1. A Placidian manufacturing company bought a truck for $35,000. After 10 years the
truck’s salvage value will be $5,000. The truck is expected to produce revenue of
$10,000/year, while maintenance costs are expected to be $1,000/year. If the annual
interest rate is 10%, the corporate tax rate is 35%, and straight-line depreciation is
applied, with no first-year rule, and considering only the cashflows mentioned in the
question, how much will the company pay in tax in the first year?
Answer:
Tax is imposed on net income, which is the difference between annual revenue and
total annual expenditure. Annual revenue is $10,000 and the total annual costs are
depreciation plus maintenance. [Presumably the truck also has a driver, otherwise
what’s the point of having it, but the driver’s salary isn’t mentioned, so we’ll ignore
it.]
Since the Placidian tax authorities [unlike Canada] use straight-line depreciation, the
annual depreciation amount is
D = (P-S)/N = (35,000-5,000)/10 = $3000 (5 points; they can have 3 points for
answering $3,500)
So total annual costs are $3,000+$1,000 = $4,000, and the before-tax income is
Income = Revenue – Costs = $10,000 - $4,000 = $6,000 (5 points; if they said 3,500
for part (i), they can have $5,500 here and still get 5 points)
So the tax due is 6,000 * 0.35 = $2,100 (5 points; if they said 5,500 for part (ii),
they would get $1,925 here)
2. An engineering project involves the purchase of a capital asset with a first cost of
$100,000, operating costs of $5,000/year, and a service life of 10 years. The expected
revenue is $20,000 per year. If the CCA rate for this asset is 25%, the MARR is 10%,
and the corporate tax rate, t, is 33%, what is the after-tax present value of the project?
Answer:
The present worth of the project is:
PW(Revenue) * (1-t) – PW(capital costs) – PW (operating costs) * (1-t) (5 points if
they are clearly using this equation)
The PW of the capital costs is:
PW = CTF * 100,000
= (1 – (0.33*0.25*(1+0.1/2))/((0.1+0.25)*(1+0.1))) * 100,000
=(1 – 0.33*0.25*1.05/ 0.385) * 100,000
=(1 – (0.0866)/ 0.385) * 100,000
=0.775* 100,000
= 0.775 * 100,000
= 77,500
(5 points; they can also get this result by adding up the present value of
tax savings over the ten years)
Therefore,
PW(Project) = 20,000(P/A,0.1,10)*(1-0.33) – 77,500 - 5,000(P/A,0.1,10)*(1-0.33)
= 20,000 * 6.1445 * 0.67 – 77,500 – 5,000 * 6.1445 *0.67
= 82,337 – 77,500 – 20,584
= -$15,747
(10 points for getting this result; if they make numerical errors
along the way, but are using the right method, 1 point off for
each error.)
(So it’s not a good project.)
3. An engineering company just bought a bending machine for $50,000. Its service
life is 10 years, at the end of which time it will be worth $2,000. It depreciates by
declining balance depreciation, both in the company books and in Revenue Canada’s
asset class for machinery of this type. The services that the machine provides bring in
$10,000 in annual revenue, and its operating costs are $2,000 per year. If the
company’s after-tax MARR is 5% and it is taxed at t = 30%, find the present worth of
the investment.
Answer:
The depreciation rate is
D = 1 – (2,000/50,000)1/10 = 0.275 (5 points)
The present worth of the investment is
PW = (10,000-2,000)(P/A,0.05,10)(1-t) – CTF*50,000 + CSF*2,000*(P/F,0.05,10)
(5 points; they may use “CCTF” and “CCTF*” in place of CSF and CTF; that’s
OK.)
Using the formulas at the back of the book,
CTF = 1 – (0.3*0.275*(1+0.05/2))/((0.05+0.275)(1+0.05)) = 0.7522 (3 points)
CSF = 1 – 0.3 * 0.275 / (0.05 + 0.275) = 0.746 (2 points)
And the present worth of the investment is therefore:
PW = 8000 * 7.7217 * (1-0.3) – 0.7522 * 50,000 + 0.746 * 2,000 * 0.6139
= 43,241 – 37,610 + 916
= $6,547 (5 points)
4. A company just bought a new piece of equipment for a million dollars. It’s a Class
8 asset, which means that Revenue Canada considers it to depreciate at 20% per
annum. However, in reality the machine is wearing out, and losing value, at 25% per
annum, and the salvage price the company will be able to get for it reflects this
depreciation rate. The company’s after-tax MARR is 8% and the corporate tax rate is
36%.
What is the after-tax present worth of the salvage price we expect to get for the
machine when we sell it in 10 years time?
Answer:
First, we calculate the salvage price we expect to get. This is:
S = 1,000,000 * (1-0.25)10
= $56,313 (5 points)
The present worth of this is
PW(S)
= 56,313 * CSF * (P/F,0.08,10)
CSF = 1 – 0.36*0.2/(0.08+0.02) = 0.7429 (5 points)
Therefore
PW(S) = 56,313*0.7429 * 0.463
= $19,376 (5 points)
So the maximum possible score for the assignment is 70 points.