# Sml Financial Corporation

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```					            UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

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%

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 does the standard deviation and CV measure?
e. In what situation is this risk relevant?

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

PROBLEM 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 if a head were flipped and zero for a tail.
a. What is the expected dollar return on the gamble?
b. Would the person choose the sure \$500,000 or the gamble?
c. If he or she chooses the sure \$500,000, is the person a risk averter or a risk seeker?

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

PROBLEM 3
Refer to Table 5.2 in UHFM.
a. Construct an equal-weighted (50/50) portfolio of Investments B and C. What is the expected rate of
return and standard deviation of the portfolio? Explain your results.
b. Construct an equal-weighted (50/50) portfolio of Investments B and D. What is the expected rate of
return and standard deviation of the portfolio? Explain your results.

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

PROBLEM 4
Suppose that the risk-free rate, RF, were 8 percent and the required rate of return on the market, R(Rm),
were 14 percent.
a. Write out the Security Market Line (SML), and explain each term.
b. Plot the SML on a sheet of paper.
c. Suppose that inflation expectations increase such that the risk-free rate, RF, increases to 10 percent
and the required rate of return on the market, R(Rm), increases to 16 percent. Write out and plot the
new SML.
d. Return to the original assumptions in this problem. Now, suppose that investors' risk aversion
increases and the required rate of return on the market, R(Rm), increases to 16 percent. (There is no
change in the risk-free rate because RF reflects the required rate of return on a riskless investment.)
Write out and plot the new SML.

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

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.
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 hold a well-diversified stock
portfolio. Are the required rates of return calculated above applicable to the investment? Explain your

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

PROBLEM 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:

Amount      Corporate Market
Project                 Invested    Beta       Beta
Walk-in clinic             \$500,000        1.5       1.1
MRI facility             \$2,000,000        1.2       1.5
Clinical laboratory      \$1,500,000        0.9       0.8
X-ray laboratory         \$1,000,000        0.5         1
\$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?

UNDERSTANDING HEALTHCARE FINANCIAL MANAGEMENT

Chapter 4 -- Financial Risk and Required Return

PROBLEM 7
Assume that HCA is evaluating the feasibility of building a new hospital in an area not currently served
by the company. The company's analysts estimate a market beta for the hospital project of 1.1, which is
somewhat higher than the 0.8 market beta of the company's average project. Financial forecasts for the
new hospital indicate an expected rate of return on the equity portion of the investment of 20 perent. If the
risk-free rate, RF, is 7 percent and the required rate of return on the market, R(Rm), is 12 percent, is the
new hospital in the best interest of HCA's shareholders? Explain your answer.