Chapter 7 Bonds and Their Valuation 223
g. Discount bond; premium bond
h. Yield to maturity (YTM); yield to call (YTC); total return; yield spread
i. Interest rate risk; reinvestment rate risk; investment horizon; default risk
j. Mortgage bond; indenture; debenture; subordinated debenture
k. Investment-grade bond; junk bond
BOND VALUATION The Pennington Corporation issued a new series of bonds on January 1,
- The bonds were sold at par ($1,000); had a 12% coupon; and mature in 30 years, on
December 31, 2014. Coupon payments are made semiannually (on June 30 and December 31).
a. What was the YTM on January 1, 1985?
b. What was the price of the bonds on January 1, 1990, 5 years later, assuming that
interest rates had fallen to 10%?
c. Find the current yield, capital gains yield, and total return on January 1, 1990, given
the price as determined in Part b.
d. On July 1, 2008, 6½ years before maturity, Pennington’s bonds sold for $916.42. What
were the YTM, the current yield, the capital gains yield, and the total return at that time?
e. Now assume that you plan to purchase an outstanding Pennington bond on March 1,
2008, when the going rate of interest given its risk was 15.5%. How large a check must
you write to complete the transaction? This is a difficult question.
SINKING FUND The Vancouver Development Company (VDC) is planning to sell a $100
million, 10-year, 12%, semiannual payment bond issue. Provisions for a sinking fund to
retire the issue over its life will be included in the indenture. Sinking fund payments will
be made at the end of each year, and each payment must be sufficient to retire 10% of the
original amount of the issue. The last sinking fund payment will retire the last of the
bonds. The bonds to be retired each period can be purchased on the open market or
obtained by calling up to 5% of the original issue at par, at VDC’s option.
a. How large must each sinking fund payment be if the company (1) uses the option to
call bonds at par or (2) decides to buy bonds on the open market? For Part (2), you
can only answer in words.
b. What will happen to debt service requirements per year associated with this issue
over its 10-year life?
c. Now consider an alternative plan where VDC sets up its sinking fund so that equal
annual amounts are paid into a sinking fund trust held by a bank, with the proceeds
being used to buy government bonds that are expected to pay 7% annual interest. The
payments, plus accumulated interest, must total $100 million at the end of 10 years,
when the proceeds will be used to retire the issue. How large must the annual sinking
fund payments be? Is this amount known with certainty, or might it be higher or lower?
d. What are the annual cash requirements for covering bond service costs under the
trusteeship arrangement described in Part c? (Note: Interest must be paid on
Vancouver’s outstanding bonds but not on bonds that have been retired.) Assume
level interest rates for purposes of answering this question.
e. What would have to happen to interest rates to cause the company to buy bonds on
the open market rather than call them under the plan where some bonds are retired
each year?
A sinking fund can be set up in one of two ways:
a. The corporation makes annual payments to the trustee, who invests the proceeds in
securities (frequently government bonds) and uses the accumulated total to retire the
bond issue at maturity.
b. The trustee uses the annual payments to retire a portion of the issue each year, calling
a given percentage of the issue by a lottery and paying a specified price per bond or
buying bonds on the open market, whichever is cheaper.
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