Time Value of Money & Financial Mathematics

Time Value of Money (TVM) Key Drivers

Opportunity cost, inflation, and future risk.

Limited Liability

Shareholders only lose what they invested and are not personally responsible for corporate debts.

Agency Problem

A conflict of interest where managers act in their own self-interest rather than in the best interest of shareholders.

Effective Annual Rate (EAR)

The annualized interest rate reflecting the impact of compounding; used to compare rates with different compounding frequencies.

Perpetuity

A constant cash flow ($C$) that continues indefinitely forever ($n = \infty$).

Bond Price and Yield Relationship

Inverse relationship: when market yield increases, bond price decreases.

Coupon Rate vs. YTM Relationships

If Coupon Rate = YTM, trades at Par Value ($P_0 = FV$); if Coupon Rate > YTM, trades at Premium ($P_0 > FV$); if Coupon Rate < YTM, trades at Discount ($P_0 < FV$).

Zero-Coupon Bond

A bond that makes no periodic interest payments and is sold at a discount, offering a single cash flow at maturity.

Ordinary Annuity vs. Annuity Due

Ordinary Annuity cash flows occur at the end of each period, whereas Annuity Due cash flows occur at the beginning of each period.

Primary vs. Secondary Market

Primary Market is where the issuing corporation directly sells securities; Secondary Market is where existing securities are traded among investors.