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PS3_Solution - PS3_Solution Chapter 5(1 Coupon rate = 8 =>...

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PS3_Solution Chapter 5 (1) Coupon rate = 8% => coupon payment = 80. r d = 9% = yield to maturity. With your financial calculator, enter the following: N = 10; I = YTM = 9%; PMT = 0.08 × 1,000 = 80; FV = 1000; PV = ? PV = $935.82. Alternatively, P=80/(1+9%)+80/((1+9%))+...+80/((1+9%)^10)+1000/((1+9%)^10) = $80((1- 1/1.09 10 )/0.09) + $1,000(1/1.09 10 ) = $513.42 + $422.40 = $935.82. (2) a . V B = ) r + (1 M + ) r + (1 INT N d t d N 1 = t = PMT((1- 1/(1+r d n ))/r d ) + FV(1/(1+r d ) n ). M = $1,000. INT = 0.09($1,000) = $90. i. $829= $90((1- 1/(1+r d 4 ))/rd) + $1,000(1/(1+r d ) 4 ). The YTM can be found by trial-and-error. If the YTM was 9 percent, the bond value would be its maturity value (face value, 1000). Since the bond sells at a discount, the YTM must be greater than 9 percent. Let's try 10 percent. At YTM=10%, V B = $968.29. $968.29 > $829.00; therefore, the bond's YTM is greater than 10 percent. Try 15 percent. At 15%, V B = $828.75. Therefore, the bond's YTM is approximately 15 percent. (You could have used financial calculator to find YTM=15%: Input N = 4, PV = -829, PMT = 90, FV = 1000, I = ? I = 14.99%) ii. $1,104 = $90((1- 1/(1+r d 4 ))/rd) + $1,000(1/(1+r d ) 4 ). Input N = 4, PV = -1104, PMT = 90, FV = 1000, I = ? I = 6.00%. b . Yes. At a price of $829, the yield to maturity, 15 percent, is greater than your required rate of return of 12 percent. If your required rate of return were 12 percent, you should be
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