Perpetual Bond Pricing

Perpetual bonds (also known as consols) are fixed-income securities that pay a steady stream of interest payments forever, with no maturity date.

The basic formula for pricing a perpetual bond is:

Price = C/r

Where:

• C is the annual coupon payment
• r is the required yield rate (as a decimal)

Some key characteristics:

• The price moves inversely to interest rates (yield)
• The price is more sensitive to rate changes at lower yield levels
• There's no maturity value to consider since the bond never matures

For example, if a perpetual bond pays $100 annually and the required yield is 5%, the price would be:

$100/0.05 = $2,000

This is a simplified model that assumes:

• Constant interest rates
• No default risk
• Payments are made in perpetuity