Exercise $1\_$ch$6\_$no$1($Sunk costs$)$: We return to the sunk costs example of Section $6\mathrm{.}2.$ You have invested $$100,000$ in a badly built house. For $$20,000$ invested today, you can fix up the house and sell it one year from today for $$90,000.$ As an alternative, you can sell the house today for $$60,000.$

a$.)$ Should you take into account the $$100,000$ cost already invested in the house?

b$.)$ If the relevant discount rate is $9\%,$ which alternative should you prefer?

c$.)$ What is the discount rate that makes you indifferent between the two alternatives?