 4 = 8% Automatically stored in I/YR 34

35 Question 1 Solving for the Payment Step 2: Solve for the Monthly PMT Press Display Comments = 180 N 180 amortization period 500,000 PV 500,000 loan amount 0 FV 0 PMT -4, Monthly PMT = \$4,

36 Mortgage Questions Table Complete the following table Mortgage Interest Amortization Payment Payment Amount Rate (years) Frequency \$500,000 j 4 = 8% 15 Monthly \$ ? j 2 = 5% 20 Monthly \$2500 \$100,000 j 2 = 7%? Monthly \$ \$200,000 j 2 =? 25 Monthly \$

37 Question 1a Solving for the Interest Only Payment Step 2: Solve for the Interest Only Monthly PMT Press Display Comments = 180 N 180 Payment Schedule 500,000 PV 500,000 loan amount 500,000 +/- FV -500,000 no amortization PV = FV PMT -3, Monthly Interest Only PMT = \$3,

38 Question 1a Solving for the Interest Only Payment Step 2: Solve for the Interest Only Monthly PMT Another Method: Press Display Comments RCL I/YR j12 rate as a percentage 12 = imo as a percentage % E -3 imo as a decimal X 500,000 = -3, Monthly Interest Only PMT Monthly Interest Only PMT = \$3,

39 Question 1a Solving for the Interest Only Payment Step 2: Solve for the Interest Only Monthly PMT Press Display Comments 1 N 1 N = any value > 1 500,000 PV 500,000 loan amount 500,000 +/- FV -500,000 no amortization PV = FV PMT -3, Monthly PMT = \$3,

40 Step 1: Interest Rate Conversion Question 2 Solving for the Mortgage Amount Convert j 2 = 5% j 12 Rate Press Display Comments 5 NOM% 5 2 P/YR 2 EFF% P/YR 12 NOM% j 12 Rate j 2 = 5% Automatically stored in I/YR 40

41 Question 2 Solving for the Mortgage Amount Step 2: Solve for the Mortgage Amount PV Press Display Comments = 240 N 240 2,500 +/- PMT -2,500 0 FV 0 PV 380, Mortgage Amount = \$380,

42 Mortgage Questions Table Complete the following table Mortgage Interest Amortization Payment Payment Amount Rate (years) Frequency \$500,000 j 4 = 8% 15 Monthly \$ \$ 380, j 2 = 5% 20 Monthly \$2500 \$100,000 j 2 = 7%? Monthly \$ \$200,000 j 2 =? 25 Monthly \$

43 Step 1: Interest Rate Conversion Question 3 Solving for the Amortization Period Convert j 2 = 7% j 12 Rate Press Display Comments 7 NOM% 7 2 P/YR 2 EFF% P/YR 12 NOM% j 12 Rate j 2 = 7% Automatically stored in I/YR 43

44 Question 3 Solving for the Amortization Period Step 2: Solve for the Amortization Period (in Years) N Press Display Comments 100,000 PV 100, /- PMT FV 0 N Amortization Period in Months 12 = Amortization Period = 20 Years 44

45 Question 4 Solving for an Interest Rate Step 1: Solve for I/YR Press Display = 300 N ,000 PV 200, /- PMT FV 0 12 P/YR 12 I/YR j 12 rate automatically stored in NOM% 45

46 Mortgage Questions Table Complete the following table Mortgage Interest Amortization Payment Payment Amount Rate (years) Frequency \$500,000 j 4 = 8% 15 Monthly \$ \$ 380, j 2 = 5% 20 Monthly \$2500 \$100,000 j 2 = 7% 20 Monthly \$ \$200,000 j 2 =? 25 Monthly \$

47 Step 2: Convert j 12 j 2 Rate Question 4 Solving for an Interest Rate Press Display Comments EFF% P/YR 2 NOM% j 2 Rate j 12 =

