Chapter 4 Intro to Valuation: Time Value of Money 4/14/2019 Chapter 4 Intro to Valuation: Time Value of Money Introduction/approach to TVM Future value of lump sum (compounding) Present value a lump sum (discounting) Determine interest rate Determine number of periods 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question If I save $3,000 per year for 40 years, earning 8% per year, how much will I have? Guess….. A. $120,000 B. $180,783 C. $240,178 D. $455,032 E. $777,170 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) “The most powerful force in the universe is compound interest.” Albert Einstein (attributed) Uses: Investing Borrowing Valuing Decision making Planning 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Introduction/approach to TVM 4/14/2019 Introduction/approach to TVM Importance of TVM Analytical approach to TVM Algebraic TVM “factors” and tables TVM on financial calculator TVM with spreadsheet 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Introduction/approach to TVM 4/14/2019 Introduction/approach to TVM Comments on using the calculator Clearing memory registers Setting periods to 1 PY TVM buttons N, I, PV, PMT, FV Cash flow buttons CFj, NPV, IRR 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Future value of lump sum (compounding) 4/14/2019 Future value of lump sum (compounding) What is the future value of $100 invested today for 3 years at 10% interest per year? 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Future value of lump sum (compounding) 4/14/2019 Future value of lump sum (compounding) What is the future value of $100 invested today for 3 years at 10% interest per year? 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Present value a lump sum (discounting) 4/14/2019 Present value a lump sum (discounting) How much would I need to invest today to have $1000 in 2 years at 7% interest rate? 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Present value a lump sum (discounting) 4/14/2019 Present value a lump sum (discounting) How much would I need to invest today to have $1000 in 2 years at 7% interest rate? 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Clicker Question (determine interest rate) 4/14/2019 Clicker Question (determine interest rate) If I have $1,000 today to invest, what return would I require to have $2000 in 8 years? A. 6.19% B. 7.42% C. 8.24% D. 9.05% E. 9.97% 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Clicker Question (determine number of periods) 4/14/2019 Clicker Question (determine number of periods) How many years would it take to double my $1,000 investment if I received an interest rate of 6%? A. 6.2 years B. 8.1 years C. 10.1 years D. 10.6 years E. 11.9 years 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Algebra for Lump Sums Solve for interest rate Solve for N periods 4/14/2019 Chapter 4: Time Value of Money (lump sums)

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question When compounding a present value: a) Future value _______________ as the interest rate increases; b) Future value ______________ as the number of periods increases. A. increases; increases B. increases; decreases C. decreases; increases D. decreases; decreases E. decreases; remains the same 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question When discounting a future value: As the interest rate decreases, present value ________;  As the number of periods decreases, present value ______ .  A. increases; increases B. increases; decreases C. decreases; increases D. decreases; decreases E. decreases; remains the same 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question At what age do you want to retire (no longer have to work)?  A. less than 55 years old B. 55 – 60 years old C. 60 – 65 years old D. 65 – 70 years old E. over 70 years old 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question How much money do you plan to have saved (in today’s dollars) by the time you retire?  A. less than $500,000 B. $500,000 - $750,000 C. $750,000 – $1 million D. $1 million – $1.5 million E. over $1.5 million 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter 4: Time Value of Money (lump sums) 4/14/2019 Clicker Question What overall, long term return do you expect to get from your future investments? A. 3 – 7% B. 7 – 10% C. 10 – 13% D. 13 – 16% E. over 16% 4/14/2019 Chapter 4: Time Value of Money (lump sums) Chapter 3: Working with Financial Statements

Chapter-end Homework Problems 4/14/2019 Chapter-end Homework Problems Chapter 4 Problems 1, 3, 5, 7, 9, 11, 13 4/14/2019 Chapter 4: Time Value of Money (lump sums)