Time Value of Money. Chapter 5 & 6 Financial Calculator and Examples. Five Factors in TVM. Annual &Non-annual Compound

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1 Chapter 5 & 6 Financial Calculator and Examples Konan Chan Financial Management, Fall 2018 Time Value of Money N: number of compounding periods I/Y: periodic rate (I/Y = APR/m) PV: present value PMT: periodic payment FV: future value N = m*n (m: number of interests paid per year; n: number of years) It s always to determine one of the five variables If you can t figure out one of the four variables, it must be the case that this one is zero Financial Management Konan Chan 3 Five Factors in TVM Present value: PV Future value: FV Discount rate: r Payment: PMT Number of periods: N Get information of four factors, and find the last one Annual &Non-annual Compound Annual Non-annual m = 1 4 (quarterly); 12 (monthly) N = n 4 * n ; 12 * n I/Y = APR APR/m Financial Management Konan Chan 2 Financial Management Konan Chan 4

2 Texas Instruments BA-II Plus N = number of periods I/Y = period interest rate (r) PV = present value PMT = payment FV = future value N I/Y PV PMT FV Tips of Financial Calculator Set up # of digits after the decimal point Press 2nd, (Format) the screen shows DEC= If you want to have 4 digits, press 4, ENTER Clean the screen 2nd, CPT (QUIT) To avoid confusion, set P/Y=1 and don t change later 2nd, I/Y (P/Y) Press 1, ENTER Financial Management Konan Chan 5 Financial Management Konan Chan 7 Tips of Financial Calculator Convert between Annuity and Annuity due END on the screen is for annuity, BGN is for annuity due 2nd, PMT check current mode (suppose current is END) 2nd, ENTER set BGN mode Press again 2nd, ENTER will covert back to END mode Time value of Money (TVM) Clear all inputs (initialization) 2nd, FV (CLR TVM) Check inputs RCL, N ; RCL, I/Y ; Clear worksheet (CF, NPV, Conv) 2nd, CE/E (CLR Work) Example 1 You are willing to pay $15,625 to purchase a perpetuity which will pay you $1,250 each year, forever. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of a perpetuity? Financial Management Konan Chan 6 Financial Management Konan Chan 8

3 Example 1 Solution Find the interest rate first PV (perpetuity) = PMT / r r=8% Find the PV of the annuity N=20 I/Y = 8 PMT = 1,250 FV = 0 CPT PV = -12,273 Financial Management Konan Chan 9 Example 2 Solution First clear all inputs: 2nd, FV(CLR TVM) Find the PV of the annuity on the monthly interest basis For $500 option: (at the time of right now) N = 12, I/Y = 5/12 = , PMT = 500, FV = 0 CPT PV = -5, For $700 option: (at the end of 3rd month) N = 9, I/Y = 5/12 = , PMT = 700, FV = 0 CPT PV = -6, Financial Management Konan Chan 11 Example 2 Your lease calls for payments of $500 at the end of each month for the next 12 months. Now your landlord offers you a new 1-year lease which calls for zero rent for 3 months, then rental payments of $700 at the end of each month for the next 9 months. You keep you money in a bank time deposit that pays a nominal annual rate of 5 percent, compounded monthly. By what amount would your net worth change if you accept the new lease? Example 2 Solution Discount the value back to present (time 0) N = 3, I/Y = , PMT = 0, FV = 6, CPT PV = -6, ( or PV = 6, / ( ) 3 = 6,094.23) Net worth change = 5, , = Financial Management Konan Chan 10 Financial Management Konan Chan 12

4 Example 3 You have just taken out a 30-year, $120,000 mortgage on your new home. This mortgage is to be repaid in 360 equal end-of-month installments. If each of the monthly installment is $1,500, what is the effective annual interest rate on this mortgage? Example 4 You just graduated, and you plan to work for 10 years and then to leave for the Australian Outback bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when you start, into an account which pays 8 percent compounding annually, what will your financial stake be when you leave for Australian 10 years from now? Financial Management Konan Chan 13 Financial Management Konan Chan 15 Example 3 Solution Findtherateofreturn(APR) N = 360, PV = 120,000, PMT = -1,500, FV = 0 CPT I/Y = (periodic rate) Nominal rate (APR) = periodic rate*12 = Find EAR Enter interest conversion worksheet 2nd, 2(Conv) NOM = 14.82, C/Y = 12 CPT EFF = (or EFF = ( ) 12-1= ) Financial Management Konan Chan 14 Example 4 Solution Find PV of uneven cash flows Enter cash flow worksheet: CF CF0 = 5,000 Enter (INS) C01 = 1,000; F01 = 5; C02 = 2,000; F02 = 5; Go to NPV worksheet: NPV let I = 8, CPT NPV = 14,427 Find the FV of a single cash flow Discount the value back to present (time 0) N = 10; I/Y = 8 ; PV = 14,427; PMT = 0 CPT FV = -31,147 ( or FV = 14,427(1.08) 10 = 31,147 ) Financial Management Konan Chan 16

5 Example 5 Excel Functions Suppose you borrow $4,500 at 6% and you are going to make annual payments of $ How long before you pay off the loan? I/Y=, PV=, PMT=, FV= CPT N = Financial Management Konan Chan 17 FV(Rate,Nper,Pmt,PV,0/1) PV(Rate,Nper,Pmt,FV,0/1) RATE(Nper,Pmt,PV,FV,0/1) NPER(Rate,Pmt,PV,FV,0/1) PMT(Rate,Nper,PV,FV,0/1) Inside parens: (RATE,NPER,PMT,PV,FV,0/1) 0/1 Ordinary annuity = 0 (default; no entry needed) Annuity Due = 1 (must be entered) Financial Management Konan Chan 19 Example 6 Suppose you borrow $15,600 from your parents to buy a smart phone. You agree to pay $ per month for 24 months. What is the monthly interest rate? N=, PV=, PMT=, FV= CPT I/Y = Financial Management Konan Chan 18