Questions:
A call provision on a bond enables the bond issues to redeem or buy back the bond at a predetermined fixed price or a sequence of payments before its date of maturity.
Typically, bond issuers exercise a call provision when interest rates fall then the issuer is able to offer a new bond at lower interest rates, which reduces his overall cost of debt (Sherman, 2011). Bond issuers often issue callable bonds as a hedge against interest rate risk.
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A discount bond is a bond is issued for less than its par value. That is, a bond with an interest rate lower than the prevailing market rate and is issued at a lower price is considered a discount bond (Kenny, 2017).
A premium bond is defined as a bond that is issued for more than its face value. Usually, premium bond offers investors a higher yield as they offer coupon rates higher than the current market rates (Kenny, 2017).
For instance, A common bond is usually issues at $1,000 par value. A bond that trades for $850 will be a discount bond while a bond trading at $1,050 will be considered a premium bond.
Interest rates and bond prices have an inverse relationship but not in direct proportion ("The Relationship Between Bonds and Interest Rates- Wells Fargo Funds", 2017). That is, when interest rates increase, bond prices are expected to decrease, and vice versa. However, the change in interest rates is not proportional to the change in bond prices. When a bond is issued, its coupon rate is usually at or close to the prevailing interest rate. The objective of any investor is to receive the best possible return from their investment (Weaver and Weston, 2001). Consequently, bond investors are always comparing their coupon rates to the current market interest rates. If the prevailing interest rate are higher than a bond’s coupon rate, the bond becomes less attractive to investors, thus they are willing to pay less for the bond. Therefore, an increase in market interest rate pushes the bond prices down. On the other hand, if the prevailing market interest rates fall below the coupon rate of a bond, the bond itself become more attractive to investors and they are willing to pay more for the bond. Therefore, the price for the bond rises.
The main difference between a coupon bond and a zero-coupon bond is that the latter does not pay coupons while bondholders of a coupon bond receive regular interest payments over the life of the bond (Finkler, 2002). An investor of a zero-coupon bond receives only the par value of the bond at the maturity date of the bond. Additionally, zero coupon bonds are issued at large discounts to their face value compared to the typical coupon bond. Hence, the gain in a zero-coupon bond is the difference between its par value and the purchase price, while the gain from the coupon bond is the regular interest payments.
Computational Problems:
For the computation problems we solve the problems algebraically as well as usinf the Excel spreadsheet
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.
Solution:
The formula for calculating the price of a zero-coupon bond is;
Zero-coupon bond value =
Where,
F = par value of bond = $1,000
r = interest rate = 5.5%/2 = 2.75%
t = number of periods = 3 years * 2 = 6
Therefore,
Bond value = = $849.78
The price for the zero-coupon bond is $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.
Solution:
We use the Excel spreadsheet to find the present value of all future interest payments (cash flows). i.e. PV (rate, nper, pmt, FV)
Where,
FV is the par value of the bond = $1000
PMT is the semi-annual interest payments = $1000*5%/2 = $25
NPER is the number of coupon payments = 10 years * 2 = 20
RATE is the market interest rate = 7.2%/2 = 3.6%
Therefore,
Price = PV “=PV(3.6%,20,25,1000,0)” = $845.07
The price of the coupon bond is $845.07
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.
Solution:
To find the Yield to Maturity we use the formula;
YTM = ,
Where,
C is the coupons payments = $1000*4.65%/2 = $23.25
F is the face value of the coupon = $1000
P is the price = $1,025.95
n is the payment periods = 18 years * 2 = 36
Therefore,
YTM == 0.0222
The semi-annual yield to maturity is 2.22% and the annual yield to maturity is 4.44%
References
Finkler, S. (2002). Finance & accounting for nonfinancial managers . Paramus: Prentice Hall Press.
Sherman, E. H. (2011). Finance and accounting for nonfinancial manager s (3rd ed.). New York, NY: American Management Association.
Weaver, S. C., & Weston, J. F. (2001). Finance and accounting for nonfinancial managers . New York, NY: McGraw-Hill.
Kenny, T. (2017). New Investor's Guide to Premium and Discount Bonds . The Balance . Retrieved 10 November 2017, from https://www.thebalance.com/premium-vs-discount-bonds-417066
The Relationship Between Bonds and Interest Rates- Wells Fargo Funds . (2017). Wellsfargofunds.com . Retrieved 10 November 2017, from https://www.wellsfargofunds.com/ind/investing-basics-and-planning/bonds-and-interest-rates.html
