Physician Life Care Planning

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Present Value

The Real Cost of a Life Care Plan

Present Value: The Real Cost of a Life Care Plan is the exclusive copyrighted intellectual property of the American Academy of Physician Life Care Planners. This web presentation of this paper has made possible with express permission of the American Academy of Physician Life Care Planners.

Copyright © 2016 – The American Academy of Physician Life Care Planners
All rights reserved.

This paper is for informational purposes only and is provided “as is” and the American Academy of Physician Life Care Planners makes no warranties, express, implied or statutory, as to the information presented herein. All content is subject to change without notice.

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ABSTRACT

Life Care Plans are expert medical assessments that quantify medical damages by answering three basic questions:

  1. What is a subject’s condition?
  2. What medically-related goods and services does a subject’s condition require?
  3. How much will the goods and services cost over time?

The question, “How much will the goods and services cost over time?” presents a quantitative challenge that is outside the professional bounds of most Life Care Planners, as the question requires the expert to consider the financial impact of the time value of money.

The time value of money is the foundational concept of financial theory. It simply maintains that money today is worth more than money tomorrow. This is true because money can earn interest. Time value of money calculations seek to equate the present value of money (what it’s worth today) to the future value of money (what it’s worth tomorrow), and vice versa.

To accurately determine how much money will be required today to pay for medical requirements which will be consumed in the future, the time value of money must be accounted for, i.e. future medical requirements must ultimately be quantified in present value.

Failure to quantify future medical requirements in present value commonly exposes ill/injured individuals to significant financial shortfalls, as any valuation which does not account for the time value of money risks undervaluing the amount of money required to cover future medially-related expenses.

Present value assessments are analyses performed by qualified experts (professional economists or credentialed financial professionals) that accurately quantify time value.

This paper presents a basic framework for the purpose of enabling readers to easily understand basic time value of money concepts, and how they are applied to Life Care Plans to quantify “the real number”, i.e. the present value of medically-related compensatory damages.

INTRODUCTION

Life Care Plans are expert assessments that quantify the cost of providing ill/injured individuals with medically-related goods and services throughout specified durations of care.

Despite their value as case management tools and their growing use in elder care and discharge planning, the vast majority of Life Care Plans are commissioned as expert medical valuations which are used as documentary evidence in personal injury torts to quantify/substantiate medically-related compensatory damages.

The Basic Medical Damages Question
How much money needs to be received today to pay for medically-related expenditures that will occur in the future?

Most Life Care Planners are not qualified to perform present value financial valuations; so most Life Care Planners calculate “total cost” using basic arithmetic and “today’s prices”, i.e. the market prices of medically-related goods and services prevailing at the time of a Life Care Plan’s production.

Nonetheless, most Life Care Plans’ cost analyses contain valuable information, e.g. baseline unit costs, specification of the timing of anticipated cash outflows, etc. What they fail to account for, however, is the time value of money, which can have a significant impact on “total cost”.

Valuations of medical damages which do not account for the time value of money can expose their subjects to significant financial shortfalls, as Life Care Plans which are not quantified in present value can significantly undervalue the true cost of providing medical care over time.

Present Value Assessments of Life Care Plans performed by qualified experts accurately account for the time value of money. To accomplish this, Present Value Assessments account for two primary factors:

  1. The impact of inflation on the prices of medically-related goods and services, and
  2. The amount of interest a person can earn between now, and the times at which their future medically-related expenditures are forecast to occur.

The time value of money is a commonly misunderstood concept. When properly presented, however, the time value of money—and the present value method of financial valuation—are easy to understand. Enabling readers to understand these concepts, as they relate to the medically-related damages specified in Life Care Plans, is the primary purpose of this paper.

LIFE CARE PLANNING & STATIC COST ANALYSIS

A primary purpose of most Life Care Plans is to determine how much it will cost to provide an ill/injured individual with medically-related goods and services over time. To answer this question, a Life Care Plan’s cost analysis accounts for four primary variables:

  1. Requirements in a Life Care Plan are those goods and services the Life Care Planner believes, based upon their education, training and professional experience, are necessary to accomplish the Clinical Objectives of Life Care Planning , which are to:
    1. Diminish or eliminate the subject’s physical and psychological pain and suffering
    2. Reach and maintain the highest level of function given a subject’s unique circumstance.
    3. Prevent complications to which a subject’s unique diagnostic conditions predispose them.
    4. Afford the subject the best possible quality of life in light of their condition.

