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Three zero coupon risk-free discount bonds of one, two and three year term to maturity are...

Three zero coupon risk-free discount bonds of one, two and three year term to maturity are selling for, respectively, $950, $890 and $800. What would be the selling price today of a 10% coupon bond of 3 year maturity (maturity value $1,000)?

Solutions

Expert Solution

Pn = FV / (1 + Zn)n

Hence, zero rate for yer n = Zn = (FV / Pn)1/n - 1 = (1,000 / Pn)1/n - 1

Hence, zero rate for year 1, Z1 = (1,000 / 950) - 1 = 5.26%

Z2 = (1,000 / 890)1/2 - 1 = 6.00%

Z3 = (1,000 / 800)1/3 - 1 = 7.72%

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Annual coupon = C = 10% x 1,000 = 100

Hence, the selling price today of a 10% coupon bond of 3 year maturity = PV of all the future coupon + PV of principal repayment = C/ (1 + Z1) + C / (1 + Z2)2 + (C + P) / (1 Z3)3 = 100 / (1 + 5.26%) + 100 / (1 + 6.00%)2 + (100 + 1,000) / (1 + 7.72%)3 =  95.00 + 89.00 + 880.00 = 1,064.00

jeff jeffy answered 2 years ago
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