48 Mortgage Questions Table Complete the following table Mortgage Interest Amortization Payment Payment Amount Rate (years) Frequency \$500,000 j 4 = 8% 15 Monthly \$ \$ 380, j 2 = 5% 20 Monthly \$2500 \$100,000 j 2 = 7% 20 Monthly \$ \$200,000 j 2 = % 25 Monthly \$

49 Standard Mortgage Questions Mathematical Method Example 1: j 2 = 9% Mortgage = \$300, year Amortization Monthly payments 49

50 Standard Mortgage Questions Mathematical Method Example 1: Step 1:Convert j 2 = 9% to i mo Calculator Steps Press Display Comments y x enter i sa 6 1/x raise to power of 1/6 = i mo as a % -1 = i mo as a decimal M i mo store in memory 50

51 Standard Mortgage Questions Mathematical Method Question 1: Step 2: Find Payment using the annuity equation i mo = n = 300 PV =\$

52 Standard Mortgage Questions Mathematical method Question 1: Step 2: Find Payment Calculator Steps Press Display Comments RM + 1 = i mo + 1 y x 300 +/ E-1 raised to n = / E-1 subtract from 1 RM = divided by i mo 1/x E-3 take the reciprocal of X 300, ,000 multiply by PV = 2, monthly PMT 52

53 Annuities Due PMT s Occur at the beginning of each period Use BEG/END Function A \$300,000 lease is negotiated with the following terms: interest rate j 2 = 9% 25 year amortization monthly lease payments in advance What is the size of the required monthly payments (due)? 53

54 EXAMPLE: Annuities Due Equation: Annuities Due PV = PMT 1 (1 + i) i n X (1+i) Solve for PV PMT = PV 1 (1 ) n + i Solve for PMT i X (1+i) NOTE: multiplying by (1+i) moves the PMTs to the beginning of the period NOTE: These equations can only be used if the payment and compounding frequencies match (interest rate conversion may be required). 54

55 EXAMPLE: Annuities Due Solution STEP 1: Convert j 2 = 9% to the equivalent nominal rate (i.e., j 12 ) to match the payment frequency. STEP 2: Calculate the required monthly lease payment due 55

56 EXAMPLE: Annuities Due Step 1: Interest Rate Conversion (using the interest rate conversion keys) Press Display Comments 9 NOM% 9 stated nominal rate 2 P/YR 2 stated compounding frequency EFF% effective rate 12 P/YR 12 desired compounding frequency NOM% j 12 equivalent rate (automatically stored in I/YR ) 56

57 EXAMPLE: Annuities Due Step 2: Payment Due Calculation Switch to Begin Mode: Press BEG/END Press Display Comments = 300 N 300 number of payment period 300,000 PV 300,000 loan amount 0 FV 0 PMT -2, monthly lease payment NOTE: Round payments to the next higher cent. PMT = 2,

58 Deferred Annuities Annuities where the payments begin at some point in the future. PV =? PMT PMT PMT PMT PMT PMT PMT PMT PMT PMT Period of Deferral Beginning of Annuity End of Annuity 58

59 Deferred Annuities ANALYSIS 2 Methods: (1) Two present values calculations (i) PV of PMT at beginning of the annuity enter as FV (ii) PV of FV at beginning of Deferral period (2) Difference between two present values (i) PV of PMT of the entire period LESS (ii) PV of PMT of the deferral period 59

60 Deferred Annuities EXAMPLE: An investor has an opportunity to receive 10 payments of \$1000 per year, however, the payments will not begin for 4 years. How much should the investor pay for the payment stream if the desired yield is j 1 = 10%? 60

61 Deferred Annuities ANALYSIS: Data: PMT = \$1000 per annum N = 10 j 1 = 10% Deferment = 4 years PV =? 61

62 Deferred Annuities Method 1: Calculate 2 PV s. Time Diagram: PV 3 = 1000 a(10,0.10) PV 3 PV 0 = FV 3 ( ) PV 0 FV

63 Deferred Annuities Equations: PV 3 = PMT a [n,i] PV 0 = FV 3 (1 + i) -3 OR PV = [PMT a [n,i]] (1 + i) -d (-d = deferment period) NOTE: PV 3 = FV 3 a[n,i] is an abbreviation of the PV of an annuity equation 63

