how to calculate present values
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2. How to calculate present values. 2-1 Future Values and present values. Calculating Future Values Future Value Amount to which investment will grow after earning interest Present Value Value today of future cash flow. 2-1 Future Values and present values. Future Value of $100 = - PowerPoint PPT PresentationTRANSCRIPT
Chapter
Brealey, Myers, and Allen
Principles of Corporate Finance
11th Global Edition
HOW TO CALCULATE PRESENT VALUES
2
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2-1 FUTURE VALUES AND PRESENT VALUES
•Calculating Future Values•Future Value
• Amount to which investment will grow after earning interest
•Present Value• Value today of future cash flow
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2-1 FUTURE VALUES AND PRESENT VALUES
• Future Value of $100 =
• Example: FV
• What is the future value of $100 if interest is compounded annually at a rate of 7% for two years?
tr)1(100$FV
49.114$)07.1(100$FV
49.114$)07.1()07.1(100$FV2
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2-1 FUTURE VALUES AND PRESENT VALUES
•Discount factor = DF = PV of $1
• Discount factors can be used to compute present value of any cash flow
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2-1 FUTURE VALUES AND PRESENT VALUES
• Given any variables in the equation, one can solve for the remaining variable
• Prior example can be reversed
10049.114PV
DFPV
2)07.1(1
22
C
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2-1 FUTURE VALUES AND PRESENT VALUES
•Valuing an Office Building• Step 1: Forecast Cash Flows
• Cost of building = C0 = $700,000
• Sale price in year 1 = C1 = $800,000
• Step 2: Estimate Opportunity Cost of Capital
• If equally risky investments in the capital market offer a return of 7%, then cost of capital = r = 7%
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2-1 FUTURE VALUES AND PRESENT VALUES
• Valuing an Office Building• Step 3: Discount future cash flows
• Step 4: Go ahead if PV of payoff exceeds investment
664,747$PV )07.1(000,800$
)1(1 rC
664,47$
000700$664,747$NPV
,
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2-1 FUTURE VALUES AND PRESENT VALUES
r
CC
1=NPV
investment requiredPV=NPV
10
•Net Present Value
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2-1 FUTURE VALUES AND PRESENT VALUES
• Risk and Present Value• Higher risk projects require a higher rate of return
• Higher required rates of return cause lower PVs
664,747$.071
$800,000PV
7%at $800,000 of PV 1
C
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2-1 FUTURE VALUES AND PRESENT VALUES
•Risk and Net Present Value
$47,664
$700,00047,6647$=NPV
investment requiredPV=NPV
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2-1 FUTURE VALUES AND PRESENT VALUES
• Net Present Value Rule• Accept investments that have positive net present value
• Using the original example: Should one accept the project given a 10% expected return?
273,27$1.1
$800,000+$700,000=NPV
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2-1 FUTURE VALUES AND PRESENT VALUES
• Rate of Return Rule• Accept investments that offer rates of return in excess of their opportunity cost of capital
• In the project listed below, the opportunity cost of capital is 12%. Is the project a wise investment?
14.3%or .143,$700,000
0,00070$000,00$8
investment
profitReturn
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2-1 FUTURE VALUES AND PRESENT VALUES
• Multiple Cash Flows• Discounted Cash Flow (DCF) formula:
tt
r
C
r
C
r
C
)1()1()1(0 ....PV 22
11
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2-2 PERPETUITIES AND ANNUITIES
•Perpetuity• Financial concept in which cash flow is theoretically received forever
PV
luepresent va
flowcash Return
Cr
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2-2 PERPETUITIES AND ANNUITIES
•Present Value of Perpetuities• What is the present value of $1 billion every year, for eternity, if the perpetual discount rate is 10%?
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2-2 PERPETUITIES AND ANNUITIES
•Present Value of Perpetuities• What if the investment does not start making money for 3 years?
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2-2 PERPETUITIES AND ANNUITIES
• Annuity• Asset that pays fixed sum each year for specified number of years
Perpetuity (first payment in year 1)
Perpetuity (first payment in year t + 1)
Annuity from year 1 to year t
Asset Year of Payment
1 2…..t t + 1
Present Value
trr
C
r
C
)1(
1
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2-2 PERPETUITIES AND ANNUITIES
• Example: Tiburon Autos offers payments of $5,000 per year, at the end of each year for 5 years. If interest rates are 7%, per year, what is the cost of the car?
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2-2 PERPETUITIES AND ANNUITIES
• Annuity• Example: The state lottery advertises a jackpot prize of $365 million, paid in 30 yearly installments of $12.167 million, at the end of each year. Find the true value of the lottery prize if interest rates are 6%.
000,500,167$
06.106.
1
06.
1167.12ValueLottery 30
Value
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2-2 PERPETUITIES AND ANNUITIES
• Future Value of an Annuity• What is the future value of $20,000 paid at the end of each of the following 5 years, assuming investment returns of 8% per year?
332,117$
08.
108.1000,20 FV
5
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2-3 GROWING PERPETUITIES AND ANNUITIES
• Constant Growth Perpetuity
• This formula can be used to value a perpetuity at any point in time
gr
C
1
0PV g = the annual growth rate of the cash flow
gr
Ctt 1PV
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2-3 GROWING PERPETUITIES AND ANNUITIES
• Constant Growth Perpetuity• What is the present value of $1 billion paid at the end of every year in perpetuity, assuming a rate of return of 10% and constant growth rate of 4%?
billion 667.16$04.10.
1PV0
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2-3 GROWING PERPETUITIES AND ANNUITIES
• Growing Annuities• Golf club membership is $5,000 for 1 year, or $12,750 for three years. Find the better deal given payment due at the end of the year and 6% expected annual price increase, discount rate 10%.
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2-4 HOW INTEREST IS PAID AND QUOTED
•Effective Annual Interest Rate (EAR)• Interest rate annualized using compound interest
•Annual Percentage Rate (APR)• Interest rate annualized using simple interest