If the company were to issue an annual zero-coupon bond with a maturity of 2 years and par value of $1,000, what would be the arbitrage-free price of that bond?

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1a. The one year spot rate can be calculated using the one year zero bond.

PV * (1 + S1) = FV

1 + S1 = 1000 / 900

S1 = 1.1111 - 1

S1 = 0.1111  

S1 = 11.11%

1b. PV of the 2 year bond = $950

Annual coupon = 1000 * 5% = $50

950 = 50 / (1 + S1) + (50 + 1000) / (1 + S2)^2

950 = 50 / 1.1111 + 1,050 / (1 + S2)^2

1,050/ (1 + S2)^2 = 950 - 45 = 905

(1 + S2)^2 = 1050 / 905

1 + S2 = 1.160221/2

S2 = 7.714%

1c. Price of the 2 year zero bond = 1,000 / (1 + 0.07714)^2

Price of the 2 year zero bond = 1,000 / 1.1602

Price of the 2 year zero bond = 861.9203586

Price of the 2 year zero bond = $861.92

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