Law Week 4 Assignment- Healthcare Finance

Chapter04UHFM8thEdPPT.pptx

Home >Law homework help >Law Week 4 Assignment- Healthcare Finance

The financial value of any asset is based on future cash flows. The process of assigning appropriate values to cash flows that occur at different points in time is called time value analysis. Of all the financial analysis techniques discussed in this class, none is more important than time value analysis.

CHAPTER 4 Time Value Analysis

Time Value of Money

Time value analysis is necessary because money has time value.

A dollar in hand today is worth more than a dollar to be received in the future. Why?

Because of time value, the values of future dollars must be adjusted before they can be compared to current dollars.

Time value analysis, also called discounted cash flow (DCF) analysis, constitutes the techniques used to account for the time value of money.

Time Lines

CF0

CF1

CF3

CF2

Tick marks designate ends of periods. Time 0 is the starting point (the beginning of Period 1), Time 1 is the end of Period 1 (the beginning of Period 2), and so on.

What is the FV after three years of a $100 lump sum invested at 10%?

FV = ?

10%

-$100

Finding future values (moving to the right along the time line) is called compounding.

For now, assume interest is paid annually.

After 1 year:

FV1 = PV + INT1 = PV + (PV x I)

= PV x (1 + I)

= $100 x 1.10 = $110.00

After 2 years:

FV2 = FV1 + INT2

= FV1 + (FV1 x I) = FV1 x (1 + I)

= PV x (1 + I) x (1 + I) = PV x (1 + I)2

= $100 x (1.10)2 = $121.00

After 3 years:

FV3 = FV2 + I3

= PV x (1 + I)3

= 100 x (1.10)3

= $133.10

In general,

FVN = PV x (1 + I)N

Spreadsheet Solution

10%

What is the PV of $100 due in three years if I = 10%?

$100

PV = ?

Finding present values (moving to the left along the time line) is called discounting.

Solve FVN = PV x (1 + I )N for PV

PV = $100 / (1.10)3

= $100(0.7513) = $75.13

PV = FVN / (1 + I )N

If I offer you $75.13 today or $100 three years from now, which would you prefer?

Spreadsheet Solution

Solving for I

Assume that a bank offers an account that will pay $200 after five years on each $75 invested. What is the implied interest rate?

Spreadsheet Solution

Solving for N

Assume an investment earns 20 percent per year. How long will it take for the investment to double?

Spreadsheet Solution

Which statement is correct?

Starting to invest early for retirement reduces the benefits of compound interest.

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

If the discount (or interest) rate is positive, the FV of an expected series of payments will always exceed the PV of the same series.

If money has time value, it is impossible for the FV of a given sum to exceed its PV.

The PV of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant.

Self-Check

Three-Year Ordinary Annuity

PMT

Three-Year Annuity Due

Types of Annuities

What is the FV of a three-year ordinary annuity of $100 invested at 10%?

$100

10%

110

121

FV = $331

Spreadsheet Solution

What is the PV of the annuity?

$100

10%

$90.91

82.65

75.13

$248.69 = PV

Spreadsheet Solution

What is the FV and PV if the annuity were an annuity due?

$100

10%

$100

FV of the Annuity

$100

10%

110

121

133

FV = $364

Spreadsheet Solution

PV of the Annuity

$100

$100.00

$100

10%

$90.91

82.64

$273.55 = PV

Spreadsheet Solution

Perpetuities

A perpetuity is an annuity that lasts forever.

What is the present value of a perpetuity?

PV (Perpetuity) =

What is the future value of a perpetuity?

PMT

Uneven Cash Flow Streams

$100

$300

10%

-$50

$ 90.91

247.93

225.40

-34.15

$530.09 = PV

Spreadsheet Solution

Return on Investment (ROI)

The financial performance of an investment is measured by its return on investment.

Time value analysis is used to calculate investment returns.

Returns can be measured either in dollar terms or in rate of return terms.

Assume that a hospital is evaluating a new MRI. The project’s expected cash flows are given on the next slide.

