Question

price E9-19 On January 1, 2021, Water World issues $26 million of 7% bonds, due in 10 years, with interest payable semiannually on June 30 and December 31 each year. Water World intends to use the funds to build the world's largest water avalanche and the "tornado"-a giant outdoor vortex in which riders spin in progressively smaller and faster circles until they drop through a small tunnel at the bottom. Required: 1. If the market rate is 6%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price. 2. If the market rate is 7%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price. 3. If the market rate is 8%, will the bonds issue at face amount, a discount, or a premium? Calculate the issue price.

Answer 1

Solution 1:

As market rate is lesser than stated rate, bonds will be issued at premium.

Computation of bond price
Table values are based on:
n=	20
i=	3.00%
Cash flow	Table Value	Amount	Present Value
Par (Maturity) Value	0.5537	$26,000,000.00	$14,396,200
Interest (Annuity)	14.8775	$910,000.00	$13,538,525
Price of bonds			$27,934,725

Solution 2:

As market rate is equal to stated rate, bonds will be issued at face amount.

Computation of bond price
Table values are based on:
n=	20
i=	3.50%
Cash flow	Table Value	Amount	Present Value
Par (Maturity) Value	0.5026	$26,000,000.00	$13,066,713
Interest (Annuity)	14.2124	$910,000.00	$12,933,287
Price of bonds			$26,000,000

Solution 3:

As market rate is higher than stated rate, bonds will be issued at discount.

Computation of bond price
Table values are based on:
n=	20
i=	4.00%
Cash flow	Table Value	Amount	Present Value
Par (Maturity) Value	0.4564	$26,000,000.00	$11,866,400
Interest (Annuity)	13.5903	$910,000.00	$12,367,173
Price of bonds			$24,233,573