A company is going to issue a $$1,000$ par value bond that pays a $7\%$ annual coupon. The company expects investors to pay $$942$ for the $20-$year bond. The expected flotation cost per bond is $$42,$ and the firm is in the $34\%$ tax bracket. Compute the following:

a$.$ the yield to maturity on the firm's bonds

b$.$ the firm's after$-$tax cost of existing debt

c$.$ the firm's after$-$tax cost of new debt