Marin Inc. manufactures cycling equipment. Recently, the vice president of operations of the company has requested construction of a new plant to meet the increasing demand for the company’s bikes. After a careful evaluation of the request, the board of directors has decided to raise funds for the new plant by issuing $3,021,900 of 10% term corporate bonds on March 1, 2017, due on March 1, 2032, with interest payable each March 1 and September 1, with the first interest payment on September 1st, 2017. At the time of issuance, the market interest rate for similar financial instruments is 12%. What is the Selling price of the bonds ?

Price of the bond is $2,605,941

Explanation:

Price of the bond is the present value of all cash flows of the bond. These cash flows include the coupon payment and the maturity payment of the bond.

According to given data

Face value of the bond is $3,021,900

Coupon payment = C = $3,021,900 x 10% = $302,190 annually = $151,095 semiannually

Number of periods = n = 15 years x 2 = 30 period

Market Rate = 12% annually = 6% semiannually

Price of the bond is calculated by following formula:

Price of the Bond = C x [ ( 1 - ( 1 + r )^-n ) / r ] + [ F / ( 1 + r )^n ]

Price of the Bond = $151,095 x [ ( 1 - ( 1 + 6% )^-30 ) / 6% ] + [ 3,021,900 / ( 1 + 6% )^30 ]

Price of the Bond = $151,095 x [ ( 1 - ( 1 + 6% )^-30 ) / 6% ] + [ 3,021,900 / ( 1 + 6% )^30 ]

Price of the Bond = $2,079,797.2 + $526,143.4 = $2,605,940.6

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