Comprehensive Accounting Notes on Bond Valuation, Present Value Mechanics, and Debt Financing

Administrative Policies & Course Structure

  • Assignment Submission & Grade Recovery Policy:

    • Completing and submitting the grade recovery assignment provides a percentage return of lost points on the lowest exam grade (up to 25 %25\,\% of points lost based on timing):
    • Submission prior to Exam 1: Reclaim up to 25 %25\,\% of lost points from the lowest exam grade.
    • Submission between Exam 1 and Exam 2: Reclaim 20 %20\,\% of lost points.
    • Submission between Exam 2 and Exam 3: Reclaim 15 %15\,\% of lost points.
    • Submission at the end of the semester: Reclaim 10 %10\,\% of lost points (delaying until the end is equivalent to relinquishing approximately 33 total grade points).
    • Students must pick up the required handouts prior to coming to class.

  • Curriculum Sequence:

    • Chapter 14 (Bonds) is covered prior to Chapter 12 (Investments).
    • Rationale: Bond fundamentals in Chapter 14 provide a clearer baseline conceptual framework for understanding financial debt instruments before analyzing investments in Chapter 12.

Introduction to Bond Financing & Debt Capital

  • Fundamental Definition of a Bond:

    • A bond is a formal debt instrument (debt issue) issued by a corporation or governmental entity to raise capital.
    • Equity distinction: A bond does not grant ownership equity or stock in a company. It represents borrowed funds.
    • Mechanics: The issuer borrows cash upfront from investors and promises to:
    1. Make periodic cash interest payments (typically semiannually).
    2. Return the face value (principal) to the bondholder on a specified future date (maturity date).

  • Corporate Context & Denominations:

    • Method of corporate financing common to virtually all non-small ("mom and pop") businesses.
    • Standard Denomination: Bonds are typically issued in face value increments of text$1,000\\text{\$}1{,}000.
    • If primary bond issuances sell out, investors must acquire them through secondary financial markets (via brokers or commercial banks).

  • Evolution of Bond Issuance Technology:

    • Historical Form (Bearer / Coupon Bonds):
    • Physical, highly engraved paper certificates.
    • Featured paper coupons printed at the bottom; holders literally cut out coupons and presented them at banks to collect periodic cash interest payments.
    • Bearer Bonds: Possession equaled ownership; if stolen or lost, the physical certificate functioned as negotiable currency.
    • Modern Form (Registered / Electronic Bonds):
    • Fully digitized and registered directly with the issuing entity.
    • Interest payments and principal repayments are transferred electronically directly to the registered owner's account, eliminating physical security risks.

Key Terminology & Types of Bonds

  • Essential Bond Terms:
    • Face Value (Par Value / Principal Amount):
    • The dollar amount printed on the bond document/contract (typically text$1,000\\text{\$}1{,}000 per bond unit) that the issuer agrees to pay back at maturity.
    • Maturity Date:
    • The specific date on which the issuer must pay the final face value amount to the bondholder.
    • Bond Indenture:
    • The formal legal contract executed between the issuing corporation and the bondholders outlining all obligations, covenants, interest rates, and payment schedules.
    • Registered Bond:
    • A bond issue tracked electronically by the issuer, ensuring payments are remitted directly to the legal owner of record.
    • Zero-Interest (Zero-Coupon) Bonds:
    • Bonds that do not pay periodic cash interest over their term.
    • Sold at a deep upfront discount relative to face value; investor returns are generated entirely by the difference between the discounted purchase price and the full face value received at maturity.
    • Convertible Bonds:
    • Debt securities offering bondholders the contractual right to exchange/convert their bonds into equity shares (preferred stock or common stock) of the issuing company under specified terms.
    • Callable Bonds:
    • Bonds containing a covenant allowing the issuer/borrower to call back (redeem/pay off) the bond prior to its scheduled maturity date.
    • Issuer Usage: Callable bonds are redeemed when prevailing market interest rates drop significantly, enabling corporations to refinance high-interest debt at lower borrowing rates.

