The Main TVM Problems Related To Healthcare Are Present

The Main Tvm Problems Relating To Healthcare Are A Present Value Of

The main TVM problems relating to healthcare are: a) present value of a lump sum b) present value of an annuity stream c) future value of a lump sum d) future value of an annuity stream. Provide an example of each of these TVM problems.

1) The Smith family is interested in buying a home. The family is applying for a $200,000 30-year mortgage. Under the terms of the mortgage, they will receive $200,000 today to help purchase their home. The loan will be fully amortized over the next 30 years. Current mortgage rates are 7.5%. Interest is compounded monthly and all payments are due at the end of the month. What is the monthly mortgage payment?

2) Miriam has saved $5,000 and intends to use his savings as a down payment on a new car. After careful examination of his income and expenses, he has concluded that the most he can afford to spend every month on his car payment is $425. The car loan that he uses to buy the car will have an APR of 10%. What is the price of the most expensive car that Miriam can afford if he finances his new car for 48 months?

Paper For Above instruction

Introduction

The time value of money (TVM) is a fundamental financial principle that recognizes the value of money changes over time due to potential earning capacity. It is especially relevant in healthcare financing, where large sums are involved and decisions about investments, loans, and savings must consider the temporal aspect of cash flows. In this paper, we explore four main TVM problems—present value of a lump sum, present value of an annuity stream, future value of a lump sum, and future value of an annuity stream—through practical healthcare-related examples, culminating in detailed calculations relating to mortgage and car loans. These examples illustrate how understanding TVM principles can aid individuals and healthcare institutions in making informed financial decisions.

1. Present Value of a Lump Sum in Healthcare

The present value of a lump sum involves discounting a future sum of money back to its value today. This is particularly relevant in healthcare when estimating the current worth of future medical settlements or insurance payouts. An example pertinent to healthcare could involve discounting future settlement amounts to determine their current value.

For instance, consider a healthcare insurer expecting a future payout of $100,000 in 10 years to settle a claim. With a discount rate of 5%, the present value (PV) of this future lump sum can be calculated as:

PV = FV / (1 + r)^n = 100,000 / (1 + 0.05)^10 ≈ $61,391.58.

This calculation helps insurers and healthcare providers assess the current worth of future liabilities or claims.

2. Present Value of an Annuity Stream

Present value of an annuity involves discounting a series of equal payments made at regular intervals to their current worth. In healthcare, this can relate to valuing recurring payments, such as periodic insurance premiums or structured settlement payments.

For example, suppose a healthcare provider expects to receive $10,000 annually for 5 years from a patient insurance plan, with a discount rate of 4%. The present value is calculated as:

PV = PMT × [(1 - (1 + r)^-n) / r] = 10,000 × [(1 - (1 + 0.04)^-5) / 0.04] ≈ $43,597.66.

Recognizing the present value of future cash flows assists healthcare organizations in financial planning and budgeting.

3. Future Value of a Lump Sum in Healthcare

The future value of a lump sum is used to determine how much a current amount will grow over time at a specified interest rate. This is relevant in healthcare savings plans or investment accounts.

For example, a healthcare organization invests $50,000 at an annual interest rate of 6% compounded annually for 15 years. The future value (FV) would be:

FV = PV × (1 + r)^n = 50,000 × (1 + 0.06)^15 ≈ $119,924.80.

This illustrates the growth of healthcare reserve funds or endowment investments over time.

4. Future Value of an Annuity Stream

The future value of an annuity stream considers the accumulated value of a series of periodic payments made over time, compounded at a certain rate.

Suppose a healthcare foundation makes annual donations of $5,000 for 10 years, earning an interest rate of 5% compounded annually. The future value is:

FV = PMT × [( (1 + r)^n - 1) / r] = 5,000 × [((1 + 0.05)^10 - 1) / 0.05] ≈ $63, 820.09.

This calculation is instrumental in planning long-term fundraising or endowment growth.

Practical Application 1: Mortgage Payment Calculation

The first example involves calculating a monthly mortgage payment, which directly applies to healthcare professionals who may seek home financing. The Smith family's mortgage of $200,000 over 30 years at 7.5% interest, compounded monthly, requires determining their monthly payments.

Using the standard mortgage amortization formula:

M = P × r(1 + r)^n / [(1 + r)^n – 1],

where P = principal ($200,000), r = monthly interest rate (0.075 / 12 ≈ 0.00625), and n = total payments (30 × 12 = 360).

Substituting these values:

M = 200,000 × 0.00625(1 + 0.00625)^360 / ((1 + 0.00625)^360 – 1)

Calculations yield a monthly payment of approximately $1,392.33. This example demonstrates how TVM principles are essential for healthcare professionals planning personal finances or funding healthcare facilities.

Practical Application 2: Car Loan Affordability

The second example relates to calculating the maximum price Miriam can afford based on her savings, income, and loan conditions. Miriam's $5,000 savings serve as a down payment, and she can afford $425 monthly payments on a car loan with an APR of 10%, funded over 48 months.

The loan amount M can be derived using the present value of an annuity formula:

M = P × r(1 + r)^n / [(1 + r)^n – 1],

where P is the loan amount, r = 0.10 / 12 ≈ 0.008333, n = 48.

Rearranged to find the maximum loan amount:

Loan = Payment × [(1 + r)^n – 1] / [r(1 + r)^n].

Plugging in the numbers:

Loan = 425 × [(1 + 0.008333)^48 – 1] / [0.008333 × (1 + 0.008333)^48],

which calculates to approximately $17,092.

Adding Miriam's down payment:

Maximum car price = loan amount + down payment = $17,092 + $5,000 ≈ $22,092.

This demonstrates how TVM calculations assist individuals in budgeting for healthcare-related purchases like vehicles, which can impact their mobility for healthcare needs.

Conclusion

Understanding the principles of time value of money is crucial in healthcare finance for making informed decisions about investments, insurance, and personal loans. Through examples such as mortgage and car loan calculations, it becomes evident how TVM concepts underpin practical financial planning. They enable consumers and healthcare institutions to evaluate the worth of future cash flows accurately, optimize investment strategies, and manage financial risks effectively.

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