Question

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 4%. 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.

Select the correct answer.

6,633

6,642

6,636

6,639

6,630

Answer 1

In this case both bond are providing same effective yield.
Bond par is issued at face value this mean in this case the coupon rate is equal to yield to maturity
Thus, the effective yield of bond OID would also be 10%.
We would calculate the present value of bond OID
Price of bond	[Coupon amount*(1-((1+r)^-n)/r] + Face value*(1/(1+r^n)
Semi annual coupon amount	20	1000*(4%/2)
Semi annual yield	5.00%	10%/2
No of payments	50	25*2
Price of bond	[20*(1-((1.05)^-50)/0.05] + 1000*(1/(1.05^50)
Price of bond	20*18.25593 + 1000*0.087204
Price of bond	$452.32
Calculation of number of OID bonds to be issued
No of OID bonds to be issued	Total bond amount to be raised/Price per bond
No of OID bonds to be issued	3000000/452.32
No of OID bonds to be issued	6632.44
The above 6632.44 is rounded to 6633.
Thus, company should issue 6,633 OID bonds.