Question

On July 1, Year 1, PPI issued $10 million of 20-year, 8% bonds, which paid interest...

On July 1, Year 1, PPI issued $10 million of 20-year, 8% bonds, which paid interest semiannually. The
bonds were issued to yield 10%. What were the proceeds of the bond issue?

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Answer #1

Face Value of Bonds = $10,000,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $10,000,000
Semiannual Coupon = $400,000

Time to Maturity = 20 years
Semiannual Period = 40

Annual YTM = 10%
Semiannual YTM = 5%

Issue Value of Bonds = $400,000 * PVIFA(5%, 40) + $10,000,000 * PVIF(5%, 40)
Issue Value of Bonds = $400,000 * (1 - (1/1.05)^40) / 0.05 + $10,000,000 / 1.05^40
Issue Value of Bonds = $400,000 * 17.15909 + $10,000,000 * 0.14205
Issue Value of Bonds = $8,284,136

So, proceeds of the bond issue is $8,284,136

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