9.1 Find the following values for a lump sum assuming annualcompounding:a. The future value of $500 invested at 8 percent for one yearb. The future value of $500 invested at 8 percent for five yearsc. The present value of $500 to be received in one year when theopportunity cost rate is 8 percentd. The present value of $500 to be received in Five years when theopportunity cost rate is 8 percent9.2 Repeat Problem 9.1 above, but assume the following compoundingconditions:a. Semiannualb. Quarterly9.7 Consider another uneven cash flow stream:Year Cash Flow0 $2,0001 2,0002 03 1,5004 2,5005 4,000a. What is the present (Year 0) value of the cash flow stream if theopportunity cost rate is 10 percent?b. What is the value of the cash flow stream at the end of Year 5 if thecash flows are invested in an account that pays 10 percent annually?c. What cash flow today (Year 0), in lieu of the $2,000 cash flow, wouldbe needed to accumulate $20,000 at the end of Year 5? (Assumethat the cash flows for Years 1 through 5 remain the same.)d. Time value analysis involves either discounting or compoundingcash flows. Many healthcare financial management decisions,such as bond refunding, capital investment, and lease versus buy,involve discounting projected future cash flows. What factors mustexecutives consider when choosing a discount rate to apply toforecasted cash flows?9.11 Consider the following investment cash flows:Year Cash Flow0 ($1,000)1 2502 4003 5004 6005 600a. What is the return expected on this investment measured in dollarterms if the opportunity cost rate is 10 percent?b. Provide an explanation, in economic terms, of your answer.c. What is the return on this investment measured in percentage terms?d. Should this investment be made? Explain your answer.10.1 Consider the following probability distribution of returns estimated fora proposed project that involves a new ultrasound machine:State of Probability of the Economy Occurrence Rate of ReturnVery poor 0.10-10.0 %Poor 0.20 0.0Average 0.40 10.0Good 0.20 20.0Very good 0.10 30.0a. 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 coefecient 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?10.2 Suppose that a person won the Florida lottery and was offered a choiceof two prizes: (1) $500,000 or (2) a coin-toss gamble in which he orshe would get $1 million for heads 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 averteror a risk seeker?10.5 A few years ago, the Value Line Investment Survey reported thefollowing market betas for the stocks of selected healthcare providers:Company BetaQuorum Health Group 0.90Beverly Enterprises 1.20HEALTHSOUTH Corporation 1.45United Healthcare 1.70At the time these betas were developed, reasonable estimates for therisk-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 ratherthan hold a well-diversified stock portfolio. Are the required rates ofreturn calculated above applicable to the investment? Explain youranswer.10.6 Suppose that Apex Health Services has four different projects. Theseprojects are listed below, along with the amount of capital invested andestimated corporate and market betas:Amount Corporate MarketProject Invested Beta BetaWalk-in clinic $ 500,000 1.5 1.1MRI facility 2,000,000 1.2 1.5Clinical laboratory 1,500,000 0.9 0.8X-ray laboratory 1,000,000 0.5 1.0$5,000,000a. Why do the corporate and market betas differ for the same project?b. What is the overall corporate beta of Apex Health Services? Is thecalculated 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 riskinessof an average stock?e. Would stock investors require a rate of return on Apex that is greaterthan, less than, or the same as the return on an average-risk stock?11.1 Assume Venture Healthcare sold bonds that have a ten-year maturity, a12 percent coupon rate with annual payments, and a $1,000 par value.a. Suppose that two years after the bonds were issued, the requiredinterest rate fell to 7 percent. What would be the bond’s value?b. Suppose that two years after the bonds were issued, the requiredinterest rate rose to 13 percent. What would be the bonds??™ value?c. What would be the value of the bonds three years after issue in eachscenario above, assuming that interest rates stayed steady at either 7percent or 13 percent?11.2 Twin Oaks Health Center has a bond issue outstanding with a couponrate of 7 percent and four years remaining until maturity. The par valueof the bond is $1,000, and the bond pays interest annually.a. Determine the current value of the bond if present market conditionsjustify a 14 percent required rate of return.b. Now, suppose Twin Oaks four-year bond had semiannual couponpayments. What would be its current value? (Assume a 7 percentsemiannual required rate of return. However, the actual rate wouldbe slightly less than 7 percent because a semiannual coupon bond isslightly less risky than an annual coupon bond.)c. Assume that Twin Oaks bond had a semiannual coupon but 20years remaining to maturity. What is the current value under theseconditions? (Again, assume a 7 percent semiannual required rate ofreturn, although the actual rate would probably be greater than 7percent because of increased price risk.)11.5 Minneapolis Health System has bonds outstanding that have fouryears remaining to maturity, a coupon interest rate of 9 percent paidannually, and a $1,000 par value.a. What is the yield to maturity on the issue if the current market priceis $829?b. If the current market price is $1,104?c. Would you be willing to buy one of these bonds for $829 if yourequired a 12 percent rate of return on the issue? Explain youranswer.11.6 Six years ago, Bradford Community Hospital issued 20-year municipalbonds with a 7 percent annual coupon rate. The bonds were calledtoday for a $70 call premium that is, bondholders received $1,070for each bond. What is the realized rate of return for those investorswho bought the bonds for $1,000 when they were issued?12.1 A person is considering buying the stock of two home health companiesthat are similar in all respects except for the proportion of earnings paidout as dividends. Both companies are expected to earn $6 per share inthe coming year, but Company D (for dividends) is expected to payout the entire amount as dividends, while Company G (for growth)is expected to pay out only one-third of its earnings, or $2 per share.The companies are equally risky, and their required rate of return is 15percent. D’s constant growth rate is zero and G’s is 8.33 percent. Whatare the intrinsic values of Stocks D and G?12.2 Medical Corporation of America (MCA) has a current stock price of$36 and its last dividend (D0) was $2.40. In view of MCA’s strongfinancial position, its required rate of return is 12 percent. If MCA’sdividends are expected to grow at a constant rate in the future, what isthe firm’s expected stock price in Five years?12.3 A broker offers to sell you shares of Bay Area Healthcare, which justpaid a dividend of $2 per share. The dividend is expected to grow at aconstant rate of 5 percent per year. The stock’s required rate of returnis 12 percent.a. What is the expected dollar dividend over the next three years?b. What is the current value of the stock and the expected stock priceat the end of each of the next three years?c. What is the expected dividend yield and capital gains yield for eachof the next three years?d. What is the expected total return for each of the next three years?E.How does the expected total return compare with the requiredrate of return on the stock? Does this make sense? Explain youranswer.12.7 Lucas Clinic’s last dividend (D0) was $1.50. Its current equilibriumstock price is $15.75, and its expected growth rate is a constant 5percent. If the stockholder’s required rate of return is 15 percent, whatis the expected dividend yield and expected capital gains yield for thecoming year?
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