part two the financial management of values
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Part Two The Financial Management of Values. Learning Objectives. Be able to compute the future value and present value Be able to compute the return on an investment Be able to use a financial calculator and a spreadsheet to solve time value of money problems - PowerPoint PPT PresentationTRANSCRIPT
Part Two
The Financial Management of Values
Learning Objectives
• Be able to compute the future value and present value
• Be able to compute the return on an investment• Be able to use a financial calculator and a
spreadsheet to solve time value of money problems
• Descibe the conception of value at risk• Understand the risk identification and risk
measurement
The Role of Time Value in Finance
• Most financial decisions involve costs & benefits that are
spread out over time.
• Time value of money allows comparison of cash flows from
different periods.
Question?
Would it be better for a company to invest $100,000 in a product that would return a total of $200,000 in
one year, or one that would return $500,000 after two years?
Answer!
It depends on the interest rate!
The Role of Time Value in Finance
• Most financial decisions involve costs & benefits that are
spread out over time.
• Time value of money allows comparison of cash flows from
different periods.
Basic Concepts
• Future Value: compounding or growth over time
• Present Value: discounting to today’s value
• Single cash flows & series of cash flows can be
considered
• Time lines are used to illustrate these relationships
Computational Aids
• Use the Equations
• Use the Financial Tables
• Use Financial Calculators
• Use Spreadsheets
Computational Aids
Computational Aids
Computational Aids
Computational Aids
Simple Interest
• Year 1: 5% of $100 = $5 + $100 = $105
• Year 2: 5% of $100 = $5 + $105 = $110
• Year 3: 5% of $100 = $5 + $110 = $115
• Year 4: 5% of $100 = $5 + $115 = $120
• Year 5: 5% of $100 = $5 + $120 = $125
With simple interest, you don’t earn interest on interest.
Compound Interest
• Year 1: 5% of $100.00 = $5.00 + $100.00 = $105.00
• Year 2: 5% of $105.00 = $5.25 + $105.00 = $110.25
• Year 3: 5% of $110.25 = $5 .51+ $110.25 = $115.76
• Year 4: 5% of $115.76 = $5.79 + $115.76 = $121.55
• Year 5: 5% of $121.55 = $6.08 + $121.55 = $127.63
With compound interest, a depositor earns interest on interest!
Time Value Terms
• PV0 = present value or beginning amount
• k = interest rate
• FVn = future value at end of “n” periods
• n = number of compounding periods
• A = an annuity (series of equal payments or
receipts)
Four Basic Models
• FVn = PV0(1+k)n = PV(F/P,k,n)
• PV0 = FVn[1/(1+k)n] = FV(P/P,k,n)
• FVAn = A (1+k)n - 1 = A(F/A,k,n) k
• PVA0 = A 1 - [1/(1+k)n] = A(P/A,k,n)
kFV: future valuePV: present valueIF: interest factorA: annuity
Future Value Example
You deposit $2,000 today at 6% interest.
How much will you have in 5 years?
$2,000 x (1.06)5 = $2,000 x (F/P,6%,5) $2,000 x 1.3382 = $2,676.40
Algebraically and Using FVIF Tables
Future Value Example
You deposit $2,000 today at 6% interest.
How much will you have in 5 years?
Using Excel
PV 2,000$ k 6.00%n 5FV? $2,676
Excel Function
=FV (interest, periods, pmt, PV)
=FV (.06, 5, , 2000)
Future Value Example A Graphic View of Future Value
Compounding More Frequently than Annually
• Compounding more frequently than once a year results in a
higher effective interest rate because you are earning on
interest on interest more frequently.
• As a result, the effective interest rate is greater than the
nominal (annual) interest rate.
• Furthermore, the effective rate of interest will increase the
more frequently interest is compounded.
Compounding More Frequently than Annually
• For example, what would be the difference in future value if
I deposit $100 for 5 years and earn 12% annual interest
compounded (a) annually, (b) semiannually, (c) quarterly,
an (d) monthly?
Annually: 100 x (1 + .12)5 = $176.23
Semiannually: 100 x (1 + .06)10 = $179.09
Quarterly: 100 x (1 + .03)20 = $180.61
Monthly: 100 x (1 + .01)60 = $181.67FVn=PV0×(1+k/m)m×n
Compounding More Frequently than Annually
Annually SemiAnnually Quarterly Monthly
PV 100.00$ 100.00$ 100.00$ 100.00$
k 12.0% 0.06 0.03 0.01
n 5 10 20 60
FV $176.23 $179.08 $180.61 $181.67
On Excel
Continuous Compounding• With continuous compounding the number of compounding
periods per year approaches infinity.
• Through the use of calculus, the equation thus becomes:
FVn (continuous compounding) = PV x (ekxn)
where “e” has a value of 2.7183.
• Continuing with the previous example, find the Future value
of the $100 deposit after 5 years if interest is compounded
continuously.
kn
m
nmn ePV
m
kPVFV
00 )1(
Continuous Compounding• With continuous compounding the number of compounding
periods per year approaches infinity.
• Through the use of calculus, the equation thus becomes:
FVn (continuous compounding) = PV x (ekxn)
where “e” has a value of 2.7183.
FVn = 100 x (2.7183).12x5 = $182.22
Nominal & Effective Rates
• The nominal interest rate is the stated or contractual rate of
interest charged by a lender or promised by a borrower.
