Why do corporations issue 100-year bonds, knowing that interest rate risk is highest for very long-term bonds? How does the interest rate risk affect the issuer?

Essentially, the issuer takes the opposite side of the interest rate risk position. By issuing long-term bonds, the corporation is essentially betting that rates won't fall significantly. If they do, the corporation will incur a loss due to borrowing at rates higher than the going market rates. On the other hand, if rates rise, the corporation benefits by having locked in its borrowing rate for up to 100 years.