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Financial Institutions and Markets (Compute present and future values…
Financial Institutions and Markets
Compute present and future values using an appropriate formula and a financial calculator (HP 10bll+).
Time value of money
what cash invested today will be worth in the future (future value or FV) or what future cash flows is worth now (present value or PV).
present value is typically equal to the price of a financial instrument
The timing of these cash flows (CFs) is critical in any evaluation
Future values (compounding/Accumulating)
compounding or interest on interest
FVn= PV(1 + i)^n
There are 4 variables. If 3 are known, the calculator will solve for the 4th
Either PV or FV must be negative
N or n = the number of years or periods
I or I/YR or i= the interest rate per year or period.
PV = present value
PMT= payment amount of an annuity (stream of equal cash flows)
FV= future value
Present Values (discounting)
FVn= PV(1 + i )^n
PV=FVn/(1+i)^n
PV=FVn[1/(1+i)]^n
Finding missing variables
Note relationship within the formulae
There are 4 variables: PV; FV; I/YR & n
If you have 3 of them, you can find the 4th.
Compute present values of annuities, annuity due and ordinary perpetuity using the appropriate formula and financial calculator
Annuities
definition
An annuity is a series of equal payments made at fixed intervals for a specified number of periods.
They differ from other instruments in that they have no further value on maturity (no ‘principal’ payment).
The interest payments from financial instruments paying a fixed rate of interest per period can be considered as a form of annuity.
PV of Ordinary annuities一般年金, is at the time stamp of when the annuity starts; one time period before the 1st payment.
PV=C[(1+i)^n-1]/[i(1+i)^n]
Annuity Due期初年金
An annuity due of n cash flows is simply an ordinary annuity of (n –1) cash flows, plus an immediate cash flow of CF
PV={C[(1+i)^n-1]/[i(1+i)^n]}*(1+i)
Understand the role of present values in determining the price of a bond.
definition of bonds
A bond is a debt instrument issued typically by a government or a corporation to raise funds.
Most bonds pay only interest on the principalduring their life (an annuity).
The principal is then returned in full when the bond matures (one time cash payment).
In contrast, most bank debt requires the regular repayment of both principal and interest.
Value of bonds on issue
definition
Bonds may be issued at a price equal to their face value or par, but they can also be issued (or selling in the market) at a discount or premium.
If market interest rates rise, the market value of fixed rate bonds should decrease. This inverse relationship also holds when interest rates fall: bond prices rise.
Yield to maturity 到期收益率
The yield to maturity (YTM) is the rate of return earned on a bond held to maturity. Also called “promised yield.”
A simple division of the interest by the market value provides what is called a “running yield” (like a dividend yield) but neglects the impact of the face value and its redemption. It is not so useful and is often misleading.
Must adjust the interest rate
When cash flows are received on a semi-annual basis as in Australia, the interest rate used for discounting or compounding must also be halved.
When doing this for the interest payments, the same adjusted rate must be used to determine the present value of the face value paid on maturity.
Perpetuity永续年金
The present value of an ordinary perpetuity：PV=C/i
C = cash flow per period
i= interest rate per period