BMAN 311 SU5: The time value of money The time value of money ( p.137) INTRODUCTION • The importance of the timing of cash flows. • Future value: compounded interest over a specific period of time. • Present value: amount to be invested today to equal the future amount at a given interest rate. • Financial managers prefer present values to future values because they make decisions before the start of the project. The time value of money LEARNING OUTCOMES Calculate the following: • the future values of a single amount and of an annuity; • the present values of a single amount, a mixed stream of cash flows and an annuity; • deposits to accumulate a future sum; • instalments to amortise a loan and • Interest or growth rates. The time value of money Future value • of a single amount • of an annuity • N.B. ALWAYS CLEAR YOUR CALCULATOR AFTER EACH CALCULATION Present value • of a single amount • of a mixed stream of cash flows • of an annuity HOW TO CLEAR A CALCULATION • HP10bII: Press 2nd function; Press" C" • SHARP EL 738: Press 2nd function; Press ALPHA button; Press "0" (twice) Example: R1 000 is invested for 2 years at an interest rate of 10% p.a., calculate the future value. Annually (once a year) • 1000 ± PV • 2N • 10 I/YR • Press FV/ Comp FV=1210 Quarterly (4 times a year) 1000 ± PV 2X4 N 10÷4 I/YR Press FV/ Comp FV=1218.40 Semi-annually (twice a year) • 1000 ± PV • 2x2 N • 10÷2 I/YR • Press FV/ Comp FV=1215.51 Monthly (12 times a year) • 1000 ± PV • 2X12 N • 10÷12 I/YR • Press FV/Comp FV= 1220.39 Present value of a single amount (p.150) • Example: R1 000 is expected 1 year from now, while you could have earned interest at a rate of 16% p.a. Calculate the PV. • 1000= FV • 1= N • 16 =I/YR • Press PV= 862.07 Future value of an annuity (p.144) • An annuity is a stream of equal annual cash flows for a specific number of periods • Ordinary annuity: payment at the end of the period. • Annuity due: payment made at the beginning of the period. Example: R1 000 is invested annually for 5 successive years at 16 % p.a., calculate FV. ORDINARY • 1000 ± PMT • 5= N • 16= I/YR • Press FV/ Comp FV = 6877.14 ANNUITY DUE • BGN/ BEG • 1000 ± PMT • 5= N • 16= I/YR • Press FV/ Comp FV = 7977.48 • NB.ALWAYS CLEAR BGN/BEG. AFTER CALCULATION. Present value of an annuity (more than 1 payment/instalment (p.154) • Example: R 1000 is expected for 5 successive years, while you could have earned interest at a rate of 12% p.a. Calculate the PV. • 1 000 PMT • 5N • 12 I/YR • Press PV/ Comp PV= 3604.78 Deposits to accumulate a future sum (p. 156) • Example: R100 000 is needed 5 years from now to replace equipment. If you wish to make equal end of year deposits in an account paying 12% p.a., determine how much you should deposit annually to receive R100 000 at the end of Year 5. • 100 000 FV 5N 12 I/YR • Press PMT / Comp PMT = 15740.97 Determining interest or growth rates (p.153) nb Example: 7.15 Calculator use: • Earliest Cash Flow- PV (2012) • Latest Cash Flow- FV (2016) • 1018 ± PV • 1600 FV • 4 N (5-1) • Press I/YR = 11.97 equipment • 1.Example: R120 000 is the value of a machine. If you needed 5 years to replace old equipment and you wish to make equal end of year deposits in an account paying 12% p.a., 1. determine how much you should deposit annually to receive R120 000 after Year 5 (no residual) 2. with residual (balloon value of R1500). 1. 