    The requirements in Life Care Plans customarily fall within the following categories:

    • Physician Services
    • Routine Diagnostics
    • Medications
    • Laboratory Studies
    • Rehabilitation Services
    • Equipment & Supplies
    • Nursing & Attendant Care
    • Environmental Modifications & Essential Services
    • Acute Care Services
  2. Unit Costs reflect the prices of individual medically-related goods and services. Unit costs are customarily priced in “today dollars”, i.e. the market prices of goods and services prevailing at the time of a Life Care Plan’s production. Because most Life Care Planners are not economists or credentialed financial professionals, the unit costs in most Life Care Plans remain static (constant) throughout the cost analysis, i.e. unit costs in most Life Care Plans do not consider the effects of inflation on prices over time.
  3. Frequencies specify how often specific goods and services will be required. Frequencies are commonly expressed in annual conventions, i.e. “number of times, per number of years”, e.g. wheel chair replacement, once every 5 years; physical therapy, 52 times per year, etc.
  4. Durations & Start Dates define how long specific requirements will be required, and in what periods the consumption of such re requirements will begin, e.g. for X years, beginning in year Y.

Together, these four variables are all that’s needed to perform a static cost analysis:

  1. Requirements: What [am I accounting for]?
  2. Unit Costs: How much [does what I’m accounting for cost today]?
  3. Frequencies: How often [will I need what I’m accounting for]?
  4. Durations & Start Dates: For how long; beginning when?

Exhibit 1: Life Care Planning
Static Cost Analysis Variables

What?
How Much $?
Requirements
Unit Cost
How Often?
For How Long?
Frequency
Duration & Start Date

If prices were static, and if earning interest was not possible, the preceding four variables would be all that’s needed to accurately determine the cost of consuming goods and services over time.

In a real world economy, however, prices are subject to inflation, and are therefore, not static. Further, earning interest on money is possible in a variety of ways. In reality, the question that needs to be answered is not “how much will the goods and services cost over time”, but rather, “how much money will I need to receive today to pay for goods and services that I will consume in the future?”

To answer this question, we must account for the effects of inflation on the future prices of goods and services, as well as the earning potential of money over time, i.e. we must account for the time value of money, and the best way to do that is to perform a present value method financial valuation.

Exhibit 2: Static Cost Analysis of
Requirement X

What?
How Much $?
"Requirement X"
$100
How Often?
For How Long?
1 unit, every 2 years
10 years, begining today

Using this example, a static cost analysis of Mrs. Doe’s care requirements would look like this:

Exhibit 3

Total Cost = 100 + 100 + 100 + 100 + 100 = 500
Year Today 1 2 3 4 5 6 7 8 9 Total
Requirement X $100.00 - $100.00 - $100.00 - $100.00 - $100.00 - $500.00

What the preceding static cost analysis does not account for, and what must be accounted for in order to quantify the time value of money, are two important economic factors:

  1. Inflation: the general rise in the prices of goods and services over time.
  2. Interest: the amount of money Mrs. Doe can earn between now and the times when her anticipated future medical expenditures are forecast to occur.

THE PRESENT VALUE METHOD OF FINANCIAL VALUATION

The present value method of financial valuation is a simple two-step process:

  • Step 1: Calculates the future values (FV) of all anticipated expenditures.
  • Step 2: Calculates the present value (PV) of the future values calculated in Step 1.

The present value method of financial valuation is no more complicated than “out, and back again”. That is, the present value method of financial valuation takes today’s prices and projects them out into the future to calculate future values; and it then discounts future values back again to present values.

Future Value

The concept of future value is basic. Follow this example: an item that costs $100 today has a present value, today, of $100. If annual inflation for that item is 6.00%, then the future value of that item one year from today is $106.00, and its future value 2 years from today is $112.36.

Exhibit 4 [2]

The following formula is used to calculate future value with compound interest (inflation):

FV = PV * (1+ r)n

PV is the present value (the prevailing market price to consume an item today), r is the [inflation] rate, and n is the number of periods. Using our example, our future value calculation looks like this:

Exhibit 5

FV (Year 1) = 100 * (1+.06)1 = $106.00

FV (Year 2) = 100 * (1+.06)2 = $112.36, or

FV (Year 2) = 106 * (1+.06)1 = $112.36

When calculating the future value of a Life Care Plan, the goal of the economist/financial professional is to project the future value of all medical expenditures in each of the periods in which the expenditures are forecast to occur. The sum of all future values equals the total future value of all care requirements.

