What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly?

PROBLEM 1                                                                                                                        

Find the following values for a lump sum:

– The future value of  $500 invested at 8 percent for one year

– The future value of $500 invested at 8 percent for five years

– The present value of $500 to be received in one year when the opportunity cost rate is 8 percent

– The present value of $500 to be received in five years when the opportunity cost rate is 8 percent

assuming:

  1. Annual compounding
  2. Semiannual compounding
  3. Quarterly compounding

PROBLEM 2                                                                                                        

What is the effective annual rate (EAR) if the stated rate is 8 percent and compounding occur semiannually? Quarterly?

ANSWER

PROBLEM 3                                                                        

Find the following values assuming a regular, or ordinary, annuity:

– The present value of $400 per year for ten years at 10 percent

– The future value of $400 per year for ten years at 10 percent

– The present value of $200 per year for five years at 5 percent

– The future value of $200 per year for five years at 5 percent

assuming:

  1. A regular or ordinary annuity
  2. An annuity due

ANSWER

PROBLEM 4                                                                                                                       

Consider the following uneven cash flow stream:

Year       Cash Flow

0              $0

1              $250

2              $400

3              $500

4              $600

5              $600

 

  1. What is the present (Year 0) value if the opportunity cost (discount) rate is 10 percent?
  2. Add an outflow (or cost) of $1,000 at Year 0. What is the present value (or net present value) of the

stream?

ANSWER

PROBLEM 5                                                                                                                        

Consider another uneven cash flow stream:

 

Year       Cash Flow

0              $2,000

1              $2,000

2              $0

3              $1,500

4              $2,500

5              $4,000

 

  1. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?
  2. What is the value of the cash flow stream at the end of Year 5 if the cash flows are invested in an

account that pays 10 percent annually?

  1. What cash flow today (Year 0), in lieu of the $2,000 cash flow, would be needed to accumulate $20,000

at the end of Year 5? (Assume that the cash flows for Years 1 through 5 remain the same.)

  1. Time value analysis involves either discounting or compounding cash flows. Many healthcare financial

management decisions—such as bond refunding, capital investment, and lease versus buy—involve

discounting projected future cash flows. What factors must executives consider when choosing a

discount rate to apply to forecasted cash flows?

ANSWER

PROBLEM 6                                                                                                                        

What is the present value of a perpetuity of $100 per year if the appropriate discount rate is 7 percent?

Suppose that interest rates doubled in the economy and the appropriate discount rate is now 14 percent.

What would happen to the present value of the perpetuity?

ANSWER

PROBLEM 7                                                                                                                        

An investment that you are considering promises to pay $2,000 semiannually for the next two years,

beginning six months from now. You have determined that the appropriate opportunity cost (discount)

rate is 8 percent, compounded quarterly. What is the present value of this investment?

ANSWER

PROBLEM 8                                                                                                                        

Consider the following investment cash flows:

 

Year       Cash Flow

0              -$1,000

1              $250

2              $400

3              $500

4              $600

5              $600

 

  1. What is the return expected on this investment measured in dollar terms if the opportunity cost rate is

10 percent?

  1. Provide an explanation, in economic terms, of your answer.
  2. What is the return on this investment measured in percentage terms?
  3. Should this investment be made? Explain your answer.

ANSWER

PROBLEM 9                                                                                                                        

Epitome Healthcare has just borrowed $1,000,000 on a five-year, annual payment term loan at a 15

percent rate. The first payment is due one year from now. Construct the amortization schedule for this

loan.

ANSWER

Chapter 5

PROBLEM 1

Consider the following probability distribution of returns estimated for a proposed project that involves a new ultrasound machine:

State of the        Probability          Rate of

economy             of occurrence    return

Very poor            0.1                          -10%

Poor                      0.2                             0%

Average               0.4                             10%

Good                     0.2                          20%

Very good           0.1                          30%

 

  1. What is the expected rate of return on the project?
  2. What is the project’s standard deviation of returns?
  3. What is the project’s coefficient of variation (CV) of returns?
  4. What type of risk does the standard deviation and CV measure?
  5. In what situation is this risk relevant?

ANSWER

PROBLEM 5                                                                                                                        

A few years ago, the Value Line Investment Survey reported the following market betas for the stocks of

selected healthcare providers:

 

Company                                             Beta

Quorum Health Group                                   0.90

Beverly Enterprises                                         1.20

HEALTHSOUTH Corporation                         1.45

United Healthcare                                           1.70

 

At the time these betas were developed, reasonable estimates for the risk-free rate, RF, and the required rate of return on the market, R(Rm), were 6.5 percent and 13.5 percent, respectively.

  1. What are the required rates of return on the four stocks?
  2. Why do their required rates of return differ?
  3. Suppose that a person is planning to invest in only one stock rather than hold a well-diversified stock

portfolio. Are the required rates of return calculated above applicable to the investment? Explain your

answer.

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