A-8 Appendix A Solutions to Self-Test Questions and Problems
Thus, on March 1, 2008, 13^2 / 3 periods were left before the bond matured.
Bond traders actually use the following procedure to determine the price of
the bond:
(1) Find the price of the bond on the next coupon date, July 1, 2008. Using a
! nancial calculator, input N! 13, I/YR! 7.75, PMT! 60, FV! 1000,
and PV!? Solve for PV! $859.76.
(2) Add the coupon, $60, to the bond price to get the total value, TV, of the
bond on the next interest payment date: TV! $859.76 $ $60.00! $919.76.
(3) Discount this total value back to the purchase date (March 1, 2008): Using
a! nancial calculator, input N! 4/6, I/YR! 7.75, PMT! 0, FV! 919.76,
and PV!? Solve for PV! $875.11.
(4) Therefore, you would have written a check for $875.11 to complete the
transaction. Of that amount, $20! (^1 / 3 )($60) would represent accrued in-
terest and $855.11 would represent the bond’s basic value. This break-
down would affect your taxes and the seller’s taxes.
(5) This problem could be solved very easily using a spreadsheet or a! nan-
cial calculator with a bond valuation function, such as the HP-12C or the
HP-17BII. This is explained in the calculator manual under the heading
“Bond Calculations.”a. (1) $100,000,000/10! $10,000,000 per year, or $5 million each 6 months. Since
the $5 million will be used to retire bonds immediately, no interest will be
earned on it.
(2) VDC will purchase bonds on the open market if they’re selling at less than
par. So the sinking fund payment will be less than $5,000,000 each period.
b. The debt service requirements will decline. As the amount of bonds
outstanding declines, so will the interest requirements (amounts given in
millions of dollars). If the bonds are called at par, the total bond service
payments are calculated as follows:Semiannual
Payment
PeriodSinking Fund
PaymentOutstanding
Bonds on
Which Interest
Is PaidInterest
PaymentaTotal
Bond
Service
(1) (2) (3) (4) (2) # (4)! (5)
1 $5 $100 $6.0 $11.0
2 5 95 5.7 10.7
3 5 90 5.4 10.4
# # # # #
20 5 5 0.3 5.3
a Interest is calculated as (0.5)(0.12) (Column 3). For example: Interest in Period 2! (0.5)
(0.12)($95)! $5.7.The company’s total cash bond service requirement will be $21.7 million per year
for the! rst year. For both options, interest will decline by 0.12($10,000,000)!
$1,200,000 per year for the remaining years. The total debt service requirement
for the open market purchases cannot be precisely determined, but the amounts
will be less than what’s shown in Column 5 of the preceding table.
c. Here we have a 10-year 7% annuity whose compound value is $100 million and
we are seeking the annual payment, PMT. The solution can be obtained with a
! nancial calculator. Input N! 10, I/YR! 7, PV! 0, and FV! 100000000 and
press the PMT key to obtain $7,237,750. This amount is not known with