64 Deferred Annuities Solution : Calculate PV 3, then discount PV 3 to find PV 0 Press Display Comments 1 P/YR 1 10 I/YR 10 j 1 = 10% /- PMT annuity payments 10 N 10 number of payments 0 FV 0 PV 6, PV 3 of 10 payments of \$1000 +/- FV - 6, enter PV 3 as FV 3 0 PMT 0 3 N 3 deferral period PV 4, PV 0 The investor should pay no more than \$4,

65 Deferred Annuities METHOD 2: Difference between two Present values. Time Diagram: PV =? Years in the future ( \$100) PV = PMT a 13, j 1 = 10% PV =? MINUS ( \$100) Years in the future PV = PMT a 3, j 1 = 10% EQUALS Years in the future ( \$100)

66 Deferred Annuities Equations: PV = PMT a[13, i = 10%] PMT a 3, [i = 10%] OR PV = [ PMT a[n + d, i]] [PMT a [d,i]] d = deferment period 66

67 Deferred Annuities Solution: Press Display Comments 1 P/YR 1 10 I/YR 10 j 1 = 10% /- PMT payments 13 N 13 entire period 0 FV 0 PV 7, PV of entire period M 7, stored in memory 3 N 3 deferment period PV 2, PV of deferred annuity M+ +/- -2, add to value in memory RM 4,

68 Deferred Annuities Cash Flow Method: Press Display Comments 1 P/YR 1 10 I/YR 10 0 CF j CF CF j CF N j n 1 3 deferment period 1000 CF j CF annuity payments 10 N j 10 number of payments NPV 4,

69 Perpetual Annuities Used in Real Estate investment analysis and appraisal and other cost/benefit situations where the cash flows are expected to endure for a very long period of time. In real estate appraisal and investment analysis the "Capitalization Rate" or Cap Rate is a direct application of perpetual annuities 69

70 Perpetual Annuities Equation: Perpetual Annuites Note: this equation can only be applied if: 1) The payments remain constant 2) The interest rate remains constant Note: PMTs occur at the END of each period 70

71 Perpetual Annuities Example: PMT = \$3,250,000 per annum Interest rate = 9% per annum Compounding Frequency = annual (P/YR =1) Calculate the Present Value when the number of PMTs = a) n = 50 b) n = 120 c) n = 999 d) n = (infinity) 71

72 Perpetual Annuities Equation: 72

73 Perpetual Annuities Time Diagram: Perpetual Annuities PV =? Qa Qb Qc Qd PMT PMT PMT PMT PMT PMT PMT

74 Perpetual Annuities Calculation Press Display Comments 1 P/YR 1 comp frq yr 9 I/YR 9 interest rate yr 3,250,000 +/- PMT 3,250,000 PMT yr 0 FV 0 reversionary value 50 N 50 # of PMTS (50) PV 35,625, = N 120 N =120 PV 36,109, = N 999 N =999 PV 36, 111, =999 74

75 Perpetual Annuities If n = - (really small!) then use the PV annuity equation becomes the PV perpetuity equation: The term (1+i) - becomes = 0 75

76 Perpetual Annuities = \$36,111, same as N =999 years 76

77 Perpetual Annuities Summary Table N = PMT Interest PV Rate/yr 50 3,250,000 9% \$35,625, PV 120 3,250,000 9% \$36,109, \$484, ,250,000 9% 36,111, \$1, ,250,000 9% 36,111, \$0 77

78 Perpetual Annuities PV vs N with PMT = \$3.25M, I/YR =9% Present Value (\$ millions) (25, 31.9m) (50, 35.6m) (120, 36.1m) (999; 36.11m) (5, 12.6m) (1, 3m) Time (Years) 78

79 Perpetual Annuities TVM: Time Value of Money Money received further in the future is worth much less today. After about 100 periods, the value of any future cash flow is effectively 0 hence we do not have to worry about reversionary values. 79

