TVM - handout

TVM - handout - Ch. 5 - The Time Value of Money Ch. Mind...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Ch. 5 - The Time Value of Money Ch. Mind Map Mind s Why?: Most long-term project have cash flows that occur at different points in time. Given that the passage of time impacts the value of cash flows, the value of a project is dependent on how we assess these differences. The purpose of this chapter is to develop the tools necessary to evaluate cash flows over time in order to make optimal decisions. Mind Map Mind s Learning objective: – Develop an understanding of how time impacts cash flows – Quantify the time/value relationship – Evaluate complex financial contracts/projects Mind Map Mind s Key words/concepts: – – – – – – – – TVM PV, FV, PVA, FVA Lump-sum, annuity Ordinary annuity vs. Annuity due Perpetuity Deferred annuity Mixed-stream cashflow WORK LOTS OF PROBLEMS! Terminology Terminology s Translate $1 today into its equivalent in Translate the future (COMPOUNDING). the (COMPOUNDING) Today Future ? Translate $1 in the future into its Translate equivalent today (DISCOUNTING). equivalent (DISCOUNTING) Today s ? Future Note: Note: s It’s easiest to use your financial functions on your calculator to solve time value problems. However, you will need a lot of practice to eliminate mistakes. s Finance and Accounting Majors: It will be helpful later to take extra time now learning to use the formulas as well as the financial functions on your calculator! Future Value Compounding problems Compounding Future Value - single sums Future If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? PV = FV = 0 1 Future Value - single sums Future If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? PV = -100 FV = ?? ?? 0 1 Mathematical Solution: FV = PV (1 + i)n FV = 100 (1.06)1 = $?? Notice that there is one equation and four variables. What does this tell you about how much information you need????? Future Value - single sums Future If you deposit $100 in an account earning 6%, how much would you have in the account after 1 year? PV = -100 FV = ?? ?? 0 1 Mathematical Solution: FV = PV (1 + i)n “FVIF” FV = 100 (1.06)1 = $?? Notice that there is one equation and four variables. What does this tell you about how much information you need????? HOW ABOUT WITH THE CALCULATOR? s There is one equation and 4 variables – So, how many unknowns can you have? I (or r or I/Y), PV, FV, and n s For almost all TVM problems, you simply play a “4 find 3” game s Three steps: 1) set-up your calculator, 2) enter the 3 known variables, and 3) solve for the unknown s Half of you will lose points on the exam because you ignore this slide!! s Two problems s Pmts per year: I will do all calculations in 1 P/Yr mode. s Set-up your calculator before each problem – HP: 2nd C All; TI: 2nd CLR TVM Future Value - single sums Future If you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? PV = FV = 0 5 Future Value - single sums Future If you deposit $100 in an account earning 6%, how much would you have in the account after 5 years? PV = -100 FV = 0 Calculator Solution: P/Y = 1 I=6 N=5 PV = -100 FV = $133.82 5 Present Value Present Present Value - single sums Present If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? PV = FV = 0 ? Present Value - single sums If you will receive $100 5 years from now, what is the PV of that $100 if your opportunity cost is 6%? PV = -74.73 PV FV = 100 0 Calculator Solution: P/Y = 1 I=6 N=5 FV = 100 PV = -74.73 5 Hint for single sum problems: Hint s In every single-sum future value and present value problem, there are 4 variables: – FV, PV, i, and n s When doing problems, you will be given 3 of these variables and asked to solve for the 4th variable. s Keeping this in mind makes TVM problems much easier! The Time Value of Money The Compounding and Discounting Cash Flow Streams 0 1 2 3 4 Annuities Annuities s Annuity: Annuity: an equally-spaced sequence of equal cash flows. equal Annuities Annuities s Annuity: Annuity: a equally-spaced sequence