ACC 371 - Supplemental Note on CCA Tax Shields
The purpose of this note is to provide more detailed information on capital budgeting decisions involving depreciable
assets. Let C be the capital cost of an asset, S be its salvage value (and assume that salvage takes place at the end of
year n), Tc be the corporate tax rate, k be the opportunity cost of capital, and d be the CCA depreciation rate for the
relevant asset class.
Consider the following formula for the present value of CCA tax shields:
∆UCCdTc
CdTc 1 + 0.5k
−
× (1 + k)−n ,
PV of CCA tax shield =
k+d
1+k
k+d
(1)
where ∆UCC is the change in the undepreciated capital cost of the asset class due to the disposition of the asset.
Intuitively, the first term on the right hand side of (1) is the present value of a perpetual tax shield starting in year 0
(adjusted for the half year rule by the term in square brackets), and the second term is the reduction in the present
value of the tax shield arising from the disposal of the asset.
The amount of ∆UCC depends on the particular circumstances. Let the undepreciated capital cost of the asset class
just before the asset is disposed of be UCC n .1 Calculate the value
X = UCCn − min(C, S).
(2)
Note that the term min(C, S) is known as the “adjusted cost of disposal”. Then:
• If X < 0, there is recaptured depreciation. X must be added to taxable income at the time of disposition, and
the UCC of the asset class is set to zero. In this case ∆UCC = UCC n (the firm loses depreciation on the entire
amount of undepreciated capital cost prior to the disposition of the asset), so we can write equation (1) more
precisely as:
UCCn dTc
CdTc 1 + 0.5k
−
× (1 + k)−n .
(3)
PV of CCA tax shield =
k+d
1+k
k+d
Also, the present value of the recapture is −XTc ×(1+k)−n, which is negative because it represents an increase
in the firm’s tax liability.
• If X > 0 and the firm has no other assets remaining in this CCA asset class, there is a terminal loss. X is
subtracted from taxable income at the time of disposition, and the UCC of the asset class is reduced to zero. In
this case:
UCCn dTc
CdTc 1 + 0.5k
−
PV of CCA tax shield =
× (1 + k)−n ,
(4)
k+d
1+k
k+d
i.e. the same as for recaptured depreciation. In addition, the present value of the terminal loss is XT c ×(1+k)−n ,
which is positive since it implies a reduction in the firm’s tax liability.
• If X > 0 and the firm does have other assets in this class, X becomes the new UCC of the asset class. In this
situation:
min(C, S)dTc
CdTc 1 + 0.5k
−
PV of CCA tax shield =
× (1 + k)−n .
(5)
k+d
1+k
k+d
Two other points:
1. If S > C, the firm has a capital gain. With the current 50% inclusion rule, the present value of the associated
increased tax liability is −0.5(S − C)Tc × (1 + k)−n .
1 Note
that if the firm only ever has this asset in the class, then UCCn = C(1 − d/2)(1 − d)n−1 .
2. As written, equation (1) has a half year rule adjustment applied to the first term but not to the second term. This
may not always be the case: the half year rule may instead be applied to both terms, neither term, or the second
term but not the first, depending on circumstances. In particular, the net acquisitions rule works as follows.
Recall that all assets of a given firm within a single CCA class are treated as part of a common pool. In practice,
firms often buy and sell many assets in a single class within a year. Define net acquisitions for an asset class as
the total capital cost of all acquisitions (in a year) less the total adjusted cost of all disposals within that class
and in that year. If net acquisitions is positive, apply the half year rule. If net acquisitions is negative, there is
no adjustment for the half year rule.2
Illustrative Problem: You are considering whether to undertake a project that will generate revenues of $50,000 per
year for 8 years and expenses of $20,000 per year for 8 years. The project requires an investment of $150,000 today
in class 8 machinery (d = 25%). Assume k = 12% and Tc = 40%, and calculate project NPV under the following
scenarios:
1. You always have many other class 8 assets and a positive UCC in that class and you can salvage the machinery
at the end of the 9th year for (i) $10,000; and (ii) $200,000. (Assume there are no other acquisitions or disposals
of class 8 assets in either the current year or in the 9th year.)
2. The machinery will always be in its own class and it can be salvaged in 9 years for (i) $10,000; (ii) $20,000; and
(iii) $200,000.
3. From this point on, the machinery will be in its own class and it can be salvaged in 9 years for $10,000. However,
you purchased one other class 8 asset 5 years ago for $200,000 which you have just sold for (i) $100,000; and
(ii) $175,000.
Solution:
1. (i)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
PV perpetual tax shield on $150,000:
PV lost tax shield:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$10,000/1.129
[$150,000(.25)(.40)/(.12 + .25)](1.06/1.12)
X = UCC9 − $10,000 > 0 by assumption;
other assets so X becomes new UCC
[−$10,000(.25)(.40)/(.12 + .25)]/(1.129)
NPV:
-$150,000.00
$149,029.19
-$59,611.68
$3,606.10
$38,368.73
-$974.62
-$19,582.28
(ii)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
PV capital gain tax:
PV perpetual tax shield on $150,000:
PV lost tax shield:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$200,000/1.129
−$50,000(.5)(.4)/1.129
[$150,000(.25)(.40)/(.12 + .25)](1.06/1.12)
X = UCC9 − $150,000 > 0 by assumption;
other assets so X becomes new UCC
[−$150,000(.25)(.40)/(.12 + .25)]/(1.129)
NPV:
2 Note
that this is not what it says in the Appendix to Chapter 7 from the text. That source is incorrect.