80 Perpetual Annuities Note: this property also explains that for given PMT amount at a certain interest rate, why extending mortgage amortization period beyond about 50 periods leads to relatively small increase to amount that can be borrowed (PV). 80

81 Perpetual Annuities Due Equation: Perpetual Annuities Due PMT PV = 1+ i ( i) Note: this equation can only be applied if: 1) The payments remain constant 2) The interest rate remains constant Multiplying by (1+i) moves the PMTs to the beginning of each period 81

### Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations

Introduction to the Hewlett-Packard (HP) 10BII Calculator and Review of Mortgage Finance Calculations Real Estate Division Sauder School of Business University of British Columbia Introduction to the Hewlett-Packard

### BASICS. Access blue functions with [Shift up] Access orange functions with [Shift down]

CALCULATOR COURSE BASICS Most keys have three functions: Primary function printed in white Secondary function printed in orange Tertiary function printed in blue Access blue functions with [Shift up] Access

### CHAPTER 2. Time Value of Money 2-1

CHAPTER 2 Time Value of Money 2-1 Time Value of Money (TVM) Time Lines Future value & Present value Rates of return Annuities & Perpetuities Uneven cash Flow Streams Amortization 2-2 Time lines 0 1 2 3

### Discounted Cash Flow Valuation

Discounted Cash Flow Valuation Chapter 5 Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### Calculator (Hewlett-Packard 10BII) Tutorial

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT Calculator (Hewlett-Packard 10BII) Tutorial To begin, look at the face of the calculator. Most keys (except a few) have two functions: Each key s primary function

### Integrated Case. 5-42 First National Bank Time Value of Money Analysis

Integrated Case 5-42 First National Bank Time Value of Money Analysis You have applied for a job with a local bank. As part of its evaluation process, you must take an examination on time value of money

### Ehrhardt Chapter 8 Page 1

Chapter 2 Time Value of Money 1 Time Value Topics Future value Present value Rates of return Amortization 2 Time lines show timing of cash flows. 0 1 2 3 I% CF 0 CF 1 CF 2 CF 3 Tick marks at ends of periods,

### DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS

Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need \$500 one

### CHAPTER 9 Time Value Analysis

Copyright 2008 by the Foundation of the American College of Healthcare Executives 6/11/07 Version 9-1 CHAPTER 9 Time Value Analysis Future and present values Lump sums Annuities Uneven cash flow streams

### Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS

Chapter 4 Time Value of Money ANSWERS TO END-OF-CHAPTER QUESTIONS 4-1 a. PV (present value) is the value today of a future payment, or stream of payments, discounted at the appropriate rate of interest.

### Hewlett-Packard 10BII Tutorial

This tutorial has been developed to be used in conjunction with Brigham and Houston s Fundamentals of Financial Management 11 th edition and Fundamentals of Financial Management: Concise Edition. In particular,

### Hewlett Packard (HP) 10BII

Hewlett Packard (HP) 10BII The HP10BII is programmed to perform two basic types of operations: statistical operations and financial operations. Various types of computations are activated by depressing

### 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?

Chapter 2 - Sample Problems 1. If you wish to accumulate \$140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will \$247,000 grow to be in

### Using Financial Calculators

Chapter 4 Discounted Cash Flow Valuation 4B-1 Appendix 4B Using Financial Calculators This appendix is intended to help you use your Hewlett-Packard or Texas Instruments BA II Plus financial calculator

### Chapter 8. Present Value Mathematics for Real Estate

Chapter 8 Present Value Mathematics for Real Estate Real estate deals almost always involve cash amounts at different points in time. Examples: Buy a property now, sell it later. Sign a lease now, pay

### Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e

Texas Instruments BAII Plus Tutorial for Use with Fundamentals 11/e and Concise 5/e This tutorial was developed for use with Brigham and Houston s Fundamentals of Financial Management, 11/e and Concise,

### Ordinary Annuities Chapter 10

Ordinary Annuities Chapter 10 Learning Objectives After completing this chapter, you will be able to: > Define and distinguish between ordinary simple annuities and ordinary general annuities. > Calculate

### Chapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.

Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values

### Using Financial And Business Calculators. Daniel J. Borgia

Using Financial And Business Calculators Daniel J. Borgia August 2000 Table of Contents I. Texas Instruments BA-35 SOLAR II. Texas Instruments BAII PLUS III. Hewlett Packard 12C IV. Hewlett Packard 17BII..