• The effective interest rate is the rate actually paid or earned.
• In general, the effective rate > nominal rate whenever
compounding occurs more than once per year
EAR = (1 + k/m) m -11
1)/1(
n nmmkEAR
Nominal & Effective Rates
• For example, what is the effective rate of interest on your
credit card if the nominal rate is 18% per year, compounded
monthly?
EAR = (1 + .18/12) 12 -1
EAR = 19.56%
Present Value• Present value is the current dollar value of a future amount
of money.
• It is based on the idea that a dollar today is worth more than
a dollar tomorrow.
• It is the amount today that must be invested at a given rate
to reach a future amount.
• It is also known as discounting, the reverse of
compounding.
• The discount rate is often also referred to as the opportunity
cost, the discount rate, the required return, and the cost of
capital.
Present Value Example
How much must you deposit today in order to have
$2,000 in 5 years if you can earn 6% interest on
your deposit?
$2,000 x [1/(1.06)5] = $2,000 x (P/F,6%,5) $2,000 x 0.74758 = $1,494.52
Algebraically and Using PVIF Tables
Present Value Example
How much must you deposit today in order to
have $2,000 in 5 years if you can earn 6% interest
on your deposit?
FV 2,000$ k 6.00%n 5PV? $1,495
Excel Function
=PV (interest, periods, pmt, FV)
=PV (.06, 5, , 2000)
Using Excel
Present Value Example A Graphic View of Present Value
Annuities• Annuities are equally-spaced cash flows of equal size.
• Annuities can be either inflows or outflows.
• An ordinary (deferred) annuity has cash flows that occur at the
end of each period.
• An annuity due has cash flows that occur at the beginning of
each period.
• The future value of an annuity due will always be greater than
the future value of an otherwise equivalent ordinary annuity
because interest will compound for an additional period.
Annuities
Future Value of an Ordinary Annuity
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you
deposit $100 at the end of each year at 5% interest for three
years.
FVA = 100(F/A,5%,3) = $315.25
Using the FVIFA Tables
0 1 2 3
100 100 100
100X1.05=105
100X(1.05)2=110.25
Future Value of an Ordinary Annuity
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you
deposit $100 at the end of each year at 5% interest for three
years.
Using Excel
PMT 100$ k 5.0%n 3FV? 315.25$
Excel Function
=FV (interest, periods, pmt, PV)
=FV (.05, 3,100, )
Future Value of an Annuity Due
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you deposit $100 at the
beginning of each year at 5% interest for three years.
FVA = 100(F/A,5%,3)(1+k) = $330.96
Using the FVIFA Tables
FVA = 100(3.152)(1.05) = $330.96
100 100 100
100*1.05=105
100*(1.05)2=110.25
100*(1.05)3=115.76
100 100 100
Future Value of an Annuity Due
• Annuity = Equal Annual Series of Cash Flows
• Example: How much will your deposits grow to if you
deposit $100 at the beginning of each year at 5% interest for
three years.
Using Excel
Excel Function
=FV (interest, periods, pmt, PV)
=FV (.05, 3,100, )x(1.05)
=315.25*(1.05)
PMT 100.00$ k 5.00%n 3FV $315.25FVA? 331.01$
Present Value of an Ordinary Annuity
• Annuity = Equal Annual Series of Cash Flows
• Example: How much could you borrow if you could afford
annual payments of $2,000 (which includes both principal
and interest) at the end of each year for three years at 10%
interest?
PVA = 2,000(P/A,10%,3) = $4,973.70
Using PVIFA Tables
2000 2000 2000
2000÷1.12000÷(1.1)2
2000÷(1.1)3
Present Value of an Ordinary Annuity
• Annuity = Equal Annual Series of Cash Flows
• Example: How much could you borrow if you could afford
annual payments of $2,000 (which includes both principal
and interest) at the end of each year for three years at 10%
interest?
Using Excel
PMT 2,000$ I 10.0%n 3PV? $4,973.70
Excel Function
=PV (interest, periods, pmt, FV)
=PV (.10, 3, 2000, )
Present Value of a Mixed Stream
• A mixed stream of cash flows reflects no particular pattern
• Find the present value of the following mixed stream
assuming a required return of 9%.
Using Tables
Year Cash Flow PVIF9%,N PV
1 400 0.917 366.80$
2 800 0.842 673.60$
3 500 0.772 386.00$
4 400 0.708 283.20$
5 300 0.650 195.00$
PV 1,904.60$
Present Value of a Mixed Stream
• A mixed stream of cash flows reflects no particular pattern
• Find the present value of the following mixed stream
assuming a required return of 9%.
Using EXCEL
Year Cash Flow
1 400
2 800
3 500
4 400
5 300
NPV $1,904.76
Excel Function
=NPV (interest, cells containing CFs)
=NPV (.09,B3:B7)
Present Value of a Perpetuity
• A perpetuity is a special kind of annuity.
• With a perpetuity, the periodic annuity or cash flow stream
continues forever.
PV = Annuity/k
• For example, how much would I have to deposit today in
order to withdraw $1,000 each year forever if I can earn 8%
on my deposit?
PV = $1,000/.08 = $12,500
…1000 1000 1000
………………
Loan Amortization
6000=Ax(P/A,10%,4)6000=Ax3.170 A=6000÷3.170=1892.74∴
Thanks for Your Attention