What Is a Perpetual Bond?
A perpetual bond, also known as a "consol bond" or "perp," is a fixed income security with no maturity date. This type of bond is often considered a type of equity, rather than debt. One major drawback to these types of bonds is that they are not redeemable. However, the major benefit of them is that they pay a steady stream of interest payments forever.
Key Takeaways
- Perpetual bonds, also known as perps or consol bonds, are bonds with no maturity date.
- Although perpetual bonds are not redeemable, they pay a steady stream of interest in forever.
- Because of the nature of these bonds, they are often viewed as a type of equity and not a debt.
Understanding Perpetual Bonds
Perpetual bonds exist within a small niche of the bond market. This is mainly due to the fact that there are very few entities that are safe enough for investors to invest in a bond where the principal will never be repaid.
Some of the notable perpetual bonds in existence are those that were issued by the British Treasury for World War I and the South Sea Bubble of 1720. Some in the U.S. believe the federal government should issue perpetual bonds, which may help it avoid the refinancing costs associated with bond issues that have maturity dates.
Example of a Perpetual Bond
Since perpetual bond payments are similar to stock dividend payments, as they both offer some sort of return for an indefinite period of time, it is logical that they would be priced the same way.
The price of a perpetual bond is, therefore, the fixed interest payment, or coupon amount, divided by some constant discount rate, which represents the speed at which money loses value over time (partly due to inflation). The discount rate denominator reduces the real value of the nominally fixed coupon amounts over time, eventually making this value equal zero. As such, perpetual bonds, even though they have no maturity date and pay interest forever, can be assigned a finite value, which in turn represents their price.
Formula for the Present Value of a Perpetual Bond
Present value = D / r
Where:
D = periodic coupon payment of the bond
r = discount rate applied to the bond
For example, if a perpetual bond pays $10,000 per year in perpetuity and the discount rate is assumed to be 4%, the present value would be:
Present value = $10,000 / 0.04 = $250,000
Note that the present value of a perpetual bond is highly sensitive to the discount rate assumed since the payment is known as fact. For example, using the above example with 3%, 4%, 5% and 6% discount rates, the present values are:
Present value (3%) = $10,000 / 0.03 = $333,333
Present value (4%) = $10,000 / 0.04 = $250,000
Present value (5%) = $10,000 / 0.05 = $200,000
Present value (6%) = $10,000 / 0.06 = $166,667
FAQs
Example of a Perpetual Bond
How to calculate the value of a perpetual bond? ›
Hence the perpetual bond price is presented as the present value of the fixed interest income or the periodic coupon payment (D), dividing D by the discount rate, r.
What is the formula for perpetual yield? ›
It is easily calculated for one-year discount bonds i = (FV–PV)/PV and perpetuities i = C/PV where C is the coupon or annual payment.
What is perpetual bond with example? ›
Perpetual bonds – which are also referred to as perpetuals or just “perps” for short – are bonds with no maturity date. They pay interest to investors in the form of coupon payments, just as with most bonds, but the bond's principal amount does not come with a set date for redemption (repayment).
How do you calculate the value of a bond example? ›
To calculate the value of a zero-coupon bond, we only need to find the present value of the face value. Carrying over from the example above, the value of a zero-coupon bond with a face value of $1,000, YTM of 3%, and two years to maturity would be $1,000 / (1.03)2, or $942.59.
How do you calculate perpetuity value? ›
The perpetuity formula proceeds as follows: Present Value (PV) = Cash Flow (CF)/Interest Rate (IR). It acts as an innate perpetuity calculator capable of determining all present and future cash flows for investments of this type.
What is the formula for perpetual bond in Excel? ›
PV = D/ (1+r) + D (1+g) / (1+r) ^2 + D (1+g) ^2 …. The perpetuity series is considered to be continued for an infinite period. One can again write and present the formula as the following example: John has invested in a bond that pays him coupon payments for an infinite period of time.
What is the formula for perpetual compounding? ›
The continuous compounding formula is nothing but the compound interest formula when the number of terms is infinite. This formula says, when an amount P is invested for the time 't' with the interest rate is r% compounded continuously, then the final amount is, A = P ert.
How do you calculate perpetual dividends? ›
In order to determine the present value of a perpetuity, an investor must divide the cash source or dividend by the discount rate, written in formula as Present Value = Dividend Discount Rate or P V = D r − g . An example of perpetuities includes the British consol.
What is the formula for yield value? ›
Yield calculation and formula
The calculation for yield differs depending on the type of yield. The common formula is income (eg from dividends or interest payments) divided by investment value. This can then be multiplied by 100 to get a percentage figure.
The region is in a state of perpetual war. He seems to have a perpetual grin on his face.
What are the problems with perpetual bonds? ›
While perpetual bonds are generally considered a secure investment, there is a credit risk for bond buyers. Investors may face losses if market interest rates surpass the bond coupon rates. To manage this risk, issuers might offer higher coupon rates for a specific period based on the current market rate.
Is a perpetual bond a liability or equity? ›
The perpetual bond is classified as an equity instrument because the issuer has no contractual obligation to deliver cash or another financial asset in any circ*mstances outside its control, except in the event of the liquidation of Company X.
How to calculate bond yield? ›
The current yield formula equals the annual coupon payment divided by the bond's current market price, expressed as a percentage.
How do you calculate the value of an I bond? ›
You can determine the value for an electronic savings bond by logging into your TreasuryDirect account. For paper bonds, use the savings bond calculator.
How to calculate the present value of a bond? ›
The present value of a bond is calculated by discounting the bond's future cash payments by the current market interest rate. In other words, the present value of a bond is the total of: The present value of the semiannual interest payments, PLUS. The present value of the principal payment on the date the bond matures.
How do you calculate perpetual annual worth? ›
The perpetual equivalent annual worth (PEAW) is the perpetuity payment that is equivalent in present value to the present value of a stream of cash flows. It can be found by equating the net present value of the stream of cash flows to the present value of a perpetuity.
How to calculate the price of a consol bond? ›
A consol has an infinite maturity, and is priced simply as [C/2]/r0.5, where we are assuming that the coupon is paid every six months, and r0.5 is the discount rate for 6 months, i.e. 2r0.5 is the annual yield on the consol. Example: If C = $10,000, and the annualized discount rate is 9%, the price is $113,557.26.
What is the formula for years purchase in perpetuity? ›
How to use this calculator
| Years Purchase, in Perpetuity |
|---|
| YP = i/100 |
| Interest Rate (%) | |
| Term (years) | |
| Amount (£) | |
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