of equal cash flows, as in: of 0 1 2 3 4 Examples of Annuities: Examples s If you buy a bond, you will receive equal coupon interest payments over the life of the bond. s If you borrow money to buy a house or a car, you will pay a stream of equal payments. Future Value - annuity Future If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 0 1 2 3 Future Value - annuity If you invest $1,000 at the end of the next 3 years, If at 8%, how much would you have after 3 years? at Mathematical Solution: Mathematical FV = PMT (1 + i)n - 1 i “FVIFA” Future Value - annuity If you invest $1,000 at the end of the next 3 years, at 8%, how much would you have after 3 years? 1000 1000 0 1 Calculator Solution: P/Y = 1 I=8 PMT = -1,000 FV = $3,246.40 1000 1000 2 N=3 3 Present Value - annuity Present What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%? 0 1 2 3 Present Value - annuity What is the PV of $1,000 at the end of each of the next 3 years, if the opportunity cost is 8%? 1000 1000 0 1 1000 1000 2 Calculator Solution: Calculator P/Y = 1 I=8 N=3 PMT = -1,000 PV = $2,577.10 3 Warm-up Question Question s Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make? – 15 – 13 – 12 – 19 – None of the above Other Cash Flow Patterns Other 0 1 2 3 Perpetuities Perpetuities s Suppose you will receive a fixed payment every period (month, year, etc.) forever. This is an example of a perpetuity. s You can think of a perpetuity as an annuity that goes on forever. Present Value of a Perpetuity Present s When we find the PV of an annuity, we think of the following relationship: PV = PMT (PVIFA i,, n ) i Mathematically, (PVIFA i, n ) = 1- 1 n (1 + i) i We said that a perpetuity is an annuity where n = infinity. What happens to this formula when n gets very, very large? Present Value of a Perpetuity s So, the PV of a perpetuity is very So, simple to find: simple PMT PV = i What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment? What should you be willing to pay in order to receive $10,000 annually forever, if you require 8% per year on the investment? PMT PMT PV = i = $?? $?? = $10,000 $10,000 .08 .08 Ordinary Annuity Ordinary vs. Annuity Due $1000 4 $1000 $1000 5 6 7 8 Begin Mode vs. End Mode Begin 1000 4 year 5 5 1000 year 6 6 1000 year 7 7 PV FV in END Mode in END Mode 8 Begin Mode vs. End Mode Begin 1000 4 5 1000 year 6 6 1000 year 7 7 year 8 8 PV FV in BEGIN Mode in BEGIN Mode Earlier, we examined this “ordinary” annuity: “ordinary” 1000 1000 0 1000 1000 1 2 Using an interest rate of 8%, we Using find that: find s The Future Value (at 3) The Future is $3,246.40. $3,246.40. s The Present Value (at 0) is The Present $2,577.10. $2,577.10. 3 What about this annuity? What 1000 1000 1000 1000 0 1 2 s Same 3-year time line, s Same 3 $1000 cash flows, but... s The cash flows occur at the The beginning of each year, rather beginning than at the end of each year. end s This is an “annuity due.” This “annuity 3 Present Value - annuity due Present What is the PV of $1,000 at the beginning of each of the next 3 years, if your opportunity cost is 8%? 0 1 2 3 Present Value - annuity due What is the PV of $1,000 at the beginning of each of the next 3 years, if your opportunity cost is 8%? 1000 1000 1000 1000 0 1 2 3 Calculator Solution: Calculator Mode = BEGIN P/Y = 1 I=8 Mode N=3 PMT = 1,000 PV = $2,783.26 $2,783.26 Future Value - annuity due If you invest $1,000 at the beginning of each of the next 3 years at 8%, how much would you have at the end of year 3? the -1000 -1000 -1000 -1000 0 1 2 3 Calculator Solution: Calculator Mode = BEGIN P/Y = 1 I=8 Mode N=3 PMT = -1,000 FV = $3,506.11 $3,506.11 Before the Exam… Before Ordinary annuities vs. annuities due s Uneven cash flows s Deferred annuities s Personal financial plan s You must practice TVM problems s HOW DOES IT APPLY TO YOU? YOU? s Suppose you are 22 years old. If you plan to retire at 65, how much do you need to save every month to have $2,000,000. Assume you can earn 12%. ...
View Full Document

Ask a homework question - tutors are online