Let’s take a look at the same cost analysis we performed in Exhibit 3, but this time, let’s calculate future value by accounting for inflation.

  • Requirement = Requirement X
  • Unit Cost = $100
  • Frequency = 1 unit, every 2 years
  • Duration = 10 years, beginning today

In order to calculate future value, an inflation rate is needed. Let’s assume inflation = 6.00%.

To calculate the future value of Requirement X in Mrs. Doe’s Life Care Plan, we use the formula for calculating future value with compound interest: FV = PV (1+ i)n.

Exhibit 6

FV = PV * (1+ r)n

FV = 100 * (1 +.06)0 + 100 * (1 +.06)2 + 100 * (1 +.06)4 + 100 * (1 +.06)6 + 100 * (1 +.06)8 =

100 + 112.36 + 126.28 + 141.85 + 159.38 = $639.87

Year Today 1 2 3 4 5 6 7 8 9 Total FV
Requirement X $100.00 - $112.36 - $126.28 - $141.85 - $159.38 - $639.87

Contrary to the static total cost ($500) calculated in Exhibit 3, the future value of providing Mrs. Doe with Requirement X, once every two years, for the next 10 years in an economic environment of 6% inflation, is $639.87, which is $139.87, or 27.8% greater than the value calculated using the static cost method.

What should be obvious from this example is, not accounting for the time value of money risks the possibility of undervaluing the true cost of future medically-related expenses.

What should also be obvious from this example is, calculating future value is easy. Now that you understand how compounding inflation is accounted for, and how it can affect future value, it’s stands to reason that inflation rate selection is very important.

Inflation

Inflation is the general rise in the prices of goods and services over time. Obviously, not all goods and services increase in price at the same rate. It is necessary, therefore, when calculating the future value of a Life Care Plan, to identify category-specific inflation rates for different types of medical requirements.

Rate selection is extremely important, as small differences in rates can result in dramatically different future values. Rate selection is one reason experts are required to perform present value analyses, as they possess the requisite education, training and professional experience to select, and in some cases, formulate rates.

Luckily for economists and financial analysts, there are economic and financial indexes that provide helpful information. Here are a few examples which are relevant to Life Care Plans:

  • The medical care indices published by the Bureau of Labor Statistics (BLS), includes historic inflation rate information for different categories of medical care
    • Hospital Services
    • Medical Care
    • Medical Care Commodities
    • Medical Care Services
    • Nonprescription Medical Equipment & Supplies
    • Nursing Home & Adult Day Care Services
    • Outpatient Hospital Services
    • Physicians’ Services
    • Prescription Drugs
    • Services by Other Medical Professionals
  • In its Consumer Price Index (CPI) Detailed Report, the Bureau of Labor Statistics also publishes indices which include data for changes in the prices of all items, (e.g. transportation, other consumer goods, etc.), as well as the Employment Cost Index (ECI) which includes data on wages and salaries for occupations.

Economists and financial analysis often perform regression analysis on historic inflation rates to forecast future rates. In some cases, rate forecasts are available from official/referenceable sources, e.g. the Congressional Budget Office’s forecast of the CPI and the ECI.

Present Value

Discounting futures value to present values is the second step in a present value method valuation.

The future value of “Requirement X”, for example, is not the same as the amount of money you would need to receive today to pay for it in the future. The reason for this is simple: any amount of money you receive today can earn interest between now and then.

In the previous example of Mrs. Doe’s Life Care Plan, any monetary award she receives to cover the cost of her future medical expenditures would most likely be received in the present year, which means Mrs. Doe’s principle can be invested, and it can earn interest until her future medical expenditures occur.

The present value of Mrs. Doe’s future medical expenditures is the amount of money it would take, if it were invested today earning compound interest, to equal the future values of her anticipated expenditures at the points in time when they are forecast to occur.

In order to calculate present value, or “discounted present value”, it is necessary to select a “discount rate”. For the purpose of calculating present value, the rate at which Mr. Doe’s principle can be invested is the discount rate, and it is the rate which makes the present value of her future expenditures and the future value of those expenditures equal, even though they are measured at different points in time.