### 5. Time value of money

1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned

### Chapter 5 & 6 Financial Calculator and Examples

Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Spring 2016 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get

### CALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time

CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses

### Introduction. Turning the Calculator On and Off

Texas Instruments BAII PLUS Calculator Tutorial to accompany Cyr, et. al. Contemporary Financial Management, 1 st Canadian Edition, 2004 Version #6, May 5, 2004 By William F. Rentz and Alfred L. Kahl Introduction

### How to calculate present values

How to calculate present values Back to the future Chapter 3 Discounted Cash Flow Analysis (Time Value of Money) Discounted Cash Flow (DCF) analysis is the foundation of valuation in corporate finance

### Chapter 1: Time Value of Money

1 Chapter 1: Time Value of Money Study Unit 1: Time Value of Money Concepts Basic Concepts Cash Flows A cash flow has 2 components: 1. The receipt or payment of money: This differs from the accounting

### Time Value of Money. If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in

Time Value of Money Future value Present value Rates of return 1 If you deposit \$100 in an account that pays 6% annual interest, what amount will you expect to have in the account at the end of the year.

### Hewlett-Packard 10B Tutorial

To begin, look at the face of the calculator. Every key (except one, the gold shift key) on the 10B has two functions: each key's primary function is noted in white on the key itself, while each key's

### TIME VALUE OF MONEY (TVM)

TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate

### hp calculators HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow

HP 17bII+ Discounting & Discounted Cash Flow Analysis It's About Time The Financial Registers versus Discounted Cash Flow Discounting a Single Sum Discounting and Compounding Discounting a Series of Sums

### Time-Value-of-Money and Amortization Worksheets

2 Time-Value-of-Money and Amortization Worksheets The Time-Value-of-Money and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or

### 3. Time value of money. We will review some tools for discounting cash flows.

1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned

### In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

Section 4: Using a Financial Calculator Tab 1: Introduction and Objectives Introduction In this section, the functions of a financial calculator will be reviewed and some sample problems will be demonstrated.

### Introduction to Real Estate Investment Appraisal

Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has

### Fin 5413 CHAPTER FOUR

Slide 1 Interest Due Slide 2 Fin 5413 CHAPTER FOUR FIXED RATE MORTGAGE LOANS Interest Due is the mirror image of interest earned In previous finance course you learned that interest earned is: Interest

### 2. How would (a) a decrease in the interest rate or (b) an increase in the holding period of a deposit affect its future value? Why?

CHAPTER 3 CONCEPT REVIEW QUESTIONS 1. Will a deposit made into an account paying compound interest (assuming compounding occurs once per year) yield a higher future value after one period than an equal-sized

### Chapter 4. The Time Value of Money

Chapter 4 The Time Value of Money 1 Learning Outcomes Chapter 4 Identify various types of cash flow patterns Compute the future value and the present value of different cash flow streams Compute the return

### Chapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams

Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present

### TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007

TT03 Financial Calculator Tutorial And Key Time Value of Money Formulas November 6, 2007 The purpose of this tutorial is to help students who use the HP 17BII+, and HP10bll+ calculators understand how

### Texas Instruments BAII PLUS Tutorial

To begin, look at the face of the calculator. Almost every key on the BAII PLUS has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### substantially more powerful. The internal rate of return feature is one of the most useful of the additions. Using the TI BA II Plus

for Actuarial Finance Calculations Introduction. This manual is being written to help actuarial students become more efficient problem solvers for the Part II examination of the Casualty Actuarial Society