MRI Investment Expected Cash Flows (thousands)

$310

$400

$500

$750

-$1,500

Where do these numbers come from?

Simple Dollar Return

$310

$400

$500

$750

310

400

500

750

$ 460 = Simple dollar return

-$1,500

Is this a good measure?

Discounted Cash Flow (DCF) Dollar Return

$310

$400

$500

$750

287

343

397

551

$ 78 = net present value (NPV)

-$1,500

Spreadsheet Solution

Opportunity Cost Rate

To find an investment’s dollar return (NPV), we need to apply a discount rate. Where does it come from?

The discount rate is the opportunity cost rate.

It is the rate that could be earned on alternative investments of similar risk.

It does not depend on the source of the investment funds.

We will apply this concept over and over in this course.

Opportunity Cost Rate (cont.)

The opportunity cost rate is found (at least in theory) as follows.

Assess the riskiness of the cash flow(s) to be discounted.

Identify alternative investments (usually securities) that have the same risk.

Estimate the expected rate of return on the similar-risk alternative investment.

When applied, the resulting PV provides a return equal to the opportunity cost rate.

In most time value situations, benchmark opportunity cost rates are known.

Opportunity Cost Rate (cont.)

When calculating NPV, the discounting process automatically recognizes the opportunity cost of capital. Thus:

A positive NPV means that the investment is expected to create value for the investor.

A negative NPV means that the investment is expected to lose value for the investor.

Rate of (Percentage) Return

$310

$400

$500

$750

282

331

376

511

$ 0.00 = NPV, so E(R) = 10.0%.

-$1,500

10%

Spreadsheet Solution

Rate of Return (cont.)

In capital investment analyses, the rate of return often is called internal rate of return (IRR).

In essence, it is the percentage return expected on the investment.

To interpret the rate of return, it must be compared to the opportunity cost of capital. In this case, 10 percent versus 8 percent.

Intra-Year Compounding

Thus far, all examples have assumed annual compounding.

When compounding occurs intra-year, the following occurs:

Interest is earned on interest during the year (more frequently).

The future value of an investment is larger than under annual compounding.

The present value of an investment is smaller than under annual compounding.

10%

134.01

-100

Annual: FV3 = 100 x (1.10)3 = 133.10

Semiannual: FV6 = 100 x (1.05)6 = 134.01

-100

133.10

-100

Effective Annual Rate (EAR)

EAR is the annual rate that causes the PV to grow to the same FV as under intra-year compounding.

What is the EAR for 10 percent, semiannual compounding?

Consider the FV of $1 invested for one

year. FV = $1 x (1.05)2 = $1.1025.

EAR = 10.25%, because this rate would

produce the same ending amount

($1.1025) under annual compounding.

The EAR Formula

= (1.05)2 - 1.0 = 0.1025 = 10.25%

EAR = 1 + - 1.0

IStated

= 1 + - 1.0

0.10

EAR of 10% at Various Compounding

EARAnnual = 10%

EARQ = (1 + 0.10/4)4 - 1.0 = 10.38%

EARM = (1 + 0.10/12)12 - 1.0 = 10.47%

EARD(365) = (1 + 0.10/360)365 - 1.0 = 10.52%

The more frequent the compounding, the greater the future value because interest is being earned more frequently.

Spreadsheet Solution

Which of the following bank accounts has the lowest effective annual rate? The one that pays:

a. 8% stated interest with monthly compounding

b. 7% stated interest with monthly compounding

c. 8% stated interest with annual compounding

d. 7% stated interest with daily compounding

e. 8% stated interest with daily compounding

Self-Check

Review of Interest Rate Types

Stated (nominal) rate = rate stated in contracts.

Periodic rate = Stated rate / number of compounding periods per year.

Effective annual rate (EAR) = rate that under annual compounding would produce the same results as a given stated rate with compounding more frequently than annual.

Review of Interest Rate Types (cont.)

If number of compounding periods per year = 1 (annual), then:

Periodic rate = stated rate = EAR

If number of compounding periods per year > 1, then:

Periodic rate < stated rate < EAR