The Three Key Accounting Steps for Bonds

  1. Record the Bond Issuance:

    • Book cash received and the debt obligation at issuance date at present value.
    • Determine and record any associated Discount on Bonds Payable or Premium on Bonds Payable.

  2. Record Periodic Interest Expense:

    • Calculate and book periodic interest expense across the life of the bond.
    • Under US GAAP, corporations are required to use the Effective Interest Rate Method to amortize discounts/premiums and determine interest expense (rather than straight-line amortization).

  3. Record Bond Retirement at Maturity:

    • Extinguish the debt payable obligation by paying back the face value to bondholders upon maturity.
    • Operational Note: Financial planning must ensure sufficient liquid funds exist at maturity to satisfy the principal repayment without forcing emergency debt refinancing.

Mechanics of Bond Pricing & Present Value Valuation

  • Interest Rates & Market Dynamics:

    • Stated Interest Rate (Coupon / Stated Rate):
    • The interest rate explicitly printed on the bond contract used to determine the periodic cash payment:
      Periodic Cash Interest=Face Value×(Stated Annual RatePeriods per Year)\text{Periodic Cash Interest} = \text{Face Value} \times \left(\frac{\text{Stated Annual Rate}}{\text{Periods per Year}}\right)
    • Market Interest Rate (Yield / Effective Rate):
    • The actual interest rate demanded by investors in the open market for debt securities with equivalent risk profiles, maturities, and industry parameters at the exact time of issuance.
    • Fluctuates constantly due to economic conditions, market shifts, regulatory developments, and company credit risk changes.

  • Relationship Between Stated Rate, Market Rate, and Bond Price:

    • Issued at Par (Face Value):
      Stated Rate=Market Rate  ⟹  Bond Price=Face Value\text{Stated Rate} = \text{Market Rate} \implies \text{Bond Price} = \text{Face Value}
    • Issued at a Premium:
      Stated Rate>Market Rate  ⟹  Bond Price>Face Value\text{Stated Rate} > \text{Market Rate} \implies \text{Bond Price} > \text{Face Value}
    • Reason: The bond pays higher periodic cash interest than current market offerings; investors pay extra upfront for the higher yield.
    • Issued at a Discount:
      Stated Rate<Market Rate  ⟹  Bond Price<Face Value\text{Stated Rate} < \text{Market Rate} \implies \text{Bond Price} < \text{Face Value}
    • Reason: The bond pays lower periodic interest than current market alternatives; issuers must lower the upfront purchase price to entice investors.

  • Present Value Valuation Formula:

    • A bond's total selling price is computed as the sum of two present value components discounted at the Market Interest Rate (ii):
    1. Present Value of the Principal (Lump Sum):
      PVprincipal=Face Value×PVsingle(i,n)PV_{\text{principal}} = \text{Face Value} \times PV_{\text{single}}(i, n)
    2. Present Value of Interest Payments (Ordinary Annuity):
      PVinterest=Periodic Cash Interest Payment×PVannuity(i,n)PV_{\text{interest}} = \text{Periodic Cash Interest Payment} \times PV_{\text{annuity}}(i, n)
    3. Total Bond Price:
      Bond Price=PVprincipal+PVinterest\text{Bond Price} = PV_{\text{principal}} + PV_{\text{interest}}

  • Crucial Period & Interest Rate Adjustments:

    • For semiannual interest payments (paying twice a year):
    • Total compounding periods (nn):
      n=Term in Years×2n = \text{Term in Years} \times 2
    • Market interest rate per period (ii):
      i=Annual Market Rate2i = \frac{\text{Annual Market Rate}}{2}
    • Stated interest rate per period:
      Stated Rate per Period=Stated Annual Rate2\text{Stated Rate per Period} = \frac{\text{Stated Annual Rate}}{2}
    • Rule: Present value table lookup factors must ALWAYS be evaluated using the Market Rate per period (ii) over Total Periods (nn).