### The Time Value of Money

The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time

### Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Chapter Outline. Multiple Cash Flows Example 2 Continued

6 Calculators Discounted Cash Flow Valuation Key Concepts and Skills Be able to compute the future value of multiple cash flows Be able to compute the present value of multiple cash flows Be able to compute

### MHSA 8630 -- Healthcare Financial Management Time Value of Money Analysis

MHSA 8630 -- Healthcare Financial Management Time Value of Money Analysis ** One of the most fundamental tenets of financial management relates to the time value of money. The old adage that a dollar in

### A Textual Explanation

NAVIGATION INSTRUCTIONS GLOSSARY FINANCIAL CALCULATIONS FOR LAWYERS LECTURES INDEX INTRODUCTION PRESENT VALUE OF A SUM FUTURE VALUE OF A SUM SINKING FUND AMORTIZATION WITH CHART PRESENT VALUE OF AN ANNUITY

### Learning Objectives. Learning Objectives. Learning Objectives. Principles Used in this Chapter. Simple Interest. Principle 2:

Learning Objectives Chapter 5 The Time Value of Money Explain the mechanics of compounding, which is how money grows over a time when it is invested. Be able to move money through time using time value

### Course FM / Exam 2. Calculator advice

Course FM / Exam 2 Introduction It wasn t very long ago that the square root key was the most advanced function of the only calculator approved by the SOA/CAS for use during an actuarial exam. Now students

### The time value of money: Part II

The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods

### Chapter 02 How to Calculate Present Values

Chapter 02 How to Calculate Present Values Multiple Choice Questions 1. The present value of \$100 expected in two years from today at a discount rate of 6% is: A. \$116.64 B. \$108.00 C. \$100.00 D. \$89.00

### THE TIME VALUE OF MONEY

QUANTITATIVE METHODS THE TIME VALUE OF MONEY Reading 5 http://proschool.imsindia.com/ 1 Learning Objective Statements (LOS) a. Interest Rates as Required rate of return, Discount Rate and Opportunity Cost

### Time Value of Money. Reading 5. IFT Notes for the 2015 Level 1 CFA exam

Time Value of Money Reading 5 IFT Notes for the 2015 Level 1 CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The Future Value

### Formulas, Symbols, Math Review, and Sample Problems

Formulas, Symbols, Math Review, and Sample Problems Mathematics and Analytical Skills Review... 1 Summary of Basic Formulas... 11 Direct Capitalization... 11 Yield Capitalization... 13 Present Value of

### Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS

Chapter 7 SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 0 1 2 3 4 5 10% PV 10,000 FV 5? FV 5 \$10,000(1.10) 5 \$10,000(FVIF 10%, 5 ) \$10,000(1.6105) \$16,105. Alternatively, with a financial calculator enter the

### Chapter The Time Value of Money

Chapter The Time Value of Money PPT 9-2 Chapter 9 - Outline Time Value of Money Future Value and Present Value Annuities Time-Value-of-Money Formulas Adjusting for Non-Annual Compounding Compound Interest

### Sharp EL-733A Tutorial

To begin, look at the face of the calculator. Almost every key on the EL-733A has two functions: each key's primary function is noted on the key itself, while each key's secondary function is noted in

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction... 2 2. Interest Rates: Interpretation... 2 3. The Future Value of a Single Cash Flow... 4 4. The

### Chapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows

1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter

### Key Concepts and Skills

McGraw-Hill/Irwin Copyright 2014 by the McGraw-Hill Companies, Inc. All rights reserved. Key Concepts and Skills Be able to compute: The future value of an investment made today The present value of cash

### Statistical Models for Forecasting and Planning

Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information

### MAT116 Project 2 Chapters 8 & 9

MAT116 Project 2 Chapters 8 & 9 1 8-1: The Project In Project 1 we made a loan workout decision based only on data from three banks that had merged into one. We did not consider issues like: What was the

### Future Value. Basic TVM Concepts. Chapter 2 Time Value of Money. \$500 cash flow. On a time line for 3 years: \$100. FV 15%, 10 yr.

