5.5 Determining the Selling Price of a Bond Payable

Determining the Selling Price of a Bond Payable

Scenario

  • XYZ Corporation issues a 500,000500,000, 8% five-year bond on January 1 of year 1 to fund expansion.
  • Interest is paid semi-annually on June 30 and December 31.
  • Effective rate is 10%.

Key Details

  • Stated Rate: 8% (rate the company is willing to pay)
  • Face Value: 500,000500,000
  • Effective Rate (Market Rate): 10%
  • Bond Term: 5 years
  • Compounding: Semi-annually

Modifications

  • Number of Compounding Periods (nn):
    • 5 years * 2 = 10 periods
  • Stated Rate (Semi-annual):
    • 8% / 2 = 4%
  • Market Rate (Semi-annual):
    • 10% / 2 = 5%

Present Value Calculations

  • Face Value (Lump Sum):
    • 500,000500,000 to be received at maturity.
    • Discounted using present value of a dollar factor at 5% for 10 periods.
  • Interest Payments (Ordinary Annuity):
    • Semi-annual interest payments.
    • Compounding factor selected using the effective rate of 5% for 10 periods.

Premium or Discount

  • Comparison: Stated Rate vs. Market Rate
  • Discount: If stated rate < market rate, the bond is issued at a discount.
    • The present value of cash flows will be less than the face value.

Selling Price of the Bond

Step 1: Present Value of Face Value
  • One lump sum of 500,000500,000 to be received at maturity.
  • Compounding factor: Present Value of a Dollar.
  • Effective rate: 5% for 10 periods.
  • Factor (from table): pull off the factor from the table
  • Present Value = 500,000 * factor = $306,957
    • Bondholders are willing to pay $306,957 today in exchange for receiving $500,000 at maturity after 5 years.
    • The difference represents the 10% interest earned compounding semi-annually.
Step 2: Present Value of Interest Payments
  • Semi-annual interest payments.
  • 500,000∗4500,000 * 4% = $20,000 (interest payment every six months)
  • 10 payments of $20,000 over 5 years.
  • Ordinary Annuity Compounding Factor.
  • Factor (from table) at 5% for 10 periods.
  • Present Value = 20,000 * factor = $154,435
    • Bondholders will pay $154,435 today in exchange for 10 payments of $20,000.
Total Selling Price
  • Sum of present values of face value and interest payments.
  • Total Selling Price = $306,957 + $154,435 = $461,392
Verification
  • Selling price is less than the face value (as expected for a discount).

Recording the Issuance of the Bond

  • Cash Proceeds: Selling price of the bond (funds raised).
  • Long-Term Liability: Bond payable reported on the balance sheet.
  • Discount on Bond Payable:
    • Difference between face value and selling price.
    • 500,000 - $461,392 = $38,608
    • Contra-liability account with a debit balance.

Balance Sheet Reporting

  • Bond payable reported at face value less the discount.
  • Carrying Value = $461,392 (amount of cash flow to extinguish the debt today).

Amortization of Bond Discount

  • Effective interest method is used to amortize the bond discount or premium.
Amortization Schedule Setup
  • Track dates (June 30 and December 31 for each year).
  • Cash Payment (based on face value and stated rate).
    • 500,000∗4500,000 * 4% = $20,000
Accruing Interest
  • Formula: Carrying Value * Market Rate of Interest
  • Carrying value is synonymous with present value
  • Market rate is 5%
  • The carrying value increases over time until it reaches the face value at maturity if it was issued at a discount.
  • The carrying value decreases over time until it reaches the face value at maturity if it was issued at a premium.
Mechanics of Amortization
  • Initial Carrying Value: Present value on the issuance date.
    • $461,392
  • First Interest Payment (June 30):
    • Cash Payment: $20,000
    • Accrued Interest: $461,392 * 5% = $23,069
    • Discount Amortization: $23,069 - $20,000 = $3,069
    • New Carrying Value: $461,392 + $3,069 = $464,461
Pattern
  • Unpaid interest causes carrying value to increase over time.
  • Amortization schedule moves toward face value.
  • If the bond was issued at a premium, carrying value would decrease over time.
  • Interest Rate increases with carrying value
  • Constant rate of interest on a changing carrying value

Interest Expense on Income Statement

  • Sum of interest accrued over the year.

Impact on Financial Statements

  • Balance Sheet: Reported in present value terms.
  • Income Statement: Interest expense affects net income.