Accounting Entries for Bond Issuance: Par, Discount, Premium, and Zero-Coupon

1. Issuance at Par Value (Ajax Example)
  • Parameters:
    • Face Value = $500,000\text{\$}500{,}000
    • Term = 55 years (n=10n = 10 semiannual periods)
    • Stated Rate = 4 %4\,\% per annum (2 %2\,\% semiannual)
    • Market Rate = 4 %4\,\% per annum (2 %2\,\% semiannual)
  • Periodic Cash Payment:
      \text{\}500{,}000 \times 2\,\% = \text{\}10{,}000
  • Journal Entry:
    • Debit: Cash $500,000\text{\$}500{,}000
    • Credit: Bonds Payable $500,000\text{\$}500{,}000
2. Issuance at a Discount (Demo Problem 14.1 - Case A)
  • Parameters:
    • Face Value = $1,300,000\text{\$}1{,}300{,}000
    • Term = 55 years (2015 to 2020; n=10n = 10 semiannual periods)
    • Stated Rate = 4 %4\,\% per annum (2 %2\,\% semiannual payment rate)
    • Market Yield = 6 %6\,\% per annum (i=3 %i = 3\,\% semiannual market rate)
  • Calculations:
    • Periodic Cash Interest = \text{\}1{,}300{,}000 \times 2\,\% = \text{\}26{,}000
    • Principal Factor (PVsingle,3 %,10PV_{\text{single}}, 3\,\%, 10 periods) = 0.744090.74409
    • PV_{\text{principal}} = \text{\}1{,}300{,}000 \times 0.74409 = \text{\$}967{,}317.07\n - Interest Annuity Factor (PV_{\text{annuity}}, 3\,\%, 10periods)=periods) =8.53020\n - PV_{\text{interest}} = \text{\}26{,}000 \times 8.53020 = \text{\$}51{,}592.95
    • Total Selling Price = \text{\}967{,}317.07 + \text{\}51{,}592.95 = \text{\$}1{,}018{,}910.02
    • Discount Amount = \text{\}1{,}300{,}000 - \text{\}1{,}018{,}910.02 = \text{\$}281{,}089.98
  • Journal Entry:
    • Debit: Cash $1,018,910.02\text{\$}1{,}018{,}910.02
    • Debit: Discount on Bonds Payable $281,089.98\text{\$}281{,}089.98
    • Credit: Bonds Payable $1,300,000.00\text{\$}1{,}300{,}000.00
3. Issuance at a Premium (Demo Problem 14.1 - Case B)
  • Parameters:
    • Face Value = $2,300,000\text{\$}2{,}300{,}000
    • Term = 88 years (n=16n = 16 semiannual periods)
    • Stated Rate = 7 %7\,\% per annum (3.5 %3.5\,\% semiannual payment rate)
    • Market Yield = 4 %4\,\% per annum (i=2 %i = 2\,\% semiannual market rate)
  • Calculations:
    • Periodic Cash Interest = \text{\}2{,}300{,}000 \times 3.5\,\% = \text{\}80{,}500
    • Principal Factor (PVsingle,2 %,16PV_{\text{single}}, 2\,\%, 16 periods) = 0.728440.72844
    • PV_{\text{principal}} = \text{\}2{,}300{,}000 \times 0.72844 = \text{\$}1{,}675{,}412.00\n - Interest Annuity Factor (PV_{\text{annuity}}, 2\,\%, 16periods)=periods) =13.57771\n - PV_{\text{interest}} = \text{\}80{,}500 \times 13.57771 = \text{\$}1{,}093{,}005.66
    • Total Selling Price = \text{\}1{,}675{,}412.00 + \text{\}1{,}093{,}005.66 = \text{\$}2{,}768{,}417.66
    • Premium Amount = \text{\}2{,}768{,}417.66 - \text{\}2{,}300{,}000.00 = \text{\$}468{,}417.66
  • Journal Entry:
    • Debit: Cash $2,768,417.66\text{\$}2{,}768{,}417.66
    • Credit: Premium on Bonds Payable $468,417.66\text{\$}468{,}417.66
    • Credit: Bonds Payable $2,300,000.00\text{\$}2{,}300{,}000.00
4. Zero-Interest (Zero-Coupon) Bond
  • Parameters:
    • Face Value = $1,000,000\text{\$}1{,}000{,}000
    • Term = 55 years (n=5n = 5 annual periods; no semiannual multiplier applied because periodic interest is zero)
    • Stated Rate = 0 %0\,\% (Periodic Cash Interest = $0\text{\$}0
    • Market Yield = 4 %4\,\% annual
  • Calculations:
    • Principal Factor (PVsingle,4 %,5PV_{\text{single}}, 4\,\%, 5 periods) = 0.821930.82193
    • Total Selling Price = \text{\}1{,}000{,}000 \times 0.82193 = \text{\}821{,}913
    • Discount Amount = \text{\}1{,}000{,}000 - \text{\}821{,}913 = \text{\$}178{,}087
  • Journal Entry:
    • Debit: Cash $821,913\text{\$}821{,}913
    • Debit: Discount on Bonds Payable $178,087\text{\$}178{,}087
    • Credit: Bonds Payable $1,000,000\text{\$}1{,}000{,}000

