Bond Amortization Schedule and Valuation Analysis

Bond Parameters and Key Valuation Variables

• Face Value / Par Value ($F$): $100000.00$
• Annual Coupon Rate ($r$): $8\%$ per annum ($0.08$)
• Coupon Payment Frequency: Semiannually ($2$ payments per year)
• Semiannual Coupon Payment ($C$):   $C = 100000.00 \times \frac{0.08}{2} = 4000.00$
• Term to Maturity ($n$): $4$ years
• Total Number of Payment Periods ($N$):   $N = 4 \times 2 = 8$
• Investor's Nominal Yield Rate ($i^{(2)}$): $6.5\%$ convertible semiannually ($0.065$)
• Effective Semiannual Yield Rate ($j$):   $j = \frac{0.065}{2} = 0.0325\text{ or }3.25\%$
• Initial Book Value ($B(0)$): $105460.97$

Amortization Schedule Formulas

• Periodic Interest Earned ($I(t)$): Represents the interest earned on the remaining book value at the semiannual yield rate $j$:   $I(t) = B(t-1) \times j$
• Principal Reduction / Amortization ($P(t)$): Represents the portion of the coupon payment applied toward writing down the bond premium:   $P(t) = C - I(t)$
• Book Value at Period $t$ ($B(t)$): Represents the remaining unamortized balance after period $t$:   $B(t) = B(t-1) - P(t)$

Step-by-Step Amortization Calculations

• Period $t = 0$:

  • Coupon Payment: $0.00$
  • Interest $I(0)$: $0.00$
  • Principal Repayment $P(0)$: $0.00$
  • Book Value $B(0)$: $105460.97$

• Period $t = 1$:

  • Coupon Payment: $4000.00$
  • Interest $I(1) = 105460.97 \times 0.0325 = 3427.48$
  • Principal Repayment $P(1) = 4000.00 - 3427.48 = 572.52$
  • Book Value $B(1) = 105460.97 - 572.52 = 104888.45$

• Period $t = 2$:

  • Coupon Payment: $4000.00$
  • Interest $I(2) = 104888.45 \times 0.0325 = 3408.87$
  • Principal Repayment $P(2) = 4000.00 - 3408.87 = 591.13$
  • Book Value $B(2) = 104888.45 - 591.13 = 104297.32$

• Period $t = 3$:

  • Coupon Payment: $4000.00$
  • Interest $I(3) = 104297.32 \times 0.0325 = 3389.66$
  • Principal Repayment $P(3) = 4000.00 - 3389.66 = 610.34$
  • Book Value $B(3) = 104297.32 - 610.34 = 103686.98$

• Period $t = 4$:

  • Coupon Payment: $4000.00$
  • Interest $I(4) = 103686.98 \times 0.0325 = 3369.83$
  • Principal Repayment $P(4) = 4000.00 - 3369.83 = 630.17$
  • Book Value $B(4) = 103686.98 - 630.17 = 103056.81$

• Period $t = 5$:

  • Coupon Payment: $4000.00$
  • Interest $I(5) = 103056.81 \times 0.0325 = 3349.35$
  • Principal Repayment $P(5) = 4000.00 - 3349.35 = 650.65$
  • Book Value $B(5) = 103056.81 - 650.65 = 102406.16$

• Period $t = 6$:

  • Coupon Payment: $4000.00$
  • Interest $I(6) = 102406.16 \times 0.0325 = 3328.20$
  • Principal Repayment $P(6) = 4000.00 - 3328.20 = 671.80$
  • Book Value $B(6) = 102406.16 - 671.80 = 101734.36$

• Period $t = 7$:

  • Coupon Payment: $4000.00$
  • Interest $I(7) = 101734.36 \times 0.0325 = 3306.37$
  • Principal Repayment $P(7) = 4000.00 - 3306.37 = 693.63$
  • Book Value $B(7) = 101734.36 - 693.63 = 101040.73$

• Period $t = 8$:

  • Coupon Payment: $4000.00$
  • Interest $I(8) = 101040.73 \times 0.0325 = 3283.82$
  • Principal Repayment $P(8) = 4000.00 - 3283.82 = 716.18$
  • Book Value $B(8) = 101040.73 - 716.18 = 100324.55$

Complete Amortization Schedule Table

• Period 0: Coupon Pmt = $0.00$, Interest $I(t)$ = $0.00$, Principal $P(t)$ = $0.00$, Book Value $B(t)$ = $105460.97$
• Period 1: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3427.48$, Principal $P(t)$ = $572.52$, Book Value $B(t)$ = $104888.45$
• Period 2: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3408.87$, Principal $P(t)$ = $591.13$, Book Value $B(t)$ = $104297.32$
• Period 3: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3389.66$, Principal $P(t)$ = $610.34$, Book Value $B(t)$ = $103686.98$
• Period 4: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3369.83$, Principal $P(t)$ = $630.17$, Book Value $B(t)$ = $103056.81$
• Period 5: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3349.35$, Principal $P(t)$ = $650.65$, Book Value $B(t)$ = $102406.16$
• Period 6: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3328.20$, Principal $P(t)$ = $671.80$, Book Value $B(t)$ = $101734.36$
• Period 7: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3306.37$, Principal $P(t)$ = $693.63$, Book Value $B(t)$ = $101040.73$
• Period 8: Coupon Pmt = $4000.00$, Interest $I(t)$ = $3283.82$, Principal $P(t)$ = $716.18$, Book Value $B(t)$ = $100324.55$