Additional Solutions: Chapter Eight: After-Tax Analysis
8S.1
This question was set in Australia, and Australian tax laws were summarised in the Powerpoint presenta-
tion of October 10. However, I will also accept as correct those answers which assume Australia to be a
province of Canada and apply Canadian tax laws.
The best approach is to calculate the present worth of the purchase price and salvage value, convert this
to an equivalent annual cost, then add on the operating expenses, which are already expressed as an
equivalent annual cost:
Under Australian tax law, the annual depreciation over the twelve-year life will be 150%/12 = 12.5%. So
the present worth of the purchase is
PW = -9 600 + 9 600(
P/A
,-12.5%, 8%, 12)× 0.5
× 0.125
We recall that (
P/A,g,i,N
) = (
P/A,i
o
,N
)/(1 +
g
)
where
i
o
= (1 +
i
)/(1 +
g
) – 1 = (1+0.08)/(1 – 0.125) -1 = 23.4%
So the PW of the purchase is -9 600 + 9 600 ×3.9307× 0.5 ×0.125 = - 7 241
After 12 years, the book value of the machine will be 9 600 (1-0.125)
12
= $1934. The salvage value is
less than this, so the company can claim the difference between the book value and the salvage value as a
loss, which can be offset against profits.
So the after-tax income from the salvage is 1,600(1-0.5) + 334(0.5) = 1934 × 0.5
and the present value of this is 1934 × 0.5× (
P/F
,0.08,12) = $372
We convert the after-tax present worths of purchase and salvage to an annuity over twelve years, and sub-
tract the after-tax annual cost of running the machine:
AW = (-7 241 + 372)(
A/P
,0.08,12) – 2 100(0.5) = -1 993
So it costs -$1 993 to run the machine. (We cannot conclude from this whether or not the company
should buy it – that depends on the value to the company of the service it provides.)