Reinegar Corporation is planning two new issues of 25-year bonds. Bond Par will be sold at its $1,000 par value, and it will have a 10% semiannual coupon. Bond OID will be an Original Issue Discount bond, and it will also have a 25-year maturity and a $1,000 par value, but its semiannual coupon will be only 7.00%. If both bonds are to provide investors with the same effective yield, how many of the OID bonds must Reinegar issue to raise $3,000,000? Disregard flotation costs, and round your final answer up to a whole number of bonds. |
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Price of Bond OID
Par Value = $1,000
Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]
Semi-annual Yield to Maturity (YTM) = 5% [10% x ½]
Maturity Years = 50 Years [25 Years x 2]
The Price of the Bond = Present Value of the Coupon payments + Present Value of Face Value
= $35[PVIFA 5%, 50 Years] + $1,000[PVIF 5%, 50 Years]
= [$35 x 18.25593] + [$1,000 x 0.08720]
= $638.96 + $87.20
= $726.16
The Price of Bond OID = $726.16 per Bond
OID bonds must Reinegar issue to raise $3,000,000
Therefore, the OID bonds must Reinegar issue to raise $3,000,000 = Amount need to be raised / Price of Bond OID
= $30,00,000 / $726.16 per Bond
= 4,132 Bonds
“Hence, the OID bonds must Reinegar issue to raise $3,000,000 would be (c). 4,132 Bonds”
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