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![money.Coupon = amount of interest payed periodicallyFace value / coupon value = principal amount of a bond, repaid on maturityCoupon rate = annual coupon divided by the face valueBond Value = Present value of the coupons + Present value of face amountBond value = C x [1 – 1/(1 + r)^t]/r + F / (1 + r)^t- The longer the time to maturity, the greater the interest rate risk- The lower the coupon rate, the greater the interest rate risk- Increasing rate decreases the bond valueDebt securities = note, debenture, or bond- Debenture = an unsecured debt, usually maturity of 10 years- Note = an unsecured debt, maturity less than 10 years- Zero Coupon Bonds = pays no coupon and hence offered at a low price- Call provision = an agreement giving the entity option to repurchase thebond at a specified price prior to maturity. The call premium is the amount bywhich the call exceeds the face value.Government Bonds- issues ordinary notes and bonds- no default risk- municipal bonds issued by cityBond Ratings- Moody and Standard and Poors (S&P) bond rating firms, assessingcreditworthiness- Highest rating is AAA and lowest is D- Rating depends on issuers financial strengthInflation and Interest Rates- Nominal = interest rates that have not been adjusted for inflation- real rates = have been adjusted for inflationFischer Equation: R = r + h + (r x h)R = nominal rate, r = real rate, h = inflation rateStock ValuationCommon stocks are more difficult to value than bonds, since the cash flowsare unknown, stock investment has no maturity, difficult to predict or measurerate of return and many more psychological factors.Current price of stock is the present value of future dividends:](./background1.png)
Topic One – Valuation of Future Cash Flows
Introduction
Time value of money can be presented by:
Future Value = Present Values (1 + r)^t
r = discount rate per period
t = the number of periods
Some other terms that are important are:
Compounding: accumulating interest over time to earn more interest
Interest on Interest: interest earned on the interest re-invested
Compound Interest: interest earned on principal and interest re-invested
Simple Interest: interest earned only on principal
Discount Cash Flow Valuation
There is a difference between the stated interest rate, APR and EAR.
Stated Interest Rate: interest paid for each period
APR (Annual Percentage Rate): interest charged per period multiplied by the
number of periods per year
EAR (Effective annual rate): interest rate as if it were compounded several
periods within the year. This is calculated by:
EAR = [ 1 + r/m]^m – 1
Annuities and Perpetuities
An annuity is a level stream of cash flows for a fixed period of time.
The present value of an annuity is:
Annuity Present Value = C x (1 – [1/(1+r)^t])/r
Annuity Future Value = C x ([1/(1+r)^t] - 1)/r
C = present value of an annuity of C dollars
There are two types of anniuties. Ordinary annuities where the cash flows
occur at the end of each period and others such as rent, which occurs at the
start of each period, these are called “Annuities Due” and are calculated as:
Annuity Due = Ordinary Annuity Value x (1 + r)
Perpetuities are like annuities however their cash flow continues forever.
Perpetuity PV = C / r
Interest Rate and Bond Valuation
A bond is a debt security used by government and companies to borrow
P = D1 / (1 + R) ^1 + D2 / (1 + R)^2 + D3 / (1 + R)^3 ……
Zero Growth = acts like perpetuity since divides are the same every year
Constant Growth
Dt = Do (1 + g)^t, where g is the growth rate
Dividend Growth Model
Pt = Dt(1 + g) / (R – g)
Websites of Interest:
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