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37 Cards in this Set

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Interest rate (r) is composed of what 5 risks?

Real risk-free interest rate, Inflation premium, Default risk premium, Liquidity premium, Maturity premium

Define: Real risk-free rate

The single-period interest rate for a completely risk-free security if no inflation were expected.

Define: Inflation premium

Compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt.

Define: Nominal risk-free interest rate

The sum of the real risk-free interest rate and the inflation premium.

Give an example of a US security that represents the nominal risk-free rate?

The 90 day t-bill represents the nominal risk-free rate over that time horizon.

Define: Default risk premium

Compensates investors for the possibility that the borrower will fail to make promised payment at the contracted time and in the contracted amount.

Define: Liquidity Premium

Compensates investors for the risk of loss relative to the investment's fair value if the investment needs to be converted to cash quickly.

Define: Maturity premium

Compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal).

Define: Present Value

The present discounted value of future cash flows.

Define: Future Value

The amount to which a payment or series of payments will grow by a stated future date.

For N=1, what is the expression for the future value of the amount PV?

FV1 = PV(1+r)

Define: Simple interest

The interest earned each period on the original investment; interest calculated on the principal only.

Define: Principal

The amount of funds originally invested.

Define: Compounding

The process of accumulating interest on interest.

What is the formula that relates the present value of an initial investment to its future value after N periods?

FV1 = PV(1+r)^N

What is the future value factor? Formula?

The future value factor is (1+r)^N, it is the amount by which the PV and FV are seperated, in time. Between each time period the PV will increase by the factor of (1+r).

With more than one compounding period per year, the future value formula can be expressed as:

FVN=PV(1+rs/m)mN

Break down the formula: FVN=PV(1+rs/m)mN

rs/m^m*N will give you your compounding factor. You then multiply that by your present value to attain the final result (future value). rs is the stated rate, m is # of compounding periods in one year, n is the number of years. You must calculate the exponent before multiplying your PV because you are compounding your interest, not your PV.

Explain the formula FVn=PV(e)^rsN

This is the continuous compounding formula. e is approximately 2.7182818 and represents the limit of compounding power to the infinite. The result of the formula will give you how much an investment will earn you if it compounds at a continuous rate rather than at discrete periods.

An $8 investment @ 8% rate compounded semi-annually yields $8.0816. Why is it not $8.08? What is the stated rate and what is the effective annual rate (EAR).

It's not $8.08 because of the semi-compounding, it would have been if it was annual compounding. The stated rate is 8% and the EAR is 8.16% and takes into account the effects of compounding.

What is the periodic rate of a stated rate of 8% compounded semi-annually? Why?

The periodic rate is 4% because semi-annually is half of a year and half of 8% is 4%.

What is the formula for the EAR?

EAR = (1+Periodic Rate)^m - 1 "Periodic rate = stated rate/m"

What is the equation for EAR for continuous compounding?

e^rs - 1

Find the periodic rate given an EAR of 8.16%.

0.0816 = (1+Periodic Rate)^2 - 1


1.0816 = (1+Periodic Rate)^2


(1.0816)^(1/2) - 1 = Periodic Rate


1.04 - 1 = Periodic Rate


4% = Periodic Rate

Calculate the continuous compound rate (stated rate with continuous compounding) corresponding to an effective annual yield of 8.33%.

0.0833 = e^rs - 1


1.0833 = e^rs


ln (1.0833) = rs


rs = 8%

Define an annuity.

An annuity is a finite set of level sequential cash flows.

Define and ordinary annuity.

An ordinary annuity has a first cash flow that occurs one period from now (indexed at t=1).

Define annuity due.

An annuity due has a first cash flow that occurs immediately (indexed at t=0).

Define a perpetuity.

A perpetual annuity, or a set of level never-ending sequential cash flows, with the first cash flow occurring one period from now.

What is the future value of an annuity formula?

FVn = A [((1+r)^n)-1))/r]

How can you calculate the future value of uneven cash flows at a constant rate?

You must find the future value at t=N for each individual period and sum them up. For example if N=3 & r=5%.


T=1;CF1=4000;4000(1.05)^2 = $4,410.00


T=2;CF2=5000;5000(1.05)^1 = $5,250.00


T=3;CF3=6000;6000(1.05)^0 = $6,000.00


The sum is $15,660.00

What is the equation for the PV of a perpetuity?

PV = A/r; this is only valid when the perpetuity has level payments.

What year do we find the PV for if the annuity payments begin in T=5? Why?

T=4; Because the first payment is one period away for a ordinary annuity or a perpetuity.

What is the growth rate formula (solving for r)?

g = ((FV/PV)1/N)-1

What is the equation to solve for the number of periods?

Generally, the formula is N = [ln(FV/PV)]/ln(1+r)

What is the present value of an annuity formula?

PV = A[(1-1/(1+r)^N)/r]

How do you solve of A or PMT?

You can solve by placing the the PV over the rest of the formula that is for the PV annuity formula. You may do the same for FV. So for example: PV/ [(1-1/(1+r)^N)/r]