Podcast
Questions and Answers
What is the formula for the price of a consol?
What is the formula for the price of a consol?
- c / r (correct)
- c + r
- c / (1 + r)
- c x r
The British government can change the coupon rate for consols at any time.
The British government can change the coupon rate for consols at any time.
False (B)
What does the yield to maturity on a consol represent?
What does the yield to maturity on a consol represent?
The yield to maturity represents the return expected on a bond if it is held until maturity.
A consol pays a coupon forever or for a very long time with no __________ date.
A consol pays a coupon forever or for a very long time with no __________ date.
Match the following terms with their descriptions:
Match the following terms with their descriptions:
If a consol is paying a £5 coupon and is selling for £100, what is the yield to maturity?
If a consol is paying a £5 coupon and is selling for £100, what is the yield to maturity?
Once a consol is purchased, the holder can expect to sell it at any price without risk.
Once a consol is purchased, the holder can expect to sell it at any price without risk.
Why do companies usually not issue consols?
Why do companies usually not issue consols?
What is the formula for the present discounted value of a growing consol?
What is the formula for the present discounted value of a growing consol?
If the growth rate g equals the interest rate r, the present value will be infinite.
If the growth rate g equals the interest rate r, the present value will be infinite.
What type of financial instrument is a typical mortgage considered?
What type of financial instrument is a typical mortgage considered?
If the interest rate is 0, then consols do not even _______.
If the interest rate is 0, then consols do not even _______.
Match the following scenarios with their corresponding financial concept:
Match the following scenarios with their corresponding financial concept:
In the context of consols, what does 'g' represent?
In the context of consols, what does 'g' represent?
Land can be considered analogous to consols because it can generate income indefinitely.
Land can be considered analogous to consols because it can generate income indefinitely.
What happens when the growth rate exceeds the interest rate?
What happens when the growth rate exceeds the interest rate?
An annuity is a financial product that makes payments starting in one year and continues for _______ years.
An annuity is a financial product that makes payments starting in one year and continues for _______ years.
Why are financial instruments like annuities designed around human imperfections?
Why are financial instruments like annuities designed around human imperfections?
The present value of an amount growing at the rate of interest will converge to a value.
The present value of an amount growing at the rate of interest will converge to a value.
Who is associated with the initiation of the Growing Consol Formula?
Who is associated with the initiation of the Growing Consol Formula?
The typical financing schedule for a mortgage is _______.
The typical financing schedule for a mortgage is _______.
Match the following concepts to their definitions:
Match the following concepts to their definitions:
Study Notes
Consols Overview
- Consols are bonds issued by the UK government with no maturity date, promising to pay a fixed coupon forever.
- Originated in the 1700s, providing a continuous stream of income to investors; adjustments made in the 1880s are still in effect.
- British government has maintained these payments without default over several hundred years.
Consol Pricing
- Present value of a consol is calculated as ( P = \frac{C}{r} ), where ( C ) is the coupon and ( r ) is the interest rate.
- Yield to maturity formula: ( YTM = \frac{C}{P} ).
- Price variations impact yield; an increase in price reduces yield (e.g., £3 coupon for £200 yields 1.5% instead of the original 3%).
Market Risk
- Bonds entail market risk even if default risk is absent; prices fluctuate based on market conditions.
- Investors eventually want to sell consols, so market prices may not reflect the original coupon rate.
Growing Consols
- A growing consol starts with a base coupon ( C ) that increases at a constant rate ( g ).
- Present value formula: ( PV = \frac{C}{r - g} ).
- If ( g ) equals ( r ), the present value is infinite; the series is non-convergent.
- If ( g > r ), the formula fails, leading to an infinite present value.
Conceptual Implications
- When interest rates are zero, traditional consols do not converge; this creates theoretical implications for pricing.
- Long-term interest rates generally exceed zero to maintain plausible asset values.
Annuitization
- Annuities provide fixed payments over a certain period, differing from consols that provide perpetual payments.
- Payments in typical mortgages are structured for monthly intervals for accessibility; balloon payments were common historically.
Historical Context
- The growing consol formula, referred to as the Gordon Rule, is attributed to Myron Gordon but traces back to Jacob Bernoulli.
- The formula remains significant in financial analysis and economic theory today.
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Description
This quiz explores the concept of consols, financial instruments that pay a fixed coupon indefinitely without a maturity date. Learn about their historical context in Britain and the formula used to value them. Test your knowledge of key financial principles surrounding these unique bonds.
