AE 18: Bonds and their Valuation, Part 2
Bond Valuation
Par Value = 1,000,000
Coupon interest rate = 10%
Original maturity = 10 years
2021
100K
2022
100K
2023
100K
2024
100K
2025
100K
2026
100K
2027
100K
2028
100K
2029
100K
2030
1M
100K
PV Lump-sum of 10% for 10 years = 0.386
PV annuity of 10% for 10 years = 6.145
PV of Bond = (1,000,000 x 0.386) + (100,000 x 6.145)
PV of Bond = 386,000 + 614,500
PV of Bond = 1,000,500
Par Value = 1,000,000
Coupon interest rate = 10%
Original maturity = 10 years
Present maturity is 5 years
2021
100K
2022
100K
2023
100K
2024
100K
2025
100K
2026
100K
PV Lump-sum of 10% for 5 years = 0.621
PV annuity of 10% for 5 years = 3.791
PV of the Bond = (1,000,000 x 0.621) + (100,000 x 3.791)
PV of the Bond = 621,000 + 379,100
PV of the Bond = 1,000,100
2027
100K
2028
100K
2029
100K
2030
1M
100K
Par Value = 1,000,000
Coupon interest rate = 10%
Market interest = 12%
Original maturity = 10 years
Present maturity – 5 years
2021
100K
2022
100K
2023
100K
2024
100K
2025
100K
2026
100K
2027
100K
2028
100K
2029
100K
2030
1M
100K
PV Lump-sum of 12% for 5 years = 0.567
PV annuity of 12% for 5 years = 3.605
PV of the Bond = (0.567 x 1,000,000) + (3.605 x 100,000)
PV of the Bond = 567,000 + 360,500
PV of the Bond = 927,500
1,000,000
(927,500)
72,500
Market Interest > Coupon Interest, bonds will sell at a lower price, price difference is the discount.
Par Value = 1,000,000
Coupon interest rate = 10%
Market interest = 8%
Original maturity = 10 years
Present Maturity = 5 years
2021
100K
2022
100K
2023
100K
2024
100K
2025
100K
2026
100K
PV Lump-sum of 8% for 5 years = 0.681
PV annuity of 8% for 5 years = 3.993
PV of the Bond = (1,000,000 x 0.681) + (100,000 x 3.993)
2027
100K
2028
100K
2029
100K
2030
1M
100K
PV of the Bond = 681,000 + 399,300
PV of the Bond = 1,080,300
1,080,300
(1,000,000)
80,300
Market Interest < Coupon Interest, bonds will sell at a higher price, price difference is the premium.
Bond Risks

Price Risk
 the risk of a decline in a bond’s price due to an increase in interest rates
 higher for bonds with longer maturities
 relates to current market value of bond portfolio

Reinvestment Risk
 the risk that a decline in interest rates will lead to a decline in income from a bond
portfolio
 higher for bonds with shorter maturities
 relates to the income the bond portfolio produces
Investment Horizon – the period of time on investor plans to hold a particular investment

Default Risk
 the risk that investors will receive less than the promised return
Bankruptcy and Reorganization
When a business becomes insolvent, a company can:
o
o
100, 15, 15%
150, 15, 10%
Liquidate – sell its assets and pay its obligations
Reorganization – negotiation between the creditors and the management
 Restructuring – reduce financial charges to level projected cash flows
 reducing interest rates of debt
 lengthening the term of maturity
 convert debt to equity – diluting position of common stockholders