On December 31, 2013, University Theatres issued $500,000 face value of bonds. T

Question

On December 31, 2013, University Theatres issued $500,000 face value of bonds. The stated rate is 8%, and interest is paid semiannually on June 30 and December 31. The bonds mature in 15 years.

If required, round your answers to the nearest whole dollar. Follow the format shown in present value tables as you complete the requirements below.

Required:

a. Assuming the market rate of interest is 6%, calculate at what price the bonds are issued.
$

b. Assuming the market rate of interest is 10%, calculate at what price the bonds are issued.
$

Explanation / Answer

a. Interest is paid semiannually the bond interest rate per period is 4%(=8%/2), the market interest rate is 3%(=6%/2) and number of time periods are 30(=15*2). Hence price of the bond is calculated as present value of all future cash flows:
Interest paid by the bond at present value 3%(for 30 years is 19.6004)=$500000*4%*19.6004
=$20000*19.6004
   =$392,009

Value of bond at present value 3%(in 30 years is 0.41199)=$500,000*0.411987
=$205,993

Therefore, issue price of the bond=Present value of interest payments+Present value of bond
=$392,009+$205,993
   =$598002

b.  Interest is paid semiannually the bond interest rate per period is 4%(=8%/2), the market interest rate is 5%(=10%/2) and number of time periods are 30(=15*2). Hence price of the bond is calculated as present value of all future cash flows:
Interest paid by the bond at present value 5%(for 30 years is 15.372)=$20000*15.372
   =$307,440

Value of bond at present value 5%(in 30 years is 0.2318)=$500000*0.2318
=$115,900

Therefore, issue price of the bond=Present value of interest payments+Present value of bond
=$307440+115900
   =$423,340

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