Chapter Time Value of Money Future Value Present Value Annuities Effective Annual Rate Uneven Cash Flows Growing Annuities Loan Amortization Summary and Conclusions Basic TVM Concepts Interest rate: abbreviated

### 3. If an individual investor buys or sells a currently owned stock through a broker, this is a primary market transaction.

Spring 2012 Finance 3130 Sample Exam 1A Questions for Review 1. The form of organization for a business is an important issue, as this decision has very significant effect on the income and wealth of the

### Chapter 4: Time Value of Money

FIN 301 Homework Solution Ch4 Chapter 4: Time Value of Money 1. a. 10,000/(1.10) 10 = 3,855.43 b. 10,000/(1.10) 20 = 1,486.44 c. 10,000/(1.05) 10 = 6,139.13 d. 10,000/(1.05) 20 = 3,768.89 2. a. \$100 (1.10)

### Chapter 28 Time Value of Money

Chapter 28 Time Value of Money Lump sum cash flows 1. For example, how much would I get if I deposit \$100 in a bank account for 5 years at an annual interest rate of 10%? Let s try using our calculator:

### Note: In the authors opinion the Ativa AT 10 is not recommended as a college financial calculator at any level of study

Appendix 1: Ativa AT 10 Instructions Note: DNS = Does Not Calculate Note: Loan and Savings Calculations Automatically round to two decimals. -Clear -Store Data in Memory -Recall Stored Data in Memory [CE]

### FinQuiz Notes 2 0 1 4

Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.

### FINANCIAL CALCULATIONS

FINANCIAL CALCULATIONS 1 Main function is to calculate payments, determine interest rates and to solve for the present or future value of a loan or an annuity 5 common keys on financial calculators: N

### Continue this process until you have cleared the stored memory positions that you wish to clear individually and keep those that you do not.

Texas Instruments (TI) BA II PLUS Professional The TI BA II PLUS Professional functions similarly to the TI BA II PLUS model. Any exceptions are noted here. The TI BA II PLUS Professional can perform two

### rate nper pmt pv Interest Number of Payment Present Future Rate Periods Amount Value Value 12.00% 1 0 \$100.00 \$112.00

In Excel language, if the initial cash flow is an inflow (positive), then the future value must be an outflow (negative). Therefore you must add a negative sign before the FV (and PV) function. The inputs

### USING THE SHARP EL 738 FINANCIAL CALCULATOR

USING THE SHARP EL 738 FINANCIAL CALCULATOR Basic financial examples with financial calculator steps Prepared by Colin C Smith 2010 Some important things to consider 1. These notes cover basic financial

### hp calculators HP 20b Time value of money basics The time value of money The time value of money application Special settings

The time value of money The time value of money application Special settings Clearing the time value of money registers Begin / End mode Periods per year Cash flow diagrams and sign conventions Practice

### Topics. Chapter 5. Future Value. Future Value - Compounding. Time Value of Money. 0 r = 5% 1

Chapter 5 Time Value of Money Topics 1. Future Value of a Lump Sum 2. Present Value of a Lump Sum 3. Future Value of Cash Flow Streams 4. Present Value of Cash Flow Streams 5. Perpetuities 6. Uneven Series

### Lease Analysis Tools

Lease Analysis Tools 2009 ELFA Lease Accountants Conference Presenter: Bill Bosco, Pres. wbleasing101@aol.com Leasing 101 914-522-3233 Overview Math of Finance Theory Glossary of terms Common calculations

### Ch. Ch. 5 Discounted Cash Flows & Valuation In Chapter 5,

Ch. 5 Discounted Cash Flows & Valuation In Chapter 5, we found the PV & FV of single cash flows--either payments or receipts. In this chapter, we will do the same for multiple cash flows. 2 Multiple Cash

### Financial Math on Spreadsheet and Calculator Version 4.0

Financial Math on Spreadsheet and Calculator Version 4.0 2002 Kent L. Womack and Andrew Brownell Tuck School of Business Dartmouth College Table of Contents INTRODUCTION...1 PERFORMING TVM CALCULATIONS

### The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)

The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL-738 Calculator Reference is made to the Appendix Tables A-1 to A-4 in the course textbook Investments:

### Hewlett-Packard 17BII Tutorial

To begin, look at the face of the calculator. Most keys on the 17BII have two functions: a key's primary function is noted in white on the key itself, while the key's secondary function is noted in gold

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

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

### Activity 3.1 Annuities & Installment Payments

Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.

