Freedom Corporation acquired a fixed asset for $$180,000.$ Its estimated life at time of purchase was $4$ years, with no estimated salvage value. Assume a discount rate of $10\%$ and an income tax rate of $40\%.($Use Exhibit $12\mathrm{.}4,$ Appendix C$,$ TABLE $1$ and Appendix C$,$ TABLE $2.)$

Required:

$1.$ What is the incremental present value of the tax benefits resulting from calculating depreciation using the sum$-$of$-$the$-$years$-$digits $($SYD$)$ method rather than the straight$-$line $($SLN$)$ method on this asset? Use the SYD and SLN functions in Excel to calculate depreciation charges.

$2.$ What is the incremental present value of the tax benefits resulting from calculating depreciation using the double$-$declining$-$balance $($DDB$)$ method rather than the straight$-$line $($SLN$)$ method on this asset? Use the SLN and DDB functions in Excel to calculate depreciation charges.

$3.$ What is the incremental present value of the tax benefits resulting from using MACRS rather than straight$-$line $($SLN$)$ depreciation? The asset qualifies as a $3-$year asset. Use the half$-$year convention.