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SOLUTIONS TO PROBLEM SET #7 – INCOME TAX CONSIDERATIONS
– Most problems involving taxation can be solved by either one of two
approaches, i.e., using a period-by-period approach, or with tax factors.
In the period-by-
period approach, after-tax cash flows are determined for every period of the project's life, using
revenues, operating expenses, tax payments and capital expenditures.
Appropriate tax regula-
tions are applied for the purpose of determining tax payments.
Then, the project's profitability
and/or whatever other required indicators are determined from the profile of cash flows.
Spreadsheet software is most suited to this approach.
In the second approach, tax factors are
applied to convert the project's before-tax estimates to after-tax values.
The desired indicators
can then be determined from these after-tax values in combination with appropriate time value
In particular circumstances, tax factors often provide a quicker and much simpler
approach to solving a problem.
However, caution should taken with this approach, because tax
factors contain particular built-in assumptions regarding the timing of tax savings.
they should only be used when these assumptions are correct and/or reasonable given the situa-
In cases when the assumptions are inappropriate, the longer period-by-period approach
Only one approach should be used at a time, otherwise, double-counting may occur.
instance, tax payments or savings should be based on the before-tax components of a project,
and not on the after-tax components derived from the application of tax factors.
As well, the
period-by-period approach may still necessitate the use of tax factors under particular circum-
In the Canadian tax system for instance, the capital tax factor is a convenient way of
handling tax credits that extend beyond a project's life when assets are depreciated by the
With practice, the problem-solver will learn to recognize the more suitable approach.
Using the estimates as given, i.e. on a before-tax basis, the rate of return is the discount
rate (r) that yields a net present value of zero.
NPV = -56 000 + 13 500 (P/A,r,7) = 0
(P/A,r,7) = 56 000 / 13 500 = 4.1481
From the compound interest factor tables,
(P/A,15%,7) = 4.1604 and (P/A,16%,7) = 4.0386
By linear interpolation,
r = 15 + (4.1604 - 4.1481) / (4.1604 - 4.0386) = 15.1%
A financial calculator yields a value of 15.10%.