-$150,000.00
$149,029.19
-$59,611.68
$72,122.00
-$3,606.10
$38,368.73
-$14,619.33
$31,682.81
2. (i)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
PV perpetual tax shield on $150,000:
PV lost tax shield:
PV terminal loss tax decrease:
NPV:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$10,000/1.129
[$150,000(.25)(.40)/(.12 + .25)](1.06/1.12)
UCC9 :
$150,000(1 − .125)(1 − .25)8 = $13,139.82
X = $13,139.82 − $10,000 = $3,139.82;
no other assets so terminal loss
[−$13,139.82(.25)(.40)/(.12 + .25)]/(1.129 )
$3,139.82(.4)/1.129
-$150,000.00
$149,029.19
-$59,611.68
$3,606.10
$38,368.73
-$1,280.64
$452.90
-$19,435.40
(ii)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
PV perpetual tax shield on $150,000:
PV lost tax shield:
PV recapture tax increase:
NPV:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$20,000/1.129
[$150,000(.25)(.40)/(.12 + .25)](1.06/1.12)
UCC9 :
$150,000(1 − .125)(1 − .25)8 = $13,139.82
X = $13,139.82 − $20,000 = −$6,860.18;
recaptured depreciation
[−$13,139.82(.25)(.40)/(.12 + .25)]/(1.129 )
−$6,860.18(.4)/1.129
-$150,000.00
$149,029.19
-$59,611.68
$7,212.20
$38,368.73
-$1,280.64
-$989.54
-$17,271.74
(iii)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
PV capital gain tax:
PV perpetual tax shield on $150,000:
PV lost tax shield:
PV recapture tax increase:
NPV:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$200,000/1.129
−$50,000(.5)(.4)/1.129
[$150,000(.25)(.40)/(.12 + .25)](1.06/1.12)
UCC9 :
$150,000(1 − .125)(1 − .25)8 = $13,139.82
X = $13,139.82 − $150,000 = −$136,860.18;
recaptured depreciation
[−$13,139.82(.25)(.40)/(.12 + .25)]/(1.129)
−$136,860.18(.4)/1.129
-$150,000.00
$149,029.19
-$59,611.68
$72,122.00
-$3,606.10
$38,368.73
-$1,280.64
-$19,741.26
$25,280.24
3. (i)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
Tax shields:
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$10,000/1.129
PV perpetual tax shield on $50,000:
PV continuing tax shield on $55,371.09:
PV lost tax shield:
PV recapture tax increase (year 9)
PV avoided recapture (today)
NPV
UCC from previous asset in class:
$200,000(1 − .125)(1 − .25)4 = $55,371.09
X = $55,371.09 − $100,000 = −$44,628.91
Net acquisitions:
$150,000 − $100,000 = $50,000
[$50,000(.25)(.40)/(.12 + .25)](1.06/1.12)
$55,371.09(.25)(.40)/(.12 + .25)
UCC9 :
$50,000(1 − .125)(1 − .25)8 +
$55,371.09(1 − .25)9 = $8,537.46
X = $8,537.46 − $10,000 = −$1,462.54;
recaptured depreciation
[−$8,537.46(.25)(.40)/(.12 + .25)]/(1.129)
−$1,462.54(.4)/1.129
$44,628.91(.4)
-$150,000.00
$149,029.19
-$59,611.68
$3,606.10
$12,789.58
$14,965.16
-$832.08
-$210.96
$17,851.56
-$12,413.13
(ii)
Cost of machine:
PV after-tax operating revenues:
PV after-tax operating expenses:
PV salvage:
Tax shields:
PV perpetual tax shield:
PV lost tax shield:
PV recapture tax increase (year 9)
PV avoided recapture (today)
NPV
(1 − .4) × $50,000 × A812%
−(1 − .4) × $20,000 × A812%
$10,000/1.129
UCC from previous asset in class:
$200,000(1 − .125)(1 − .25)4 = $55,371.09
X = $55,371.09 − $175,000 = −$119,628.91
Net acquisitions:
$150,000 − $175,000 = −$25,000
Perpetual tax shield will be on:
$55,371.09 − $175,000 + $150,000 = $30,371.09
[$30,371.09(.25)(.40)/(.12 + .25)]
UCC9 :
$30,371.09(1 − .25)9 = $2,280.40
X = $2,280.40 − $10,000 = −$7,719.60;
recaptured depreciation
[−$2,280.40(.25)(.40)/(.12 + .25)]/(1.129)
−$7,719.60(.4)/1.129
$119,628.91(.4)
-$150,000.00
$149,029.19
-$59,611.68
$3,606.10
$8,208.40
-$222.25
-$1,113.51
$47,851.56
-$2,252.19