Coupon bond practice problems

A Zero Coupon Bonds. D Bonds with continuous compounding. The amount needed or desired at the end of the holding period is not necessary we assume it to be the bond's face value. Here is an easy step to find the value of such a bond:. Here, "rate" corresponds to the interest rate that will be applied to the face value of the bond.

Since our bond is maturing in 20 years, we have 20 periods. The bond provides coupons annually and pays a coupon amount of 0.

Bond Pricing

The semiannual coupon rate is 1. Continuous compounding refers to interest being compounded constantly. As we saw above, we can have compounding that is based on an annual, bi-annual basis or any discrete number of periods we would like. However, continuous compounding has an infinite number of compounding periods. The cash flow is discounted by the exponential factor. The clean price of a bond does not include the accrued interest to maturity of the coupon payments.

How to calculate the bond price and yield to maturity

This is the price of a newly issued bond in the primary market. When a bond changes hands in the secondary market , its value should reflect the interest accrued previously since the last coupon payment. This is referred to as the dirty price of the bond. Excel provides a very useful formula to price bonds. The PV function is flexible enough to provide the price of bonds without annuities or with different types of annuities, such as annual or bi-annual. Fixed Income Essentials. Municipal Bonds. Company B. Company C. Cannot be determined with the given information.

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French Bond : French Bond for the Akhtala mines issued in The decision of whether to refund a particular debt issue is usually based on a capital budgeting present value analysis. The principal benefit, or cash inflow, is the present value of the after-tax interest savings over the life of the issue.

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Step 2: Calculate the net investment net cash outflow at time 0. This involves computing the after-tax call premium, the issuance cost of the new issue, the issuance cost of the old issue, and the overlapping interest. The call premium is a cash outflow. Skip to main content.

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Learning Objectives Calculate the present value of an annuity. Key Takeaways Key Points The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments. Key Terms discount rate : The interest rate used to discount future cash flows of a financial instrument; the annual interest rate used to decrease the amounts of future cash flow to yield their present value.

Par Value at Maturity Par value is stated value or face value, with a typical bond making a repayment of par value at maturity. Key Takeaways Key Points A bond selling at par has a coupon rate such that the bond is worth an amount equivalent to its original issue value or its value upon redemption at maturity. Par value of a bond usually does not change, except for inflation -linked bonds whose par value is adjusted by inflation rates every predetermined period of time.

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Key Terms inflation-linked bonds : Inflation-indexed bonds also known as inflation-linked bonds or colloquially as linkers are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment. Yield to Maturity Yield to maturity is the discount rate at which the sum of all future cash flows from the bond are equal to the price of the bond. Learning Objectives Classify a bond based on its market value and Yield to Maturity. Key Takeaways Key Points The Yield to maturity is the internal rate of return earned by an investor who bought the bond today at the market price, assuming that the bond will be held until maturity, and that all coupon and principal payments will be made on schedule.

There are some variants of YTM: yield to call, yield to put, yield to worst… Key Terms quote : To name the current price, notably of a financial security. The rate of return on an investment which causes the net present value of all future cash flows to be zero. Inflation Premium An inflation premium is the part of prevailing interest rates that results from lenders compensating for expected inflation. Learning Objectives Explain how to determine and use an inflation premium. Key Takeaways Key Points Investors seek this premium to compensate for the erosion in the value of their capital due to inflation.

Key Terms systematic risks : In finance and economics, systematic risk sometimes called aggregate risk, market risk, or undiversifiable risk is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggregate income. Learning Objectives Differentiate between real and nominal interest rates. Key Takeaways Key Points Nominal rate refers to the rate before adjustment for inflation; the real rate is the nominal rate minus inflation.

Key Terms purchasing power : Purchasing power sometimes retroactively called adjusted for inflation is the amount of goods or services that can be purchased with a unit of currency. Key Takeaways Key Points The maturity can be any length of time, but debt securities with a term of less than one year are generally not designated as bonds. Instead, they are considered money market instruments. In the market for United States Treasury securities, there are three categories of bond maturities: short-term, medium-term and long-term bonds. A bond that takes longer to mature necessarily has a greater duration.

The bond price in this type of a situation, therefore, is more sensitive to changes in interest rates.

What it is:

Impact of Payment Frequency on Bond Prices Payment frequency can be annual, semi annual, quarterly, or monthly; the more frequently a bond makes coupon payments, the higher the bond price. Learning Objectives Calculate the price of a bond. Key Takeaways Key Points Payment frequency can be annual, semi annual, quarterly, monthly, weekly, daily, or continuous. Bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments. The present value of face value received at maturity is the same.

The more frequent a bond makes coupon payments, the higher the bond price, given equal coupon, par, and face. For example, a retirement annuity paid to a public officer following his or her retirement. Deciding to Refund Bonds Refunding occurs when an entity that has issued callable bonds calls those debt securities to issue new debt at a lower coupon rate. Learning Objectives Explain when to refund a debt issue. Key Takeaways Key Points The issue of new, lower- interest debt allows the company to prematurely refund the older, higher-interest debt.

Bond refunding occurs when a interest rates in the market are sufficiently less than the coupon rate on the old bond, b the price of the old bond is less than par.