Your firm lost a product liability suit and is obligated to pay out $$6$ million in $2$ years and $$4$

million in $5$ years. You estimate that the appropriate yield to maturity is $8\%.$

A$)$ What is the duration of your liability?

B$)$ Your firm wants to immunize its liability position by buying a combination of zero$-$coupon

bonds with two years until maturity and $6\%$ dividend perpetuities with an $8\%$ yield to maturity.

What percentage of the firm's portfolio should you allocate to each, if these are the only two

assets funding the plan? How much money should you invest in each?