Describe the relationship between interest rates and bond prices

A call provision allows bond issuers to call back a portion of a bond before it reaches its maturity date (Investopedia, 2017). Bond issuers would use a call provision if the market interest rate had fallen by the time of the call date, allowing them to refinance the debt at a reduced level.

Define the terms discount bond and premium bond. Please provide instances of each. A discount bond is one which is issued for an amount that is less than its face value (Russo, 2014). Examples of discount bonds include the U.S. Treasury bills and U.S. savings bonds.

A premium bond is one that is issued at an amount that is more than its face value (Russo, 2014). An example of a premium bond is the Canada Premium Bond.

Describe the relationship between interest rates and bond prices.

Interest rate and bond prices vary inversely with each other (Anspach, 2017). However, this variation is not directly proportional. One can estimate the bond price by examining the difference between the interest rate and the coupon rate. A large difference means that the bond has a long time before it reaches maturity.

Describe the differences between a coupon bond and a zero-coupon bond.

A coupon bond is one in which the interest is paid using coupons and initially trades near its face value (Finance Formula, 2017). On the other hand, a zero-coupon bond is one which trades at a deep discount in relation to the face value but does not attract any interest (Finance Formula, 2017). As such, bondholders will only gain the difference of what they had paid for the bond and what they will receive at bond maturity.

Problems

In either a Word document or Excel spreadsheet, complete the following problems.

You may solve the problems algebraically, or you may use a financial calculator or an Excel spreadsheet.

If you choose to solve the problems algebraically, be sure to show your computations.

If you use a financial calculator, show your input values.

If you use an Excel spreadsheet, show your input values and formulas.

In addition to your solution to each computational problem, you must show the supporting work leading to your solution to receive credit for your answer.

Compute the following:

Assuming semi-annual compounding, what is the price of a zero coupon bond that matures in 3 years if the market interest rate is 5.5 percent? Assume par value is $1000.

Semi-annual interest rate, r, = 5.5/2 = 2.75%

Number of periods, n = 3 x 2 = 6

Par value, V = $1,000

= $849.78

Using semi-annual compounding, what is the price of a 5 percent coupon bond with 10 years left to maturity and a market interest rate of 7.2 percent? Assume that interest payments are paid semi-annually, and that par value is $1000.

V = Par value = $1,000

C = Coupon payment = par value * coupon rate = 1,000 * 5% = $50

k = Number of coupons = 10 * 2 = 20

n = number of coupon payments in a year = 2

r = market interest rate = 7.2%/2 = 3.6% = 0.036

Using semi-annual compounding, what is the yield to maturity on a 4.65 percent coupon bond with 18 years left to maturity that is offered for sale at $1,025.95? Assume par value is $1000.

V = Par value = $1,000

C = Coupon payment = par value * coupon rate = 1,000 * 4.65% = $46.5

k = Number of coupons = 10 * 2 = 20

n = number of coupon payments in a year = 2

Bond price = 1025.95

R = 0.024 and this is semi annual hence annual = 0.024 * 2 = 0.048 = 4.8%

Anspach, D. (2017). How Rising Interest Rates Affect Bond Prices. The Balance. Retrieved 25 November 2017, from https://www.thebalance.com/why-do-bond-prices-go-down-when-interest-rates-rise-2388565

Zero Coupon Bond Value - Formula and Calculator. (2017). Financeformulas.net. Retrieved 25 November 2017, from http://financeformulas.net/Zero_Coupon_Bond_Value.html

Investopedia. (2017). Call Provision. Investopedia. Retrieved 25 November 2017, from https://www.investopedia.com/terms/c/callprovision.asp

Russo, R. (2014). What’s the Difference Between Premium Bonds and Discount Bonds?. Rodgers-associates.com. Retrieved 25 November 2017, from https://rodgers-associates.com/blog/difference-premium-bonds-discount-bonds/