Suppose a bond has a term of 17 years and has annual coupons. The bond has a fac

Question

Suppose a bond has a term of 17 years and has annual coupons. The bond has a face value of 509 and a redemption value of 514. The bond may be called at any time on or after the 11th coupon payment. The price paid for the bond is 528. The minimum yield rate is denoted by i. The coupon rate, r,  is equal to 1.1*i. Determine the minimum yield rate an investor would receive. (hint: The "unknown coupon rate" was used so that the equation you get will be solvable without needing a financial calculator. Determine when the bond will be called based on the relationship between price and redemption value. Then set up an equation using one of the bond pricing formulas and using that r = 1.1i so help you solve for i). Round your answer to four decimal places.

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Explanation / Answer

Bond Term = 17 years

Face Value =$509

Redemption Value =$514

Price =$528

Minimum Yield =i%

Coupon Rate =1.10*i %

528 = (1.10ix509) x {(1-(1+i)-17)/i} + 514/(1+i)17

Solving for i using Trial and Error Method,

For i =0.04, RHS=536

For i =0.05, RHS=540

For i =0.03, RHS=532

For i =0.02, RHS=527

For i =0.02163, RHS=528

Hence, the minimum yield rate is 2.163%

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