Step-by-Step Problem Walkthroughs & Excel Applications

  • Excel PV Function Setup:
    • In financial software, bond price is determined using present value syntax: =PV(rate, nper, pmt, [fv], [type])
    • rate = Market Interest Rate per period (ii)
    • nper = Total Payment Periods (nn)
    • pmt = Periodic Cash Interest Payment (Face Value×Stated Rate per Period\text{Face Value} \times \text{Stated Rate per Period})
    • fv = Face Value Principal (Lump sum at maturity)
    • type = Timing of payment (00 for payment at end of period [ordinary annuity]; 11 for beginning of period)

In-Class Practice Problem 14.1 & Entry Calculations

  • Problem Parameters:

    • Principal / Face Value = $1,000,000\text{\$}1{,}000{,}000
    • Stated Annual Interest Rate = 3 %3\,\% (1.5 %1.5\,\% per semiannual period)
    • Maturity Term = 66 years (n=12n = 12 semiannual periods)
    • Market Yield per Period (ii) = 3 %3\,\% (Annualized Market Yield = 6 %6\,\%)

  • Step-by-Step Variable Identification:

    • Principal (FVFV): $1,000,000\text{\$}1{,}000{,}000
    • Periodic Cash Interest Payment (PMTPMT):
          \text{\}1{,}000{,}000 \times 1.5\,\% = \text{\}15{,}000
    • Total Periods (nn):
      6 years×2=12 periods6 \text{ years} \times 2 = 12 \text{ periods}
    • Market Rate per Period (ii): 3 %3\,\%

  • Present Value Table Factors & Calculations:

    1. Principal Valuation:
    • Table 2 (PVsinglePV_{\text{single}} at 3 %3\,\% for 1212 periods) factor = 0.701380.70138
    • PV_{\text{principal}} = \text{\}1{,}000{,}000 \times 0.70138 = \text{\$}701{,}308\n 2. **Interest Payments Valuation**:\n - Table 4 (PV_{\text{annuity}}atat3\,\%forfor12periods)factor=periods) factor =9.95400\n - PV_{\text{interest}} = \text{\}15{,}000 \times 9.95400 = \text{\$}149{,}310
    1. Total Bond Selling Price:
    • \text{Bond Selling Price} = \text{\}701{,}308 + \text{\}149{,}310 = \text{\}850{,}618$
    1. Discount Calculation:
    • \text{Discount on Bonds Payable} = \text{\}1{,}000{,}000 - \text{\}850{,}618 = \text{\}149{,}382$

  • Complete Issuance Journal Entry:

    • Debit: Cash $850,618\text{\$}850{,}618
    • Debit: Discount on Bonds Payable $149,382\text{\$}149{,}382
    • Credit: Bonds Payable $1,000,000\text{\$}1{,}000{,}000