The Heinrich Tire Company recalled a tire in its subcompact line in December $2024.$ Costs associated with the recall were originally thought to approximate $$62$ million. Now, though, while management feels it is probable the company will incur substantial costs, all discussions indicate that $$62$ million is an excessive amount. Based on prior recalls in the industry, management has provided the following probability distribution for the potential loss:

Note: Use tables, Excel, or a financial calculator. $($FV of $$1,$ PV of $$1,$ FVA of $$1,$ PVA of $$1,$ FVAD of $$1$ and PVAD of $$1)$

Loss Amount Probability

$ $52$ million $20\%$

$ $42$ million $50\%$

$ $32$ million $30\%$

An arrangement with a consortium of distributors requires that all recall costs be settled at the end of $2025.$ The risk$-$free rate of interest is $4\%.$

Required:

$1.$ & $2.$ By the traditional approach to measuring loss contingencies, what amount would Heinrich record at the end of $2024$ for the loss and contingent liability? For the remainder of this problem, apply the expected cash flow approach of SFAC No$.7.$ Estimate Heinrich$$s liability at the end of the $2024$ fiscal year.

$3.$ to $5.$ Prepare the necessary journal entries.