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A new piece of Machinery was purchased for $200,000. The machinery has an economic life of...

A new piece of Machinery was purchased for $200,000. The machinery has an economic life of 4 years and falls under Class 8 with a CCA of 20%. The machinery is expected to have a salvage value of $25,000 after 4 years of use. The firms tax rate is 28%, and its overall WACC is 10%. Using the declining balance method, calculate the PV of the CCA tax shield.

Solutions

Expert Solution

Now in the given question CCA rate is given= 20%

Value of machinery= 200000

Under CCA depreciation in the first year = 50% of ( Asset cost* CCA rate)

= 50% ( 200000*20/100)= 20000

Now for the subsequent n years Depreciation = Value of asset in (n-1) year after depreciation * CCA rate

Therefore for second-year depreciation expense= 180000*20/100= 36000

Similarly, the calculations have been given for year 3 and 4 in the table( Note here salvage value is not used in calculation of tax shield)

After we get depreciation we can find tax shield for each year (Tax shield = rate of tax*depreciation expense) for the year

For example in first-year tax shield =28%* 20000= 5600

Similarly we will get tax shield for all years given in the table below

Now to get PV of tax shield we need to calculate the PV of tax shield for each year (PV = Cash flow/(1+r)^n

Here r= 10%

n= year of measurement

For first-year Present value = 5600/(1.1^1)= 5090.9

Similarly we will calculate all present values and the sum of these will give PV of tax shield

Year Asset value Depreciation Tax shield PV of tax shield
1 200000 20000 5600 5090.9
2 180000 36000 10080 8330.6
3 144000 28800 8064 6058.6
4 115200 23040 6451.2 4406.3
Total Present value of tax shield 23886.3

Thus PV of tax shield=23886.3


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