Bonds

Discount bond — Effective Interest Method

Interest Expense = Beginning Carry Amount * Market rate (Increases each period)

Discount Amortization = Interest Expense - Cash Interest Paid

Discount Bond — Straight Line Method

= Total Discount / Number of interest periods
(Discount Amortization is the same each period)

Interest Expense = Cash interest paid + equal discount amortization

Discount Bond carrying amount relationship

Carrying Amount increases as bond is amortized

Discount Bond Amortization relationship between methods

In early periods, Effective Interest method amortizes less than the straight-line method because the beginning carrying amount is lower
In later periods, Effective Interest method amortizes more than the straight-line method because carry amount is higher

• At maturity, there’s no difference in carrying amount

Premium Bonds — Effective Interest Method

Interest Expense = Beginning Carry Amount * Market rate (Decreases each period)

Premium Amortization = Cash Interest Paid - Interest Expense

Premium Bonds — Straight Line Method

= Total Premium / Number of interest periods
(same each period)

Interest expense = Cash interest paid - equal premium amortization

Premium Bond carrying amount relationship

Carrying amount decreases as bond gets amortized

Premium Bond Amortization relationship between methods

In early periods, effective interest method amortizes less than straight line method because it has higher interest expenses

In later periods, effective interest method amortizes more than straight line method because it has lower interest expenses as carry amount reduces

• At maturity there’s no difference in carry amount

Discount Bond

Stated rate < Market Rate

Premium Bond

Stated rate > Market rate

Par Bond

Stated rate = Market rate

Bond step 1:

Identify bond issuance type: discount, premium, par

Bond step 2:

Convert annual amounts to periodic amounts (only for semi-annual bond payments)
- Periodic rate: Annual rate / 2
- Number of periods: Years to maturity * 2

Bond step 3:

Calculate cash interest payment:

• Cash interest paid = Face Value * stated rate * time fraction

• (semi-annual) Cash Interest Paid = Face Value * (stated rate/2)

Bond step 4:

Calculate bond issuance price:

Bond issue price = PV of principal payment + PV of interest payments

• PV of principal = Face Value * PV factor of $1

• PV of interest payments = Periodic cash payment * PV annuity factor

For zero-coupon bonds: Issue Price = Face Value * PV factor of $1

Bond step 5:

Calculate initial discount/premium:
- Discount = Face Value - Issue Price

- Premium = Issue Price - Face Value

Bond step 6: Effective Interest Method

Calculate Interest Expense:

= Beginning Carry Value * Market rate

If discount; amortization = Interest expense - cash interest paid

End carry value = Beginning carry value + discount amortization

If premium; amortization = Cash interest paid - Interest expense

End carry value = Beginning carry value - premium amortization

Bond step 6: Straight Line method

Calculate amortization: (same each period)

= total discount/premium / number of interest periods

Discount Interest expense = cash interest paid + discount amortized

Premium Interest expense = cash interest paid - premium amortized

Bond comparison rules: Discount bond

• Effective — Interest expense increases over time

• Effective — Discount Amortization increases over time

• Carrying value increases over time towards bond’s face value

• Straight line — carries higher value than effective interest method in early periods

• Straight line — carries lower value than effective interest method in later periods

Bond comparison rules: Premium Bond

• Effective Interest — Interest expense decreases over time

• Effective Interest — Premium Amortization increases over time

• Carry value decreases towards face value

• Straight line — carries lower value than effective interest method in early periods

• Straight line — carries higher value than effective interest method in later periods

Interest Paid vs Interest Expense

Cash Interest Paid = Face Value * stated rate

Interest Expense = Carry Value * Market rate

Under *BOTH* Methods:

Discount bonds: Interest expense > Interest paid

Premium bonds: Interest paid > interest expense

Exam Sequence Key (concise)

1. Find cash interest paid = Face Value * stated rate

2. Find interest expense = Beg. carry value * market rate

3. Find amortization by comparing interest expense and interest paid

4. Update carrying amount towards Face Value