### REVIEW MATERIALS FOR REAL ESTATE ANALYSIS

REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS

### Calculator and QuickCalc USA

Investit Software Inc. www.investitsoftware.com. Calculator and QuickCalc USA TABLE OF CONTENTS Steps in Using the Calculator Time Value on Money Calculator Is used for compound interest calculations involving

### Time Value of Money. Background

Time Value of Money (Text reference: Chapter 4) Topics Background One period case - single cash flow Multi-period case - single cash flow Multi-period case - compounding periods Multi-period case - multiple

### This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1).

This is Time Value of Money: Multiple Flows, chapter 7 from the book Finance for Managers (index.html) (v. 0.1). This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/

### Real Estate. Refinancing

Introduction This Solutions Handbook has been designed to supplement the HP-2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or step-by-step keystroke procedures

### PRESENT VALUE ANALYSIS. Time value of money equal dollar amounts have different values at different points in time.

PRESENT VALUE ANALYSIS Time value of money equal dollar amounts have different values at different points in time. Present value analysis tool to convert CFs at different points in time to comparable values

### Discounted Cash Flow Valuation

6 Formulas Discounted Cash Flow Valuation McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter Outline Future and Present Values of Multiple Cash Flows Valuing

### 10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans

10. Time Value of Money 2: Inflation, Real Returns, Annuities, and Amortized Loans Introduction This chapter continues the discussion on the time value of money. In this chapter, you will learn how inflation

### Mortgage Math. months plus \$10,000 paid 15 months from. What is PV of \$1000 per month for 15. now at 10% nominal annual interest?

Mortgage Math What is PV of \$1000 per month for 15 months plus \$10,000 paid 15 months from now at 10% nominal annual interest? \$1,000 \$22,875 = + L + 1 +.10 12 \$1,000 \$10,000 ( 1 +.10 12 ) 15 ( 1 +.10

### Module 5: Interest concepts of future and present value

file:///f /Courses/2010-11/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present

### HOW TO USE YOUR HP 12 C CALCULATOR

HOW TO USE YOUR HP 12 C CALCULATOR This document is designed to provide you with (1) the basics of how your HP 12C financial calculator operates, and (2) the typical keystrokes that will be required on

### Time Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam

Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The

### TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION

TIME VALUE OF MONEY PROBLEM #7: MORTGAGE AMORTIZATION Professor Peter Harris Mathematics by Sharon Petrushka Introduction This problem will focus on calculating mortgage payments. Knowledge of Time Value

### Math 120 Basic finance percent problems from prior courses (amount = % X base)

Math 120 Basic finance percent problems from prior courses (amount = % X base) 1) Given a sales tax rate of 8%, a) find the tax on an item priced at \$250, b) find the total amount due (which includes both

### The Time Value of Money Guide

The Time Value of Money Guide Institute of Financial Planning CFP Certification Global Excellence in Financial Planning TM Page 1 Contents Page Introduction 4 1. The Principles of Compound Interest 5 2.

### Compounding Assumptions. Compounding Assumptions. Financial Calculations on the Texas Instruments BAII Plus. Compounding Assumptions.

Compounding Assumptions Financial Calculations on the Texas Instruments BAII Plus This is a first draft, and may contain errors. Feedback is appreciated The TI BAII Plus has built-in preset assumptions

### Chapter F: Finance. Section F.1-F.4

Chapter F: Finance Section F.1-F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given