Understanding Future Values, Compound Interest, and Bond Valuation
CH5 Future Values and Compound Interest
Key Concepts:
- Future Value: The amount an investment will grow to after earning interest.
- Compound Interest: Interest earned on both the initial investment and accumulated interest.
- Simple Interest: Interest earned only on the original investment.
Examples:
- Simple Interest: $100 at 6% for 5 years earns $6 per year, resulting in a final balance of $130.
- Compound Interest: $100 at 6% compounded annually for 5 years grows to $133.82.
Future Value Formula:
FV = PV(1+r)^t
- FV: Future Value
- PV: Present Value
- r: Interest rate per period
- t: Number of periods
Present Value Formula:
PV = FV / (1+r)^t
Discounting:
Finding the present value of a future amount.
Discount Rate:
The implied interest rate of an investment, calculated as r = (FV/PV)^(1/t) – 1.
Finding Time Periods:
t = ln(FV/PV) / ln(1+r)
Uneven Cash Flows:
Perpetuity:
A stream of equal payments that continues forever.
Annuity:
A series of equal payments made at regular intervals for a limited time.
- Ordinary Annuity: Payments made at the end of each period.
- Annuity Due: Payments made at the beginning of each period.
Present Value of a Perpetuity:
PV = C / r
- C: Cash payment
- r: Interest rate
APR and EAR:
- Annual Percentage Rate (APR): Interest rate annualized using simple interest.
- Effective Annual Rate (EAR): Interest rate annualized using compound interest.
CH6 Valuing Bonds
Bond Terminology:
- Bond: A security representing a loan made by an investor to a borrower.
- Coupon: The periodic interest payment made to the bondholder.
- Face Value: The amount repaid to the bondholder at maturity.
- Coupon Rate: The annual interest payment as a percentage of face value.
Bond Pricing:
The present value of all future cash flows (coupons and face value) discounted at the required rate of return.
Interest Rate Risk:
As interest rates rise, bond prices fall, and vice versa.
Yield to Maturity (YTM):
The approximate market rate of return, assuming the bond is held until maturity.
Corporate Bonds and Default Risk:
The yield on corporate bonds includes a premium to compensate for the risk of default.
Bond Ratings:
Agencies like Moody’s and Standard & Poor’s assess the creditworthiness of bonds.
CH7 Valuing Common Stocks: Dividend Discount Model
Cash Flows from Stocks:
- Dividends
- Sale of shares
Dividend Discount Model (DDM):
No Growth:
P0 = Div / r
Constant Growth:
P0 = D1 / (r – g)
- P0: Current stock price
- Div: Dividend
- D1: Expected dividend next period
- r: Required rate of return
- g: Dividend growth rate
Estimating Expected Rate of Return:
r = (D1 / P0) + g