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Chapter $13|$ Bonds and Sinking Funds

Raising Money Through Bonds

Seth, a business student in college, recently learned that bonds can be categorized as either investment grade bonds or junk bonds. Investment grade bonds are issued by established, low$-$risk companies, whereas junk bonds are issued by high$-$risk companies.

Intrigued by the concept of junk bonds, Seth followed a company called Holdings Software Developers Inc. $($HSD$)-$ a highrisk company that issued junk bonds. The company had a low credit rating in the market and its bonds were considered very risky investments, which is why it had to offer high interest payments to the holders of the bond. Although these bonds were junk bonds, surprisingly, there were many wealthy people who purchased its bonds, selling them shortly afterwards for a quick return on their investment.

In one particular case, HSD required $$1,000,000$ for an expansion project and raised the money by issuing $$5000$ bonds that were redeemable in ten years. The bonds were rated as junk bonds and offered an $11\%$ coupon rate paid semi$-$annually.

HSD had wanted to increase the rating of its bond by gaining the confidence of its investors, so HSD created a ten$-$year sinking fund to ensure that enough money would be available at the time of maturity of the bonds. The fund was growing at $2\mathrm{.}5\%$ compounded monthly and they made equal deposits into the fund at the end of every six months.

a$.$ What was the discount on the bond at the time of issue if its yield rate was $14\%$ compounded semi$-$annualiy?

b$.$ What was the premium on the bond at the time of issue if the yield rate was $9\%$ compounded quarterly?

c$.$ If an investor purchased a bond at the time of issue at a yield rate of $14\%$ compounded semi$-$annually, and sold it two years later when the market required a yield rate of only $13\%$ compounded semi$-$annually, how much would the investor gain or lose on this investment?

d$.$ What was the purchase price of the bond if an investor wanted to purchase it $6$ years and $2$ months before its redemption date and have the bond yield $12\mathrm{.}5\%$ compounded semi$-$annually?

e$.$ If the bond was purchased seven years before maturity for $103\mathrm{.}4,$ what was its yield rate?

f$.$ Two years before maturity, an investor purchased the bond at a yield rate of $15\%$ compounded semi$-$annually. Construct a bond schedule for the investor showing the amortization of discount.

g$.$ What was the size of the periodic sinking fund deposit $($rounded up to the next cent$)$ and what was the total interest earned during the period?

h$.$ Construct a sinking fund schedule illustrating details of the fund.