Let’s calculate the present values of the future values calculated in Exhibit 6:

Year Today 1 2 3 4 5 6 7 8 9 Total FV
Requirement X $100.00 - $112.36 - $126.28 - $141.85 - $159.38 - $639.87

The following formula is used to calculate present value with compound interest:

Exhibit 7 [3]

PV = FV / (1+r)t

In this formula, FV is a future value, r is the [discount] rate, and t is the number of periods. Let’s assume Mrs. Doe is able to earn 4.00% interest on her money, i.e. let’s use 4.00% as the discount rate to calculate present values.

Using our previous example, our present value calculation looks like this:

Exhibit 8

PV = FV / (1+r)t

PV = 100 / (1+.04)0 + 112.36 / (1+.04)2 + 126.28 / (1+.04)4 + 141.85 / (1+.04)6 + 159.38 / (1+.04)8 =
100 + 103.88 + 107.94 + 112.11 + 116.46 = $540.39

As the calculation reveals, the present value of Requirement X in Mrs. Doe’s Life Care Plan = $540.39.

This result says if Mrs. Doe were to receive $540.39 today, and if she were able to earn 4.00% interest on her money, she would be able to pay for $639.87 in total future value expenditures on the dates on which the expenditures are forecast to occur.

So, why is this important? It’s important because the static cost analysis in Mrs. Doe’s Life Care Plan quantified the total cost of Requirement X at $500, when in actuality, the discounted present value, i.e. the “real cost” of Requirement X, is $540.39. In this example, not accounting for the time value of money would have undervalued Mrs. Doe’s care requirements by 8.1%. Now assume that Mrs. Doe’s entire Life Care Plan = $2MM on a static cost basis. An equivalent failure to quantify the time value of money would have exposed Mrs. Doe to >$160K ($2MM *.081) of unaccounted financial liability.

Discount Rates

Discount rates, just like inflation rates, can have a strong effect on present value. When performing a present value assessment, appropriate discount rate selection is important.

When selecting discount rates, two primary factors must be considered:

  1. Risk: Rate is synonymous with return; return is a function of risk; and risk and return increase in relative proportion to one an other. An appropriate rate selection accurately reflects the risk profile/investment objectives of the person/entity for which the present value assessment is being performed.

    When selecting discount rates for a present value assessment of a Life Care Plan, rates should accurately reflect the risk profile/investment objectives of the plan’s subject.

    In the case of our example, Mrs. Doe’s money would be invested to pay for future medical expenses due to her chronic/catastrophic injury, and her money therefore, absolutely has to be there when she needs it. That is to say, Mrs. Doe cannot afford to place her money at risk, and her primary investment objective is capital preservation, which means it would be appropriate to select relatively risk-free (low rate) financial instruments to perform an appropriately risk-adjusted, discounted present value calculation.

  2. Tax Consequences: Taxes reduce return on investments and add complexity to investment analysis. Therefore, taxes on the interest earned on the investment of a potential award must be considered.

    Common securities used in discount present value assessments of Life Care Plans include United States Treasuries, AAA Rated Tax-Exempt Municipal Bonds, Structured Settlement Annuities, and other low-risk fixed income securities.

RATE RELATIVITY

Rate Relativity refers to the relative value of rates, i.e. inflation rates relative to discount rates, and vice versa. Rate relativity is the primary determinate of whether accounting for the time value of money will increase or decrease the value of an asset or liability.

In Mrs. Doe’s case, we performed a present value assessment of a liability, something which represents, or something which will result in future cash outflows for Mrs. Doe, i.e. her future medical expenses.

In the present value calculation we performed earlier, the discounted present value of Requirement X ($540.39) was greater than the value of Requirement X when calculated using a static costs analysis ($500). In our example, accounting for the time value of money resulted in a present value that is greater than the “total cost” in the static cost analysis. So, why is this the case? The answer can be found by examining the relative values of the rates we used to perform our calculations.

In our future value calculations, we used an inflation rate of 6.00% to calculate the future values of Requirement X; and in our present value calculations, we used a discount rate of 4.00% to discount the future values of Requirement X to present values.

Remember: the present value method of financial valuation is no more complicated than the concept of “out, and back again”. That is, the present value method of financial valuation takes today’s prices and projects them out into the future [using inflation rates] to calculate future values; and it then discounts future values back again [using discount rates] to calculate present values.

