Question

Whipple Corp. just issued 280,000 bonds with a coupon rate of 6.02 percent paid semiannually that mature in 25 years. The bonds have a YTM of 6.46 percent and have a par value of $2,000. How much money was raised from the sale of the bonds?

Answer 1

Answer:

529.64 million or $529,639,600 was received from the sale of bonds.

Explanation:

Money Raised from the sale is based on the current value of the bond. Price of bond is the present value of future cash flows, to calculate Price of the bond use following formula:

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

As per given data

Face Value = $2,000

Coupon payment = $2,000 x 6.02% = $120.4 /2 = $60.2 semiannually

Number of period = n = 25 years x 2 period per year = 50 period

Yield to maturity = 6.46% annually = 6.46% / 2  = 3.23% semiannually

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

Price of the Bond = $60.2 x [ ( 1 - ( 1 + 3.23% )^-50 ) / 3.23% ] + [ 2,000 / ( 1 + 3.23% )^50 ]

Price of the Bond = $1,483.51 + $408.06 = $1,891.57

Cash received = Number of bonds x Price per bond = 280,000 x $1,891.57 = $529,639,600