Question

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 worlds 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 6% calculate the issue price. (FV of $1, PV of $1, FVA of $1, and PVA of $1)

2-a. If the market rate is 7% calculate the issue price

3-a. If the market rate is 8% calculate the issue price

Answer 1

To calculate the issue price of the bonds, we can use the present value formula for a bond. For a market rate of 6%, the issue price is approximately $27.36 million. For a market rate of 7%, the issue price is approximately $26 million. For a market rate of 8%, the issue price is approximately $24.71 million.

Step-by-step explanation:

1-a. If the market rate is 6% calculate the issue price:

To calculate the issue price, we can use the present value formula for a bond.

Present Value (PV) = Coupon Payment / (1 + Market Rate/2)^n + Par Value / (1 + Market Rate/2)^n

Where:

• Coupon Payment is the periodic interest payment to bondholders
• Market Rate is the interest rate prevailing in the market
• n is the number of periods until the bond matures
• Par Value is the face value of the bond

For this question, the coupon payment is $3.5 million ($26 million * 7%), the market rate is 6%, n is 20 (10 years * 2 semiannual periods), and the par value is $26 million.

Plugging these values into the formula:

PV = $3.5 million / (1 + 0.06/2)^20 + $26 million / (1 + 0.06/2)^20

Using a financial calculator or spreadsheet, the issue price is approximately $27.36 million.

2-a. If the market rate is 7% calculate the issue price:

Using the same formula, but now with a market rate of 7%:

PV = $3.5 million / (1 + 0.07/2)^20 + $26 million / (1 + 0.07/2)^20

Using a financial calculator or spreadsheet, the issue price is approximately $26 million.

3-a. If the market rate is 8% calculate the issue price:

Again, using the same formula with a market rate of 8%:

PV = $3.5 million / (1 + 0.08/2)^20 + $26 million / (1 + 0.08/2)^20

Using a financial calculator or spreadsheet, the issue price is approximately $24.71 million.