It stands to reason then, if you project “out” using a rate which is relatively higher than the rate at which you discount “back again”, then accounting for the time value of money is likely to increase the value of an asset of liability. Similarly, if you project “out” using a rate which is relatively lower than the rate at which you discount “back again”, then accounting for the time value of money is likely to decrease the value of an asset of liability.

Rate Relativity in Real World Valuation

For purposes of enabling you to understand basic time value of money concepts, the examples we’ve used throughout this paper have been extremely simple. Rate relativity in real-world present value assessments of Life Care Plans however, can be very complex. Complexity is affected by two primary factors: 1) rate variation between care categories, and 2) the timing of future care requirements.

Let’s explore another example using the following categorical inflation rates:

Exhibit 9

  • Physician Services 3.10%
  • Services by Other Medical Professionals 2.70%
  • Hospital Services 6.80%
  • Nursing Care CBO Forecast of the ECI
CBO Forecast of the ECI
Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023
2024
CBO forecast
of ECI
1.80% 2.10% 2.90% 3.90% 4.00% 4.20% 4.00% 3.80% 3.70% 3.60% 3.60% 3.50% 3.90%

What should be apparent from an examination of the preceding rates is, the types of care requirements that are included in a Life Care Plan can have a big impact on rate relativity.

Let’s assume a Life Care Plan consists of Physician Services (3.10%) and Hospital Services (6.80%), and let’s assume we’re performing a present value assessment using a discount rate of 4.00%. As you’ll notice, the discount rate (4.00%) is higher than Physician Services, but lower than Hospital Services, so using basic “out and back again” intuition to predict whether accounting for the time value of money will increase or decrease present value becomes more difficult.

In this case, rate relativity is dependent on the relative composition of care requirements. If the care requirements were heavily weighted by Physician Services (3.10%), relative to Hospital Services (6.80%), then it stands to reason that accounting for the time value of money would likely decrease the value of Mrs. Doe’s liability, as the predominate inflation rate is less than the discount rate. Similarly, if Mrs. Doe’s care requirements are predominately weighted by Hospital Services (6.80%) relative to Physician Services (3.10%), then it stand to reason that accounting for the time value of money would likely increase the value of Mrs. Doe’s liability, as the predominate inflation rate is greater than the discount rate. Now assume 50 care requirements in 10 care categories, and it’s easy to see how quickly the complexity of rate relatively can increase.

Here’s another example: Let’s assume Mrs. Does Life Care Plan consists solely of nursing care, which uses rates from the Congressional Budget Office’s (CBO) forecast of the Employment Cost Index (ECI). What you’ll notice is rates in the CBO Forecast change over time. This adds an additional level of complexity. If we were to perform a present value analysis of the nursing care in Mrs. Does Life Care Plan using the CBO forecast of ECI [inflation], and a discount rate of 4.00%, then rate relativity is an effect of time, i.e. the periods in which Mrs. Doe’s nursing care is required. In years 2012 – 2015, the CBO’s rates are lower than the 4.00% discount rate; in 2015 they are equivalent to the discount rate, and in 2016 and beyond they are higher than the discount rate.

Let’s now examine discount rates. Exhibit A contains U.S. AAA municipal bond rates

As Exhibit 10 demonstrates discount rates, like many categorical inflation rates, do not remain static between periods, and their effect on rate relativity is dependent on time, i.e. the periods of time in which discounting occurs.

If you were to discount care requirements using the discount rates in Exhibit 9, a care requirement occurring in Year 6 would be discounted at a rate of 1.86%; a care requirement occurring in Year 17 would be discounted at a rate of 3.89%; and a care requirement occurring in Year 30 would be discounted at a rate of 4.54%. If you were discounting a care requirement in the Physician Services care category, whose future value was calculated using an inflation rate of 3.10%, then rate relativity changes dramatically depending on the period in which you’re discounting. Now assume the value Physician Services Requirements are unequally distributed between periods, and you’ll quickly realize how complex rate relativity, or “weighted rate relativity” can become.

The big takeaway in this discussion of rate relativity is, rate selection is critically important, as it significantly impacts the results of present value analyses. The selection, application and defense of inflation/discount rates must be performed by a qualified expert.

