MGTB09H3 – Principles of Finance
A note on calculating the PV of the CCA tax shield
(Topic V. Capital Budgeting, B&C Chapter 14)
This note explains how to calculate the present value of the CCA tax shield, using both the time line
approach and the formulas, when:
1) The asset class remains open, no capital gains (this is similar to the example on slides 47 to 53,
Note: we do not discuss the case where the asset class remains open and there are capital gains
2) The asset class is closed, no capital gains
3) The asset class is closed, capital gains
Note that formulas 14‐3 and 14‐9 from the book contain a small error, which is explained below.
1) Asset class remains open, no capital gains
Consider the following example. Java Café is considering investing in a project with:
‐ Initial investment $40,000
‐ Salvage value $30,000
‐ CCA rate 10%
‐ Length of project 3 years
The cost of capital is 8% and the tax rate is 45%. Calculate the present value of the CCA tax shield.
Note that since the salvage value is less than the original purchase price, there are no capital gains. The
asset class remains open.
Time line approach:
First, calculate the CCA tax shield in years 1 to 3:
Year UCC beg CCA UCC end CCA tax shield
1 $40,000 $2,000 (=0.10*0.5*40,000) $38,000 $900 (=0.45*2000)
2 $38,000 $3,800 (=0.10*38,000) $34,200
3 $34,200 $3,420 $30,780 $1,539
The UCC at the end of year 3 is $30,780, and the salvage value is $30,000. Since the asset class remains
open after the asset is sold, the difference of $780 continues to generate a tax shield after year 3. The
additional tax shield in year 4 is $780*0.10*0.45 = $35.10. This will grow at a constant rate of ‐10%
forever. Hence, this can be seen as a growing perpetuity and the present value at t=3 of all future CCA
tax shields as of year 4 equals: $35.10 / (k+d) = $35.10 / 0.18 = $195. We can now calculate the present
value at t=0 of all CCA tax shields:
2 3 3
PV = 900/1.08 + 1710/1.08 + 1539/1.08 + 195/1.08 = $3,675.89
Alternatively, we can use the formula given on slide 46 (i.e. formula 14‐7 from the book) to calculate the
PV of the CCA tax shield. This should always lead to the same answer as the time line approach.
(C 0)( )( ) (1 0.5 ) (SV n)( )( ) 1
PV CCA_ta_shield × − × n
d + k (1+ k) (d + k) (1+ )k
40,000⋅0.10⋅0.45 1.04 30,0000⋅0.10⋅0.45 1
PV CCA_ta_shield × − ×
0.10+ 0.08 1.08 0.10+ 0.08 1.083
PV = $3,675.89(same answer as time line approach!)
2) Asset class closed, no capital gains
When the asset class is closed, we have to check whether there is a CCA recapture or a terminal loss.
Again, we can calculate the PV of all CCA tax shields using the time line approach and the formula
approach and both should lead to the same answer.
Time line approach:
The CCA tax shields in years 1, 2 and 3 are still the same as before (i.e. $900, $1,710 and $1,539). Two
things change, compared to the situation when the asset class remains open.
1) Since the asset class is now terminated, the difference between the ending UCC of $30,780 and
the salvage value of $30,000 won’t generate any other future tax shields after the asset is sold.
(i.e. we should NOT include the $195 in our calculations)
2) Since the asset class is terminated, we should check whether there is a CCA recapture or
terminal loss. The ending UCC exceeds the salvage value, which implies that there is a termina