Question

1. A $5,000 bond, redeemable at 105 on Sep. 1, 2014, has semiannual coupons at j2 = 2r. It is purchased for $5,203.69 on March 1, 1993, to yield j2 = 12.5%. Find r.

2. A bond with $80 annual coupons is purchased at a discount to yield j2 = 7.5%. The write-up for the first year is $22. What was the purchase price?

Answer 1

1 1. Determine the semiannual coupon rate (t) as follows: 2 3 Face value of bond $5,000.00 4 Redeemable on Sept. 1, 2014 at 105.00% 5 Redemption price on Sept. 1, 2014 (FV) $5,250.00 6 Issue price of bond on Mar. 1, 1993 (PV) $5,203.691 7 Semiannual yield (RATE) 6.25% Number of semiannual periods between 8 Mar. 1, 1993 and Sep. 1, 2014 (NPER) 43 9 Therefore, 10 Semiannual coupon payment $325.00 11 And, 12 Semiannual coupon rate, 6.50% 13 14 2. Calculate the purchase price of the bond as follows: 15 16 Annual coupon payment $80.00 17 Write-up for the first year $22.00 18 Interest expense for the first year $102.00 19 Yield 7.50%) 20 Therefore, 21 Purchase price $1,360.00

The figures shown above have been calculated in MS Excel in the following manner:

1 1. Determine the semiannual coupon rate (c) as follows: 5000 1.05 =B3*B4 5203.69 = 12.5%/2 3 Face value of bond 4 Redeemable on Sept. 1, 2014 at 5 Redemption price on Sept. 1, 2014 (FV) 6 Issue price of bond on Mar. 1, 1993 (PV) 7 Semiannual yield (RATE) Number of semiannual periods between 8 Mar. 1, 1993 and Sep. 1, 2014 (NPER) 9 Therefore, 10 Semiannual coupon payment 11 And, 12 Semiannual coupon rate,r 43 =PMT(B7,38,-B6,B5,0) =B10/B3 13 14 2. Calculate the purchase price of the bond as follows: 15 16 Annual coupon payment 17 Write-up for the first year 22 18 Interest expense for the first year =B16+B17 19 Yield 0.075 20 Therefore, 21 Purchase price =B18/B19