Question

Chinook Inc. has available for issue a $3,245,000 bond due in eight years. Interest at the rate of 10.50% is to be paid semiannually. Calculate the issue price if the market interest rate is: (Do not round intermediate calculations. Round the final answers to the nearest whole dollar amount.)

a.10.00%

b.10.50%

c.11.25%

Answer 1

Calculation of issue price:

A) When Market Interest Rate is : 10%

                Issue Price = Present Value of Lumpsum + Present Value of Interest Payments

                Number of Periods = 16

                Market Rate = 5% ( semi anually)

                Interest Rate = 5.25% ( semi anually)

                Issued at $3,245,000

                Present value of lumpsum = $3,245,000/[(1.05) Power 16] = $1,486,571.89

                Present value of interest payments = ($3,245,000*5.25%)*(1/(1.0525 power 16) and GT)

                                                                                      = $170362.50*10.6475

                                                                                      = $1,813,934.72

                Issue Price = $1486571.89 + $1813934.72 = $3,300,507 (rounded off)

B) When Market Rate and Interest Rate are same Issue Price Will also be same i.e., $3,245,000

C)When Market Rate is : 11.25%

Issue Price = Present Value of Lumpsum + Present Value of Interest Payments

                Number of Periods = 16

                Market Rate = 5.625% ( semi anually)

                Interest Rate = 5.25% ( semi anually)

                Issued at $3,245,000

                Present value of lumpsum = $3,245,000/[(1.05625) Power 16] = $1,351,908.04

                Present value of interest payments = ($3,245,000*5.25%)*(1/(1.0525 power 16) and GT)

                                                                                      = $170362.50*10.6475

                                                                                      = $1,813,934.72

                Issue Price = $1351908.04 + $1813934.72 = $3,165,843 (Rounded off)