Unit 6 math Assignment

Business Investments

Unit 6 focus on business investment concepts covered in your reading of Chapter 14: “Annuities and Sinking Funds.”

For this Assignment you will write an essay to address the requirements described below. Your essay must be carefully planned and written using well-constructed sentences and paragraphs. Make sure that your grammar and spelling are correct. Points will be awarded for content as well as composition. Your essay must be a minimum of 1 page in length with standard 1 inch margins and is required to have at least one reference from a reliable source. This means that you cannot use sites like Wikipedia, Ask.com®, and Yahoo® answers and that only references from reliable sources will earn points. All resources should be cited both as an in-text citation as well as being listed on a reference page in APA format.

Assignments must be submitted as a Microsoft® Word® document and uploaded to the Dropbox for Unit 6. Include your essay directly in this document following the instructions.

All Assignments are due by Tuesday at 11:59 p.m. ET of the assigned unit.

Your Assignment is to write an essay discussing how you, as a business owner, can use annuities to achieve business goals. Financial decisions require careful planning and prioritizing, especially when large, capital-intensive purchases are involved. As you establish a process to achieve your company goals, you will need to demonstrate your math skills, consider different investment options, and describe how different investment vehicles can be used effectively to accomplish business goals.

Scenario:

As the owner of a vinyl fencing company, you are making plans for two large purchases in the next 3 to 5 years to achieve your business goals.

Purchase 1:

You plan to expand your vinyl fence company in the future, and must purchase a new warehouse facility to achieve this goal. Your insurance company is offering you two very attractive investment options, an ordinary annuity and an annuity due, both compounding quarterly and paying 8% annual interest over a 5-year period. Your 5-year budget includes saving $2,500.00 each quarter. To evaluate which option will benefit the business most, you must evaluate both annuity options by calculating the future value of each option and explain how the investment will help you to carry out your goals.

Purchase 2: After careful review of your maintenance log, you also realized that you will need to replace a fence post molding machine that sells for $45,000.00. You estimate that you will need to purchase a new machine in 3 years’ time as this machine reaches the end of its useful life. You plan to save for this purchase using a sinking fund that compounds semi-annually, and earns a 12% annual rate.

Your essay should in include the following information

1. Calculate the future value of both the ordinary annuity and the annuity due options being offered by your insurance company. Explain the differences between these two investment options. Select the best annuity option for your business and explain why that option is preferable.

Don’t forget to adjust the rate and number of periods since this is not being compounded annually.

Ordinary Annuity:

This answer should be between $60,700 and $60,900. Below is a list of the steps to go through when solving this type of problem.

The first step you will want to do is to find the Periodic Rate. This is done by taking the Annual Rate (0.04) divided by 12. It is divided by 12 due to the fact that this is a monthly deposit, and there are 12 months in a year. This turns the formula into:

The next step is to add the 1 and the 0.00333333333333333333333333333333. This turns the formula into:

Next you will want to take the 1.00333333333333333333333333333333 to the power of 48. This turns the formula into:

Next you will want to take the 1.1731986699758545110444767696162 and subtract the 1. This turns the formula into:

Next you will want to do what is inside the (). This turns the formula into:

Multiplication is the last step which results in this answer:

Annuity Due:

This uses the same formula as Ordinary Annuity. Once you have the Ordinary Annuity answer you then have to take the answer X (1 + r) to get the Annuity Due answer. This will be between $61,800 and $62,000.

2. Calculate the sinking fund payment required for the fence post molding machine.

Sinking Fund Payment:

Should be between $6,400 and $6,600.

3. Compare and contrast the shorter timeframe and higher interest rate of the sinking fund with the longer term warehouse annuity option you chose. Be sure to calculate and report how much interest you will earn from the annuity chosen for the warehouse and the amount of the sinking fund investment.

For both of these you have to find the amount invested (number of payments X payment amount). Then you can take the FV – the amount invested. One of your answers should be between $6,200 and $6,400, and the other should be between $11,800 and $12,000.

4. Develop a plan to prioritize these two purchases, and discuss the potential impact that these will have on the future of your business. For example, is expanding your business more important than saving for and paying cash for a fence post molding machine? Remember, you could borrow money to finance the fence post molding machine when it eventually breaks, but financing will cost the business in finance charges.

Remember, this Assignment is worth 40 points so it should be complete and cover each point as outlined above. Be sure to include at least one APA formatted reference.