PRESENT VALUE ASSESSMENT IN TODAY’S MACROECONOMIC ENVIRONMENT

In today’s macroeconomic environment, present value assessments of future medical requirements are as, if not more important than ever.

Exhibit 10 shows Daily Treasury Rates published by the U.S. Department of Treasury, as of September 26, 2014.

Exhibit 10

As discussed earlier, rate relativity has a significant impact on whether a present value analysis is likely to increase or decrease the value of a Life Care Plan’s static cost analysis. In finance, treasury rates are referred to as “risk free” rates, and all other rates are said to reflect “market risk premium”, that is, they reflect additional levels of risk [increases in rate], relative to the risk free rate. As also discussed earlier, the appropriate investment objective for an ill/injured person’s medical damages is capital preservation, which means medical damages will be invested at, or at least very near, the risk free rate, which is close to historic low levels.

Using Bureau of Labor Statistics data, the following growth rates for medical care are calculated as the 12-year average nominal growth rate per category, for the period 2001-2011 (if available) [4].

Exhibit 11

  • Physician Services 3.10%
  • Services by Other Medical Professionals 2.70%
  • Nursing Home & Adult Day Care Services 4.20%
  • Nursing Care CBO Forecast ECI
  • Attendant Care CBO Forecast (CPI)
  • Hospital Services 6.80%
  • Medical Equipment & Supplies CBO Forecast (CPI)
  • Prescription Drugs 3.70%
  • Non-Prescription Drugs CBO Forecast (CPI)
  • Transportation 3.30%
  • Consumer Price Index CBO Forecast (CPI)

Congressional Budget Office Forecast of the ECI [5]

Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023
2024
CBO forecast
of ECI
2.10% 1.60% 1.90% 2.10% 2.10% 2.20% 2.30% 2.30% 2.30% 2.30% 2.30% 2.30% 2.80%

Congressional Budget Office Forecast of the CPI [6]

Year 2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022 2023
2024
CBO forecast
of ECI
1.80% 2.10% 2.90% 3.90% 4.00% 4.20% 4.00% 3.80% 3.70% 3.60% 3.60% 3.50% 3.90%

As Exhibit 11 demonstrates, in today’s macroeconomic environment, a majority of the inflation rates which are commonly used to calculate the future value of medical damages are higher than the appropriately risk-adjusted, presently available rates of return used to discount future values to present values. This means, in today’s macroeconomic environment, the present value of a Life Care Plans is likely to be greater than the “total cost” exhibited in a Life Care Plan’s static cost analysis.

Valuations of medical damages which do not account for the time value of money can expose their subjects to significant financial shortfalls, as Life Care Plans which are not ultimately quantified in present value can significantly undervalue the true cost of providing medical care over time.

CHARACTERISTICS OF A HIGH QUALITY PRESENT VALUE ASSESSMENT

  • Accuracy: Present Value Assessments of Life Care Plans can require complex mathematics and can involve thousands of individual calculations. Accuracy is critical; as any calculation error not only undermines the validity of an individual value, it can jeopardize the validity and defensibility of an entire valuation exercise.
  • Appropriate/Defensible Rate Selection: Rate selection can significantly affect the present value of any asset or liability. Appropriate rate selection largely determines the defensibility of any present value method valuation, and therefore, rates must be selected by qualified economists or credentialed financial analysts.
  • Transparency: A present value assessment of a Life Care Plan should be characterized by complete transparency, i.e. it should contain sufficient information to enable its reader to perform comprehensive independent proof testing. In order to do that, Present Value Assessments must exhibit all variables used to formulate all calculations, and it must specify, in detail, the precise quantitative methods used to calculate all values.

Sources

  1. Gonzales J, Zotovas A. Life Care Planning: A Natural Domain of Physiatry. PM&R: The Journal of Injury Function and Rehabilitation. 2013; Volume 6, Issue 2, 184 – 187
  2. Ross AR, Randolph WW, Jeffery J, Corporate Finance, New York; McGraw-Hill; 2002; 71
  3. Ross AR, Randolph WW, Jeffery J, Corporate Finance, New York; McGraw-Hill; 2002; 78
  4. Bureau of Labor Statistics Consumer Price Index-All Urban Consumers Medical Care Categories, Annual Average Indexes, 2011
  5. CPI Forecast by the CBO to 2023, February 2013
  6. Data for category begins in 2009; CPI Forecast by the CBO to 2023, February 2013