You work at an investment bank and are advising a firm that wishes to issue a $10$ year bond. You have researched other similar firms and have found that bonds issued by those other companies tend to pay on average a $6\%$ coupon and have a $9\%$ yield to maturity. The company wishes to mimic these companies and issue a bond with a $$100$ face value and annual coupon with an APR of $6\%.$

a$.$ How much would you tell your client they should expect to be able to sell each bond for?

b$.$ Your client is disgusted at the idea of their bonds trading at a discount thinking it signifies financial weakness and makes borrowing more expensive. What is the lowest coupon rate you could suggest that you would expect the bond to not trade at a discount?

c$.$ What do you think of your clients reasoning that the a lower coupon rate makes borrowing more expensive? What are some real consequences $($what actually. shanges$)$ if they select the higher coupon rate.