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# Estimating the current value of given bond

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Twin Oaks Health Center has a bond issue outstanding with a coupon rate of 7% 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% required rate of return.

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

c) Assuming that Twin Oak' bond had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Assume a 7% semiannual rate of return. However, the actual rate would be slightly less than 7%, although the actual rate would probably be greater than 7% because of increased price risk.)

#### Solution Preview

Please refer attached file for solution in MS Excel.

a) Determine the current value of the bond if present market conditions justify a 14% required rate of return.
Maturity amount=M=\$1000
Coupon Amount=1000*7%=\$70
Number of coupon payments left=n=4
Required rate of return=r=14%

Current price of bond=C/r*(1-1/(1+r)^n)+M/(1+r)^n
=70/14%*(1-1/(1+14%)^4)+1000/(1+14%)^4
...

#### Solution Summary

Solution describes the steps to calculate current value of a bond by using formulas as well as by using functions in MS Excel.

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Assume Venture Healthcare sold bonds that have a 10-year maturity, a 12% coupon rate with annual payments, and a \$1,000 par value. Suppose that two years after the bonds were issued, the required interest rate fell to 7%. What would be the bonds value? Suppose that two years after the bonds were issued, the required interest rate rose to 13%. What would be the bonds value? 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% or 13%?

Twin Oaks Center has a bond issue outstanding with a coupon rate of 7% and 4 years remaining until maturity. The par value of the bond is \$1,000, and the bond pays interest annually.
a) what is the current value of the bond if present market conditions justify a 14% required rate of return?
b)If Twin oaks' four year bond had semiannual coupon payments. What would be it current value?
c) Assume that it had a semiannual coupon but 20 years remaining to maturity. What is the current value under these conditions? (Assuming a 7% semiannual required rate of return).

Minneapolis health system has bonds outstanding that have four years remaining to maturity, a coupon interest rate of 9% 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 \$1104
c) Would you be willing to buy one of these bonds for \$829 if you required a 12% rate of return on the issue?

Six years ago, Bradford Hospital issued 20 year municipal bonds with a 7% annual coupon rate. The bonds were called today for a \$70 call premium- that is, bondholders received \$1070 for each bond. What is the realized rate of return for those investors who bought the bonds for \$1,000 when they were issued.

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