Question

1. Zenith Corporation has a 5% $1,000,000 bond issue with a maturity of 12 years. Due to a sudden surge in inflation due to our national debt, the market rate of interest is currently 7%. Interest is paid semi-annually. Show work!

1. Will the bond be sold at a “premium”, “par”, or “discount”?

2. What will be the price and the proceeds?

2) Four years after the original issue (#1 above), with 8 years remaining on the original bond, all banks are taken over the federal government and the current market rate of interest for all “new” bonds will be 3% (market rate of interest) and the current owner decides to sell the bond and move to Australia which has a stronger form of capitalism.

1. Will the bond be sold at a “premium”, “par”, or “discount”?
2. What will be the price and the proceeds?

Answer 1

1]
a]	The bond prices have an inverse relationship with market
	rates of interest.
	When market rate = coupon rate, Price = Face value
	When market rate > coupon rate, Price < Face value
	When market rate < coupon rate, Price < Face value
	Here, as the market interest rate is greater than the coupon
	rate, the Price<Face value. Hence, the bond is sold at a
	discount.
b]	The price of a bond is the sum of the following:
	1] The present value of the maturity value [which
	is usually the face value], and
	2] The present value of the coupons that are to be
	received periodically till the maturity of the bond.
	The coupons constitute an annuity [half yearly]
	For discounting, the discount rate to be used is the
	market interest rate-half yearly.
	Price [for the total bond issue] = 1000000/1.035^24+1000000*2.5%*(1.035^24-1)/(0.025*1.025^24) =	$ 1,147,477.83
	Price per bond = 1000/1.035^24+1000*2.5%*(1.035^24-1)/(0.025*1.025^24) =	$             1,147.48
2]
a]	As the market interest rate is now less than the coupon rate
	the bond's price will be higher than the face value and hence
	the bond is a premium bond.
	Price [for the total bond issue] = 1000000/1.015^16+1000000*2.5%*(1.015^16-1)/(0.015*1.015^16) =	$ 1,141,312.64
	Price per bond = 1000/1.015^16+1000*2.5%*(1.015^16-1)/(0.015*1.015^16) =	$             1,141.31