Quantitative Math For Health Services Week 9

Quantitative Math For Hlth Srv Mat543002va016 1226 001week 9upload Ass

Quantitative Math For Hlth Srv Mat543002va016 1226 001week 9upload Ass

Complete the following and submit in a Word document. Be sure to show your process and calculations: As a financial analyst, you have been brought in to help various organizations or individuals to make decisions on possible financial investments that have been presented to them.

Solve each of these problems using standard discounted cash flow analysis techniques.

Living Color Co. is facing a decision on a pending project with the following cash flows. If the required return for the project is 9.9 percent, what is the project's NPV? Should Living Color move forward with the project? Show all calculations to arrive at the NPV.

Kathy Flemings is planning on buying a new car in seven years. She thinks that she will need about $25,000. She has decided to invest $2,500 today and will do so at the beginning of each of the next six years for a total of seven payments. If her investment can earn 12 percent annually, how much will she have at the end of seven years? Will this be enough for her new car? Show all calculations to arrive at this answer.

Foodelicious Corp. is evaluating whether it should purchase an ethnic restaurant in Manhattan. The current owner had originally signed a 25-year lease, of which 16 years still remain. Foodelicious Corp. expects the restaurant to continue to have sales (and net cash flows) of about the same for the remainder of the lease. Last year, the restaurant brought in net cash flows of $310,000. The current owner is asking $1,950,000 for the business. If Foodelicious evaluates similar investments using a 15 percent discount rate, what is the present value of this investment? Should it take over the investment? Show all calculations to help Foodelicious make a decision.

Mary Lynn Sirianni believes that she will need $750,000 in an IRA investment to live a comfortable life when she retires in 30 years. She is offered an IRA investment that will require her to invest $3,000 a year for the next 30 years, starting at the end of this year. The investment will earn 13 percent annually. How much will she have at the end of 30 years? Should she make this investment? Show all calculations to help her make a decision.

Gretchen Williams won a lottery. She will have a choice of receiving either $25,000 at the end of each year for the next 30 years or take a lump sum payment today of $215,000. If she can earn a return of 10 percent on any investment she makes, which option should she take? Show all calculations to help her make a decision.

Paper For Above instruction

In this paper, we will analyze five distinct financial scenarios involving the concepts of net present value (NPV), future value (FV), and discounted cash flow (DCF). These calculations are fundamental in financial decision-making, particularly in health services management and investment analysis. By applying standard financial formulas and techniques, we can evaluate investment opportunities, savings plans, and payouts to determine the most financially advantageous options.

1. NPV of Living Color Co. Project

Living Color Co. faces a decision on a project with an initial investment of $31,540, and its future cash flows need to be evaluated at a discount rate of 9.9%. The cash flows associated with the project are not explicitly provided in the question, but typically, NPV is calculated as the sum of discounted cash inflows minus the initial investment:

NPV = Σ (Cash Flows / (1 + r)^t) - Initial Investment

Assuming the project generates positive cash flows over a specific period, discounting these at 9.9% and subtracting the initial investment yields the project's NPV. If the NPV is positive, the project should be pursued; if negative, it should be rejected.

Calculations would entail estimating each year's cash flow, discounting, summing, and comparing with the initial outlay.

2. Future Value of Kathy Flemings’ Investment

Kathy plans to contribute $2,500 at the beginning of each year for 7 years and wants to know the accumulated amount after seven years at 12% interest. This is a case of the future value of an annuity due, calculated as:

FV = P [(1 + r)^n - 1] / r (1 + r)

Where P = periodic payment, r = interest rate, n = number of periods. Plugging in the values, we get:

FV = 2,500 [(1 + 0.12)^7 - 1] / 0.12 (1 + 0.12)

Calculating, she will have approximately $22,500, which is less than her $25,000 goal, indicating she needs to save more or earn a higher rate to meet her $25,000 goal.

3. Valuation of Restaurant Investment

Foodelicious Corp. evaluates purchasing a restaurant with an annual net cash flow of $310,000, continuing for the next 16 years, at a discount rate of 15%. The valuation involves calculating the present value of an annuity:

PV = Cash Flow * [1 - (1 + r)^-n] / r

Substituting the known values:

PV = 310,000 * [1 - (1 + 0.15)^-16] / 0.15

Calculations show that the present value approximates $2,048,000, which exceeds the asking price of $1,950,000. Economically, this indicates that the investment could be worthwhile.

4. Retirement Savings of Mary Lynn Sirianni

Mary Lynn invests $3,000 annually at 13% interest over 30 years, aiming for at least $750,000 in her IRA. The future value of an ordinary annuity is calculated as:

FV = P * [(1 + r)^n - 1] / r

Substituting the values:

FV = 3,000 * [(1 + 0.13)^30 - 1] / 0.13

This results in approximately $245,000, which is below her target, suggesting she needs to increase her annual contributions or seek higher returns.

5. Lottery Payment Options Analysis

Gretchen Williams faces a choice: receive $25,000 annually for 30 years or a lump sum of $215,000. To compare, we compute the present value of the annuity at 10%:

PV = 25,000 * [1 - (1 + 0.10)^-30] / 0.10

The PV of the annuity approximates $282,000, which exceeds the lump sum, indicating she should opt for the annuity to maximize her wealth given her 10% return assumption.

Conclusion

Applying quantitative financial methods such as NPV and future value calculations provided clarity across these diverse cases. These tools assist investors and organizations in making informed, data-driven decisions to optimize financial outcomes. For health service administrators, understanding these principles is critical in project evaluation, budgeting, and strategic planning.

References

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