5.2 Accounting for Bonds
Before we launch further into Fixed Income Mathematics, it behooves us to examine how the accountant reports bond liabilities on the financial statements. In so doing, we will be able to assess the accuracy of GAAP reporting. Can the financial analyst rely on these data? We will start out with a “given” bond, then calculate its price and, last, examine how the price – and thus the reported liability – changes over time as per the accountant’s perspective.
Exercise
Try calculating the solution without glancing at it below.
- Given:
Principal = $1,000,000
Coupon = .07
Annual Payment
Maturity = 3 Years
Solution
PV (Price) = $70,000 (2.6730) + $1,000,000 (.8396) = $1,026,710 = 102.671%
Review Questions
- What would the bond price be if the coupon were 0%? (Answer: 83.96%)
- What would the bond price be if the coupon instead were paid semi-annually? Why should it be different?
PV = $35,000 (5.4172) + $1,000,000 (0.8375) = $1,027,102 or 102.7102%
The price is greater than just before (when we had once yearly coupon payments) because half the coupon payments are received earlier and thus have greater present values.
- Note that, in order to be mathematically consistent, the par value must also reflect the same discounting frequency as the coupons… (see below, Problem Five).
We will utilize this same bond again on the next few pages in order to illustrate Fixed Income Accounting.
At this point, the student should be able to calculate both Dollar Price and YTM for a given bond using a financial calculator.
