It is February, $2022$ and Beta Co$.$ will issue $$1$ million in bonds in August. Beta is worried interest rates will rise between now and then. Current interest rates are $7\%$ for the $25-$year issue. But Beta fears rates might rise by $1\%$ by June. June T$-$bond futures are priced at $111-20.$

$1)$ Without hedging, what happens if interest rates increase $1\%,$ i$.$e$.,$ at a yield of $8\%,$ how much will the $$1$ million worth of $25$ year $7\%$ semi$-$annual coupon bonds be worth?

$2)$ Set up the hedging and what is the effectiveness of the hedge? Please demonstrate with calculations.