I$\text{'}$m curious about a question I received which I wasn't sure what the formula was for. I$\text{'}$m trying to find the net cash outflow of a particular set of a requirements. The question is similar, but not the same, to what is below.

Firm X is considering the replacement of an old machine with one that has a purchase price of $$85,000.$ The current market value of the old machine is $$24,000$ but the book value is $$43,000.$ The firm's combined tax rate is $35\%.$ What is the net cash outflow for the new machine after considering the sale of the old machine? Disregard the effect of depreciation of the new machine if acquired.

What I thought I should do is the following.

Take the initial purchase price as the initial outflow

Take the book value and subtract the market value to get the tax shield

Apply the $35\%$ to the result of $2$

Subtract the result of $3$ from $1$

Add $24$k as a inflow

Clearly this is not right. What am I doing wrong in my thought process here?