Advanced Placement (AP) College

On January 1, 2021, Frontier World issues $40.0 million of 8% bonds, due in 15 years, with interest payable semiannually on June 30 and December 31 each year. The proceeds will be used to build a new ride that combines a roller coaster, a water ride, a dark tunnel, and the great smell of outdoor barbeque, all in one ride. 3-a. If the market rate is 9%, 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. Enter your answers in dollars not in millions. Round "Market interest rate" to 1 decimal place. Round your final answers to the nearest whole dollar.)

Answers

Answer 1
To calculate the issue price of the bonds, we need to use the present value formula and the appropriate factor(s) from the tables provided. Here are the steps:

1. Determine the number of periods. Since the bonds have a maturity of 15 years and interest is payable semiannually, there will be 30 periods (15 years * 2 periods per year).

2. Determine the periodic interest rate. The market rate is given as 9%. Since interest is payable semiannually, the periodic interest rate is half of the annual rate, which is 4.5% (9% / 2).

3. Calculate the present value of the interest payments. The bonds have a coupon rate of 8%, which is applied to the face value of $40.0 million. The interest payments are semiannual, so we need to divide the coupon rate by 2. Using the Present Value of an Ordinary Annuity (PVA) table, find the factor for 30 periods and a periodic interest rate of 4.5%. The factor is 13.218. Multiply this factor by the semiannual interest payment of $40.0 million * 8% / 2 = $1.6 million. The present value of the interest payments is $21.148 million ($1.6 million * 13.218).

4. Calculate the present value of the principal payment. To calculate the present value of the principal, we need to use the Present Value of a Single Amount (PV) table. Find the factor for 30 periods and a periodic interest rate of 4.5%. The factor is 0.335. Multiply this factor by the face value of $40.0 million to get the present value of the principal payment, which is $13.4 million ($40.0 million * 0.335).

5. Calculate the issue price. The issue price is the sum of the present value of the interest payments and the present value of the principal payment. Add $21.148 million and $13.4 million to get the issue price, which is $34.548 million.

Therefore, the issue price of the bonds is $34.548 million.

Related Questions

assuming stp and a stoichiometric amount of nh3 and no in an expandable container originally at 15 L, what is the final volume if the reaction goes to completion? 4NH3 (g) + 6NO (g) —> 5N2 (g) + 6H2O (g)

Answers

Answer:

16.5 L

Explanation:

We are given the following factors (they are all essential):

4 moles NH3 gas (15 L initially)6 moles NO gasContainer volume = 15 L initially at STP

Given reaction:

4NH3 (g) + 6NO (g) -> 5N2 (g) + 6H2O (g)

Using the mole ratios from the balanced chemical equation:

For every 4 moles NH3, there will be 6 moles NO and they will react to produce:

5 moles N26 moles H2O

Initial moles of gas:

4 moles NH36 moles NOTotal = 10 moles

Final moles of gas:

5 moles N26 moles H2OTotal = 11 moles

By Avogadro's law, volume is directly proportional to moles of gas at constant temperature and pressure.

Since we have 11 moles of gas after the reaction compared to 10 moles initially, the final volume will be:

(11 moles gas)(15 L initial)/(10 moles initial)

= 16.5 L

So in summary, the final volume of the gas mixture after the reaction goes to completion will be 16.5 L, assuming a constant temperature and pressure within the expandable container.

The general approach is to calculate the mole ratios and number of moles of gases before and after the reaction, then use proportionality to determine how the volume will change accordingly.

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