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