On January 1, 2018, Water World issues $25.5 million of 5% bonds, due in 15 year

Question

On January 1, 2018, Water World issues $25.5 million of 5% bonds, due in 15 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.

1-a. If the market rate is 4%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Round "Market interest rate" to 1 decimal place. Enter your answers in dollars not in millions.)

Bond Characteristics:

Face amount?

Interest payment?

Market interest rate?

Payments to maturity?

Issue price?

1-b. The bonds will issue at

2-a. If the market rate is 5%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Round "Market interest rate" to 1 decimal place. Enter your answers in dollars not in millions.)

Bond Characteristics:

Face amount?

Interest Payment?

Market Interest rate?

Payments to maturity?

Issue price?

2-b. The bonds will issue at

3-a. If the market rate is 6%, calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use appropriate factor(s) from the tables provided. Do not round interest rate factors. Round "Market interest rate" to 1 decimal place. Enter your answers in dollars not in millions.)

Bond Characteristics:

Face amount?

Interest payment?

Market interest rate?

Payments to maturity?

Issue price?

3-b. The bonds will issue at

Explanation / Answer

Answer 1.

Face Value = $25,500,000
Annual Coupon Rate = 5%
Semi-annual Coupon Rate = 2.5%
Semi-annual Coupon = 2.5%*$25,500,000 = $637,500
Semi-annual Period to maturity = 30
Semi-annual Market Rate = 2%

Issue Price = $637,500 * PVA of $1 (2%, 30) + $25,500,000 * PV of $1 (2%, 30)
Issue Price = $637,500 * 22.3965 + $25,500,000 * 0.5521
Issue Price = $28,355,548

So, Bonds are issued at premium

Answer 2.

Face Value = $25,500,000
Annual Coupon Rate = 5%
Semi-annual Coupon Rate = 2.5%
Semi-annual Coupon = 2.5%*$25,500,000 = $637,500
Semi-annual Period to maturity = 30
Semi-annual Market Rate = 2.5%

Issue Price = $637,500 * PVA of $1 (2.5%, 30) + $25,500,000 * PV of $1 (2.5%, 30)
Issue Price = $637,500 * 20.9303 + $25,500,000 * 0.4767
Issue Price = $25,500,000

So, Bonds are issued at face amount

Answer 3.

Face Value = $25,500,000
Annual Coupon Rate = 5%
Semi-annual Coupon Rate = 2.5%
Semi-annual Coupon = 2.5%*$25,500,000 = $637,500
Semi-annual Period to maturity = 30
Semi-annual Market Rate = 3%

Issue Price = $637,500 * PVA of $1 (3%, 30) + $25,500,000 * PV of $1 (3%, 30)
Issue Price = $637,500 * 19.6004 + $25,500,000 * 0.4120
Issue Price = $23,000,944

So, Bonds are issued at discount

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