Forward Rates – Self Study
� The t-period forward rate for a loan
repaid in period n is denoted n-tfn
� E.g., 2f5 is the 3-period forward rate for a loan
repaid in period 5 (and borrowed in period 2)
� The following formula is useful for
calculating t-period forward rates:
1+n-tfn = [(1+rn)n / (1+rn-t)n-t]1/t
� Given the data presented below, determine 1f3
and 2f5
If we observe r1 = 8%,
r2 = 9%,
r3 = 9.5%,
r4 = 9.75% and
r5 = 9.875%
� Results: 1f3=10.257795%; 2f5=10.462232%
________________________________________________________
Selected CCA classes
Class
Rate
Asset
1
4%
Brick buildings (acquired after 1987)
6
10%
Fences and frame buildings
8
20%
Manufacturing and processing equipment
10
30%
Vans, trucks, tractors, and computer
equipment
16
40%
Taxicabs and rental cars
22
50%
Excavating equipment
Steps to Calculate Yearly CCA Deductions and CCA Tax Shields
1. Determine the asset class and relevant CCA rate. See table
above.
2. Determine the first CCA deduction (assumed to be at the end of
the first year). Revenue Canada imposes the “half-year rule” (or
50-percent rule) for the first CCA deduction.
CCA1 = ½∙C∙d
where C = initial cost of the asset, d = CCA rate
3. Calculate CCA tax shield (tax saving):
CCA tax shieldt = CCAt∙Tc
4
5.
6.
7.
Determine the undepreciated capital cost (UCC) remaining for
the beginning of the next year.
For t>1, UCCt,beginning = UCCt-1,ending = UCC t-1beginning –
CCA t-1
Determine the next CCA deduction. (The “half-year rule” does
not apply after the 1st CCA deduction.)
For t>1, CCAt = UCCt,beginning∙ d
Go to step 3 and continue.
Note: Since only a percentage of UCC is deducted each year as
CCA, the UCC will never drop to zero. Thus, the CCA and CCA
tax shields will also continue forever.
If an asset is sold in a future time period, then the UCC at that
time is reduced by the sale price. This results in lower CCA
deductions and lower CCA tax shields following the asset sale.
Example: DuoCity Taxi is considering expanding its fleet.
 The cost of the new taxis is $1,000,000 now.
 Taxis fall under CCA Class 16 and are allowed a CCA
rate of 40%.
 DuoCity’s tax rate is 45% and the relevant
opportunity cost of capital is 15%.
 Assume the taxis relevant to this project will be sold
at the beginning of the 6th year for $100,000.
 The project will generate revenues in excess of
expenditures of $450,000 per year for 5 years.
 The project will also require an immediate working capital
increase of $50,000, no intermediate changes, and a
reversion to normal working capital requirements at the
end of 5 years.

Year
CCA
CCA tax shield
Ending UCCt = Beginning
UCC t+1
CCA
CCA tax shield
Ending UCCt = Beginning
UCCt+1
1000,000*.4
*1/2 = 200,000
800,000 * .4 =
320,000
192000
200,000* .45
=90000
320,000 * .45 =
144000
86,400
1000,000 -200,000 =
800,000
800,000 – 320,000 =
480,000
288,000
1
2
3
4
5
Year
1
2
3
4
5
Year
115200
51,840
172,800
69120
31,104
3,680
0 ($)
Asset
Purchase/sale -1,000,000
Net Revenue
0
less Expense
Working Capital
-50,000
Net
-1,050,000
1 ($)
2 ($)
3 ($)
4 ($)
5 ($)
0
0
0
0
100,000
247,500
247,500
247,500
247,500
247,500
0
0
0
0
50,000
247,500
247,500
247,500
247,500
397,500
NPV of above cash flows =-$145,765.10
PV of CCA tax shields =$289,657.62
NPV of the project =$143,892.52 with CCA tax shield formula but
NPV with the yearly CCA tax deduction approach is $143,293.73
 If the asset is sold for an amount greater than its initial cost,
a capital gain is said to occur.
Capital Gain = Sales Price – Initial Cost
 When there is capital gain, the UCC is reduced in the year of
the sale by the initial cost, C, and an additional tax is applied
to the capital gain.
Capital Gains Tax = ½∙capital gain∙Tc
 Calculate the PV of CCA tax shield and the PV of capital gains
tax assuming the taxis were sold for…
 $500,000
 $1,200,000
IF No Capital gain then use this formula for PV CCA tax shield
 k
1  
C  d  Tc  2 
S  d  Tc
1
PVCCA Tax Shields 
 n

k  d 1  k 
k  d 1  k n
IF Capital gain then use this formula for PV CCA tax shield
PVCCA Tax Shields (when Sn C)
 k
1  
C  d  Tc  2 
C  d  Tc
1



k  d (1  k )
k  d (1  k ) n
 When calculating the project NPV, don’t forget to deduct the PV of the capital
gains tax too by using Capital Gains Tax = ½∙capital gain∙Tc.