Question

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.

Answer 1

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