$1.$ Assume Venture Healthcare sold bonds that have a ten$-$year maturity, a $12$ percent coupon rate with annual payments, and a $$1,000$ par value.

a$.$ Suppose that two years after the bonds were issued, the required interest rate fell to $7$ percent. What would be the bond's value?

b$.$ Suppose that two years after the bonds were issued, the required interest rate rose to $13$ percent. What would be the bond's value?

c$.$ What would be the value of the bonds three years after issue in each scenario above, assuming that interest rates stayed steady at either $7$ percent or $13$ percent?

$2.$ Twin Oaks Health Center has a bond issue outstanding with a coupon rate of $7$ percent and four years remaining until maturity. The par value of the bond is $$1,000,$ and the bond pays interest annually.

a$.$ Determine the current value of the bond if present market conditions justify a $14$ percent required rate of return.

b$.$ Now, suppose Twin Oaks' four$-$year bond had semiannual coupon payments. What would be its current value? $($Assume a $7$ percent semiannual required rate of return. However, the actual rate would be slightly less than $7$ percent because a semiannual bond is slightly less risky than an annual coupon bond.$)$

c$.$ Assume that Twin Oaks' bond had a semiannual coupon but $20$ years remaining to maturity. What is the current value under these conditions? $($Again$,$ assume a $7$ percent semiannual required rate of return, although the actual rate would probably be greater than $7$ percent because of increased price risk.$)$

$3.$ Minneapolis Health System has bonds outstanding that have four years remaining to maturity, a coupon interest rate of $9$ percent paid annually, and a $$1,000$ par value.

a$.$ What is the yield to maturity on the issue if the current market price is $$829?$

b$.$ If the current market price is $$1,104?$

c$.$ Would you be willing to buy one of these bonds for $$829$ if you required a $12$ percent rate of return on the issue? Explain your answer.

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$4.$ Six years ago, Bradford Community Hospital issued $20-$year municipal bonds with a $7$ percent annual coupon rate. The bonds were called today for a $$70$ call premium$--$that is$,$ bondholders received $$1,070$ for each bond. What is the realized rate of return for those investors who bought the bonds for $$1,000$ when they were issued?

$5.$ Rex Healthcare recently issued a bond with a $30-$year maturity, an annual coupon rate of $10$ percent, a face value of $$1,000,$ and semiannual interest payments. If the current rate of interest is a $9$ percent yield to maturity on this investment, what is the current price of the bond?

$6.$ A person is considering buying the stock of two home health companies that are similar in all respects except for the proportion of earnings paid out as dividends. Both companies are expected to earn $$6$ per share in the coming year, but Company D $($for dividends$)$ is expected to pay out the entire amount one year from now as dividends, while Company G $($for growth$)$ is expected to pay out only one$-$third of its earnings or $$2$ per share. The companies are equally risky, and their required rate of return is $15$ percent. D$\text{'}$s constant growth rate is zero and G$\text{'}$s is $8\mathrm{.}33$ percent. What are the expected prices of Stocks D and G$?$