Question: Consider a small, simplified CMBS deal based on a $100m pool of commercial mortgages, comprised of 10 identical sized loans. Each mortgage is a five-year, 6.5% interest-only, annual payment balloon loan. The loans are all of similar credit quality on a stand-alone basis. Each loan has a 75% loan-to-value ratio and each of the 10 properties are valued at prices implying cap rates equal or close to 8.5%. The mortgage pool has been carved into two tranches or classes of bonds as follows:
In this simplified world, both tranches have the same coupon as the underlying mortgages, and hence neither will sell at par.
a. Determine the implied loan-to-value (LTV) and debt coverage ratio (DCR) of the AAA class.
b. Determine the minimum yield to maturity or required return of investors in the B-rated securities that makes this deal work; that is, the YTM at which the total value of the securities equals the $100m par value. Compare the yield you determine to the mortgage rate on the whole loans and the YTM required by investors in the AAA bonds and explain the differences. (Hint: First, value the AAA bonds, then back out the implied maximum value of the B-rated bonds, and then determine the ytm.)