Question

Bond Analysis

Issue data Purchase date Maturity date Par value Coupon rate Frequency Market price

October 12,2002 September 26,2012 November 24,2019 2279 1.5100% annually 94%

All values must be rounded up to 2 decimals

Characteristics Value

1 Yield to maturity <>

2 Macaulay duration <>

3 Modified duration <>

4 If the yield-to-maturity increases by 100 bps,the bond

price will be changed by (calculate it precisely) <>

5 If the yield-to- maturity increases by 10 bps, the bond

price will be changed by (calculate it precisely) <>

Bond price vs time

<>

Answer 1

Coupon rate = 5% = 0.05

YTM of Bond 1 = 4.5% = 0.045

semi- annual coupon value, C = (coupon rate/2)* par value = (0.05/2)*10,000= $ 250

par value of Bond , M = $10,000

price of bond = present value of coupons + present value of maturity amount

maturity of bond = m = 20 years

no. of semi-annual periods , n = m*2 = 20*2 = 40

semi-annual YTM = 4.5/2 = 2.25% = 0.0225

Present value of coupons = C*PVIFA( 2.25% , 40)

PVIFA( 2.25% , 40) = present value interest rate factor of annuity

= [((1+YTM)ⁿ - 1)/((1+YTM)ⁿ*YTM)] = [((1.0225)⁴⁰ - 1)/((1.0225)⁴⁰*0.0225)] = 26.19352221

Present value(PV) of coupons = C*PVIFA( 11% , 15 years) = 250*26.19352221 = 6548.3805514

PV of maturity amount = par value/(1+YTM)ⁿ = 10,000/(1.0225)⁴⁰ = 4106.4575037

Price of bond when YTM is 4.5% = 6548.3805514 + 4106.4575037 = $10,654.8380551 or $10,654.8381 ( after rounding off )

current yield = Annual coupon/ market price = 500/10654.8380551 = 0.0469270 or4.69270% or 4.6927%( after rounding off)

period in which bond becomes callable, c = 8 years

No. of semi-annual periods , n = c*2 = 8*2 = 16

YTC = 4.5% = 0.045

semi-annual YTC = 2.25% = 0.0225

Bond 1's valuation at call = price of bond - call premium = 10,654.8380551 - 200 = 10,454.8380551 or 10,654.8381 ( affter rounding off)