Posted: June 20th, 2022

# Find the following values for a lump sum assuming annual compounding

.1 Find the following values for a lump sum assuming annual compounding:

a. The future value of \$500 invested at 8 percent for one year

b. The future value of \$500 invested at 8 percent for five years

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

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

9.2 Repeat Problem 9.1 above, but assume the following compounding conditions:

a. Semiannual

b. Quarterly

9.7 Consider the following uneven cash flow stream:

Year Cash Flow

0 \$2,000

1 2,000

2 0

3 1,500

4 2,500

5 4,000

a. What is the present (Year 0) value of the cash flow stream if the opportunity cost rate is 10 percent?

b. What is the future (Year 5) value of the cash flow stream if the cash flows are invested in an account that pays 10 percent annually?

c. What cash flow today (Year 0), in lied 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.)

d. Time value analysis involves either discounting or compounding cash flows. Many health care financial management decisions-such as bonding 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?

9.11 Consider the following investment cash flows:

Year Cash Flow0 \$1,000

1 250

2 400

3 500

4 600

5 600

a. What is the return expected on this investment measured in dollar terms if the opportunity cost rate is 10 percent?

b. Provide an explanation, in economic terms, of your response

c. What is the return on this investment measured in percentage terms?

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

State of the economy Probability of Occurrence Rate of Return

Very poor 0.10 −10.0%

Poor 0.20 0.0

Average 0.40 10.0

Good 0.20 20.0

Very good 0.10 30.0

a. What is the expected rate of return on the project?

b. What is the project’s standard deviation of returns?

c. What is the project’s coefficient of variation (CV) of returns?

d. What type of risk do the standard deviation and CV measure?

e. In what situation is this risk relevant?

10.2 Suppose that a person won the Florida lottery and was offered a choice of two prizes: (1) \$500,000 or (2) a coin-toss gamble in which he or she would get \$1 million for heads and zero for tails.

a. What is the expected dollar return on the gamble?

b. Would the person choose the sure \$500,000 or the gamble?

c. If she chooses the sure \$500,000, is the person a risk averter or a risk seeker?

10.5 Several 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 Corp. 1.45

United Healthcare 1.70

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

a. What are the required rates of return on the four stocks?

b. Why do their required rates of return differ?

c. Suppose that a person is planning to invest in only one stock rather than a well-diversified stock portfolio. Are the required rates of return calculated above applicable to the investment? Explain your answer?

10.6 Suppose that Apex Health Services has four different projects. These projects are listed below, along with the amount of capital invested and estimated corporate and market betas:

Project Amount Invested Corporate Beta Market Beta

Walk-in clinic \$ 500,000 1.5 1.1

MRI facility 2,000,000 1.2 1.5

Clinical lab. 1,500,000 0.9 0.8

X-ray lab. 1,000,000 0.5 1.0

\$5,000,000

a. Why do the corporate and market betas differ for the same project?

b. What is the overall corporate beta of Apex Health Services? Is the calculated beta consistent with corporate risk theory?

c. What is the overall market beta of Apex Health Services?

d. How does the riskiness of Apex’s stock compare with the riskiness of an average stock?

e. Would stock investors require a rate of return on Apex that is greater than, less than, or the same as the return on an average-risk stock?

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