The Meaning of Interest Rates (Chapter 4)

Present value of a simple loan

The current value of a future sum of money or stream of cash flow given a specified rate of return

Net present value

The difference between the present value of cash inflows and the present value of cash outflows over a period of time

Yield to Maturity

The interest rate that equates the present value of all cash flow payments received from a debt instrument with its value today (price)

Relationship between price of a coupon bond and ytm

• When P = FV, YTM = coupon rate

• P and YTM are negatively related

• YTM > coupon rate when P < FV

YTM on a consol/perpetuity

YTM on a discount bond

Coupon rate

coupon payment / FV

Current yield

annual coupons / current bond price

Capital Gains Yield

Rate of Return

current yield + rate of capital gain

Relationship between interest rates and returns

• Return = YTM only if the holding period = time to maturity

• Rise in interest rates → fall in bond prices → capital loss IF time to maturity > holding period

• The more distant a bond’s maturity, the greater the size of the % price change associated with % interest change

• The more distant a bond’s maturity, the lower the rate of return that occurs as a result of an increase in the interest rate

• Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise