In: Finance
A 5-year project requires a $300,000 investment in a machine that is expected to worth $50,000 when the project ends. Operating expenses are expected to be $75,000 in the first year and are expected to increase 3% per year over the life of the project. The appropriate discount rate is 8%, the company’s tax rate is 20%, and the CCA rate is 30%. What is the present value of the CCA tax shield? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Omit any commas and the $ sign in your response. For example, an answer of $1,000.50 should be entered as 1000.50.)
PVCCATS=(IdTcd+k) (1+.5k1+k)− (SndTcd+k) (1(1+k)n)PVCCATS=IdTcd+k 1+.5k1+k- SndTcd+k 1(1+k)
Solution
In CCA method declining balance is used and also in the first year only 50% of CCA Depreciation rate is allowed. In subsequent years full CCA rate can be used
Now Book value at the beginning of year 1 =300000
CCA allowance= 30%/2*300000= 45000
Now tax rate = 20%
Therefore tax shield for first year = 20% of 45000 = 9000 (Tax shield= Depreciation*tax rate)
Present value of tax shield for 1st year = 9000/(1+.08)^1 (Formula PV= Tax shield/(1+r)^n
Where r= rate of discounting , n= year in consideration
=8333.33
Now for second year Beginning book value= Book value 1st year- Depreciation allowance= 300000-45000
=255000
Depreciation allowance= 30% of 255000= 76500
Tax shield= 20% of 76500= 15300
Present value of tax shield=15300/(1.08^2)
=13117.28
Similarly we will get present value of tax shield for subsequent years
Sum of all present values will give present value of tax shield
Present value of tax shield=39034.71
Year | Book value | Depreciation | Depreciation Allowance | Present value |
1 | 300000.00 | 45000.00 | 9000.00 | 8333.33 |
2 | 255000.00 | 76500.00 | 15300.00 | 13117.28 |
3 | 178500.00 | 53550.00 | 10710.00 | 8501.94 |
4 | 124950.00 | 37485.00 | 7497.00 | 5510.52 |
5 | 87465.00 | 26239.50 | 5247.90 | 3571.63 |
Total PV | 39034.71 |