Question

1. Kebt Corporation's Class Semi bonds have a 12-year maturity and an 8.75% coupon paid semiannually (4.375% each 6 months), and those bonds sell at their $1,000 par value. The firm's Class Ann bonds have the same risk, maturity, nominal interest rate, and par value, but these bonds pay interest annually. Neither bond is callable. At what price should the annual payment bond sell?

   	a.	$ 937.56
   	b.	$1,036.18
   	c.	$ 986.25
   	d.	$ 961.60
   	e.	$1,010.91

Answer 1

Answer : Correct Option is (c.)986.25

Since Discount rate is not given in the question we have to assume Coupon rate as discount Rate but Compounded Semiannully

Therefore Discount Rate = [1 + (Coupon Rate / 2 )]2 - 1

Given Coupon Rate = 8.75% or 0.0875

Discount Rate = [ 1 + (0.0875 / 2 )2] - 1

= [ 1 + 0.04375)2 ] - 1

= 1.0894140625 - 1

= 0.0894140625

Now we need to calculate Present Value of Coupon Payment

= Coupon * {[1 - (1 + rate)-n ] / r } ;where n = 12

= 87.50 {[ 1 - (1 + 0.0894140625)-12 ] / 0.0894140625 }

= 87.50 * { 1 - 0.35783620244 ]  / 0.0894140625 }

= 87.50 * { 0.64216379756 / 0.0894140625 }

= $628.417171923

Present Value of Face Value = $1000 / [(1 + 0.0894140625)12]

= 1000 / 2.79457470534

= $357.836202442

Price of Annual payment bond= Present Value of Coupon Payment + Present Value of Face Value

= 628.417171923 + 357.836202442

= $986.253374365 or $986.25