An asset is bought for $$15,000$ and will be used on a project for five years after which it will be disposed of$.$ Tax is payable at $20\%,$ one year in arrears, and tax$-$allowable depreciation is available at $25\%$ reducing balance.

$($a$)$ Calculate the tax$-$allowable depreciation and hence the tax savings for each year if the proceeds on disposal of the asset are $$2,500.$

$($b$)$ How would your answer change if the asset were sold for $$7,000?$

$($c$)$ If net trading income from the project is $$9,500$ per year, based on your answer to part $($a$)$ and a cost of capital of $12\%,$ calculate the NPV of the project