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Directions: Be sure to make an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be four (4) pages in length; refer to the “Assignment Format” page for specific format requirements.
Respond to the items below.
Part A
Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?
Year 1 $15,000
Year 2 $20,000
Year 3 $30,000
Years 4 through 6 $0
Year 7 $150,000
Part B
County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for 25 years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and the price is the same as present value.
Part C
A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement?
Part D
Your dream of becoming rich has just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5 million jackpot. You can take annual payments of $250,000 for the next 20 years or $2,867,480 today.
a. If your investment rate over the next 20 years is 8%, which payoff will you choose?
b. If your investment rate over the next 20 years is 5%, which payoff will you choose?
c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480?
Hide Rubrics
Rubric Name: Assignment 4 Rubric
Criteria
Exemplary
Satisfactory
Unsatisfactory
Unacceptable
Criterion Score
Part A – Future Value
2
5 points
Student accurately calculates the future value of the cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year.
2
0 points
Student mostly accurately calculates the future value of the cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year.
15 points
Student partially or incorrectly calculates the future value of the cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year.
0 points
Student did not calculate the future value of the cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year.
Score of Part A – Future Value,/ 25
Part B – Guaranteed Annuity
25 points
Student accurately calculates the price that should be set on the contract.
20 points
Student mostly accurately calculates the price that should be set on the contract.
15 points
Student partially or incorrectly calculates the price that should be set on the contract.
0 points
Student does not calculate the price that should be set on the contract.
Score of Part B – Guaranteed Annuity,/ 25
Part C – Investment Rate
25 points
Student accurately calculates the investment rate the trust must earn to break even.
20 points
Student mostly accurately calculates the investment rate the trust must earn to break even.
15 points
Student partially or incorrectly calculates the investment rate the trust must earn to break even.
0 points
Student did not calculate the investment rate the trust must earn to break even.
Score of Part C – Investment Rate,/ 25
Part D – (a.) Lottery – Payoff at 8%
10 points
Student accurately calculates the payoff at 8%.
7 points
Student mostly accurately calculates the payoff at 8%.
4 points
Student partially or incorrectly calculates the payoff at 8%.
0 points
Student does not calculate the payoff at 8%.
Score of Part D – (a.) Lottery – Payoff at 8%,/ 10
Part D – (b.) Lottery – Payoff at 5%
10 points
Student accurately calculates the payoff at 5%.
7 points
Student mostly accurately calculates the payoff at 5%.
4 points
Student partially or incorrectly calculates the payoff at 5%.
0 points
Student does not calculate the payoff at 5%.
Score of Part D – (b.) Lottery – Payoff at 5%,/ 10
Part D – (c.) Lottery – Investment Rate
5 points
Student accurately calculates the investment rate.
4 points
Student mostly accurately calculates the investment rate.
2 points
Student partially or incorrectly calculates the investment rate.
0 points
Student did not calculate the investment rate.
Score of Part D – (c.) Lottery – Investment Rate,/ 5
Total
Score of Assignment 4 Rubric,/ 100
