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32 Cards in this Set
- Front
- Back
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Interest Rate in 3 ways
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1. Required rates of return for a given investment
2. Discount rate 3. Opportunity cost -- what is forgone to have the money today rather than at a later date |
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Composition of Interest Rates
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r=real risk free rate +
1. Inflation Premium 2. Default risk premium 3. liquidity premium 4. maturity premium |
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Inflation premium
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compensates investors for expected inflation and reflects average inflation rate over maturity of the debt.
Sum of real risk free rate and INFLATION PREMIUM is the Nominal risk free interest rate |
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Default risk premium
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possibility that teh borrower will fail to make promised payment on time and in correct amount
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Liquidity Premium
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risk of loss in the event that assets need to be liquidated with lack of liquidity
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Maturity Premium
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Compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates
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Future value of a single cash flow with no compounding
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FV=PV(1+r)
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Future value of a single cash flow with compounding
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FV=PV(1+r)^n
n= number of periods |
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Stated annual interest rate AKA quoted interest rate
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The periodic compounded rate that banks will quote as an annual number
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Future value of a cash flow with more than one compounding period per year
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FV=PV(1+rs/m)^mn
rs=stated annual rate m=number of compounding periods per year. N=number of years |
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Effective Annual Rate
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the annual rate of return actually being earned after adjustmetns have been made for different compounding periods
EAR=(1+periodic rate)^m-1 m=number of compounding periods per year Periodic Rate=stated return/m |
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Calculate EAR for a stated rate of 12% compounded quarterly
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EAR=(1+.03)^4-1
EAR=.1255 EAR=12.55% |
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Future Value AKA Compound Value
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the amount to which a current deposit will grow over time when it is placed in an account paying compound interest
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FV formula for a single cash flow
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FV=PV(1+I/Y)^n
PV=amount of deposit I/Y=rate of return per compounding period N=total number of compounding periods |
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Future Value Factor AKA Future Value Interest Factor
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(1+I/Y)^n
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Annuity
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Finite set of level sequential cash flows
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Ordinary annuity
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has a first cash flow that occurs one period from now
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annuity due
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has a first cash flow that occurs immediately
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perpetuity
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a set of level never-ending sequential cash flows with the first cash flow occurring one period from now
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General Annuity Formula
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FV=A((1+r)^n)/r
A=annuity amount per period r=rate of return n=number of periods |
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Present Value of a single cash cash flow
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PV=FV(1/(1+r)^N which equals
PV=FV(1+r)^-N |
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Example of Present value of a single cash flow: An insurance company has issued a contract agreeing to pay 100,000 in 6 years with an 8% return rate. What amount of money must the investor invest today at 8% to make the promised payment
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PV=100,000(1.08)^-6
PV=63,016.96 |
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Formula for Present value with more than 1 compounding period per year
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PV=FV(1+rs/m)^-mN
rs=quoted annual rate N=number of years m=number of compounding periods per year |
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Ex. of PV with more than one compounding period per year: A pension fund manager wants 5mm 10 years from now. There is an investment that will give 6%/year compounded monthly. How much should be invested today to meet the liability
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PV=FV(1+rs/m)^-mN
PV=5,000,000(1+6/12)^-12*10 PV=2,748,163.67 |
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Present Value of an ordinary annuity
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PV=(1-1/(1+r)^N)/r
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Example of PV of ordinary annuity: an asset promises to pay 1,000 per year for 5 years (first payment is one year from now) with a 12% discount rate. What should you pay for this
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PV=A(1-(1/1.12)^5)/.12
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Annuity Due: when payments start at t=0 -- How to solve for present value
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First subtract 1 from total amount of payments. Use this new value as N, and add subtracted amount to the total to find PV
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A pension fund manager needs to begin funding retirees @1mm/year that will begin 10 years from now. Discount rate is 5%. What is the PV of the liability?
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PMT=1,000,000
I/Y=5% N=30 FV=0 CPT=PV=15,372,451.03 takes us to end of year 9 T=0=9,909,219 |
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The present value of a perpetuity
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PV=PMT/r
Therefore a stock that pays a dividend of 10/year with a 20% required ror values the perpituity at: 10/.2=50 |
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Value of a perpetuity when it starts in five years from now
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Step 1: use the perpetuity formula to find PV
Step 2: Use PV formula to discount it to t=0 |
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Calculating a growth rate
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g=(FVn/PV)^1
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Use the calculator to calculate a growth rate
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FV=FV
PV=PV -- MAKE NEGATIVE N=periods CPT=I/Y |