120 000 = PV; 5 = N; 12 = I/Y; 0 = FV COMP PMT = - 33 289.17 2. 120 000 Pv ; 5N 12 I/YR -1500 FV Press COMP PMT = 33 053.05 Loan amortisation (annual instalment)-p.157 • Example: R6 000 000 is borrowed at an interest rate of 14% p.a., and is payable in equal annual instalments over 10 years. Calculate the annual instalment. • 6 000 000 PV • 10 N • 14 I/YR • Press PMT/ Comp PMT: 1 150 281.25 Amortisation schedule • shows the Interest and Principal payments for the whole repayment period. • (Table 7.7,p.144) is an example of an Amortization Schedule. • EXAMPLE: STEP 1: CALCULATE PMT (LOAN PAYMENT). STEP 2: CALCULATE THE PRINCIPAL (amount reducing loan), INTEREST, AND OUTSTANDING BALANCE (still owing). Details for 4th payment HP Calculator (Example,T.B. p.157) not ideal Press 4; INPUT; 2nd function; AMORT 4-4 Press = PRINCIPAL=459 695.32 Press = INTEREST=690 585.93 Press = BAL=4 473 061.31 Details for 8th payment Press 8; INPUT; 2nd function; AMORT 8-8 Press = PRINCIPAL=776 407.08 Press = INTEREST=373 874.17 Press = BAL=1 894 122.70 Final year of payment (10th year) HP Calculator 10; INPUT; 2nd function; AMORT 10-10 = PRINCIPAL=1 009 018,64 = INTEREST=141 262,61 = BALANCE=0,00 Details for 4th payment SHARP calculator (Example,T.B. P.157) DO LAST ACTIVITY SCREEN DISPLAY Press AMRT; 1 ; ENTER AMRT P1=1.00 Press 4 ; ENTER AMRT P1=4.00 ; AMRT P2=4.00 BAL =4 473 061.30 Press ⧩ PRINCIPAL=459 695.32 Press ⧩ INTEREST=690 585.93 Details for 8th payment Press ⧩; 8 ; ENTER AMRT P1=8.00 Press ⧩; 8; ENTER AMRT P2=8.00 Press ⧩ BAL=1 894 122,65 Press ⧩ PRINCIPAL=776 407,09 Press ⧩ INTEREST=373 874,16 ⧩ ; 10; ENTER AMRT P1= 10.00 ⧩ ; 10; ENTER AMRT P2=10.00 ⧩ BAL=0,08 ⧩ PRINCIPAL=1 009 018,65 Loan amortisation (monthly instalment) • Example: R6 000 000 is borrowed at an interest rate of 14% p.a., and is payable in equal monthly instalments over 10 years. Calculate the monthly instalment. • 6 000 000 PV 10x12 N 14÷12 I/YR • Press PMT/ Comp PMT: 93 159.86 Details after 4 years of payment (4X12=48) SHARP calculator AMRT; 1; ENTER AMRT P1=1.00 48; ENTER AMRT P1=48 ⧩ 48; ENTER AMRT P2=48 ⧩ Balance= 4 521 063,82 ⧩ Principal=39 948,05 ⧩ Interest =53 211,81 Details after 7 years of payment (7x12=84) ⧩ 84; ENTER AMRT P1=84 ⧩ 84; ENTER AMRT P2=84 ⧩ Balance= 2 725 755,67 ⧩ Principal=60 651,77 ⧩ Interest =32 508,09 Details of final year of payment (109 – 120)-Sharp Calculator ⧩ 109 ;ENTER AMRT P1=109 ⧩120; ENTER AMRT=120 ⧩ Balance= 0,35 ⧩ Principal= 1 037 563,73 ⧩ Interest=80 354,59 Details after 4 years of payment (4x12=48) HP10 b II 48; INPUT; 2nd function AMORT 48-48 = Principal=39 948,06 = Interest=53 211,80 = Balance=4 521 063,71 Details after 7 years of payment (7x12=84) 84; INPUT; 2nd function; AMORT 84-84 = Principal=60 651,78 = Interest=32 508,09 = Balance=2 725 755,47 Details of final year of payment ( 109-120) 109; INPUT ; 120; 2nd function AMORT 109-120 = Principal=1 037 563,78 = Interest=80 354,55 = Balance=0,01 Loan amortisation (monthly instalment • Calculate the following from the previous example: ie. Pmt, pv, fv, interest i/r, period=N (a) Details after 4 years of payment. (b) Details after 7 years of payment. (c) Details of the final year of payment. STEP 1: CALCULATE PMT. STEP 2: CALCULATE THE REQUIRED DETAILS. TIME VALUE OF MONEY • Time value of money classwork (E- Fundi) • Amortisation exercise (send on E- Fundi)- Practice questions • Study Guide, p 16 to p18: Exercise 5.3; 5.4 and 5.5