Personal and corporate taxation: formula sheet

Key formulas

Average tax rate

Average rate = Tax paid ÷ Income × 100%

Use total income as the base. This is the test for progressive, proportional or regressive.

Marginal tax rate

Marginal rate = Change in tax ÷ Change in income

This is the rate on the next rupee earned. Under a progressive system the marginal rate is above the average rate.

Progressive tax

Average rate rises as income rises

Higher earners pay a larger percentage of income.

Proportional tax

Average rate is constant at all incomes

A flat percentage. Tax amount still rises with income.

Regressive tax

Average rate falls as income rises

Lower earners pay a larger percentage of income, even if they pay fewer rupees.

Adam Smith's four canons

Equity, Certainty, Convenience, Economy

Memory aid: ECCE. Extra canons include productivity, flexibility and simplicity.

Taxable income

Taxable income = Total income − allowances − deductions

Total income is the sum of salary, interest, dividends, rent and other income. Use only the deductions the question allows.

Slab (progressive) tax

Tax = Σ (rate in slab × income falling in that slab)

Apply each rate only to the part of income inside its band, not to the whole income.

Marginal rate

Marginal rate = rate of the highest slab that your taxable income reaches

Use it to tax an extra rupee of income, or to compare investments at the margin.

Average tax rate

Average rate = Total tax ÷ Total income

Always below the marginal rate in a progressive system once income passes the first taxed slab.

Capital gain

Gain = Sale proceeds − selling costs − purchase cost (adjusted if the question allows indexation)

A negative figure is a capital loss. Loss set-off rules must come from the question.

Capital gains tax

Tax = rate × (gain − any exempt amount)

Choose the short-term or long-term rate from the holding period. Never tax below zero.

After-tax return

After-tax return = pre-tax return × (1 − t)

t is the tax rate on that type of income. Use it to compare interest, dividends and gains.

Taxable profit

Taxable profit = Accounting profit + accounting depreciation + disallowable expenses − capital allowances − exempt income

Start from profit before tax. Use only the adjustments the question gives.

Tax payable

Tax payable = Taxable profit × tax rate

Apply the rate to taxable profit, never to accounting profit. If taxable profit is negative, tax payable is zero and a loss arises.

Reducing balance allowance

Allowance in year t = rate × tax written-down value at start of year t

Tax written-down value = cost − allowances already claimed.

Straight-line allowance

Annual allowance = (cost − residual value) ÷ number of years

Use only when the question says the allowance is straight line.

Tax saving from allowance

Tax saving = capital allowance × tax rate

Discount it from the date the tax is actually saved or paid.

Loss carried forward

Taxable profit after loss relief = profit before loss relief − loss brought forward (not below zero)

Any unused loss is carried forward again, if the rules allow.

Interest tax shield (annual)

Tax shield = Tc × interest = Tc × rd × D

Tc is the corporate tax rate, rd the interest rate and D the debt. Assumes the company has enough taxable profit to use the deduction.

After-tax cost of debt

kd(after tax) = rd × (1 − Tc)

Use this in WACC. For redeemable debt, find the IRR using after-tax interest and redemption cash flows.

MM proposition I with corporate tax

VL = VU + Tc × D

Assumes permanent, risk-free debt, no distress costs and no personal taxes. VL is the geared firm value and VU the ungeared value.

MM proposition II with corporate tax

ke(L) = ke(U) + (ke(U) − kd) × (1 − Tc) × D ÷ E

The cost of equity rises with gearing, but less steeply than without tax. kd is the pre-tax cost of debt. E is the market value of equity.

WACC with tax

WACC = [E ÷ (E + D)] × ke + [D ÷ (E + D)] × kd × (1 − Tc)

Use market values for E and D where possible.

Present value of a perpetual shield

PV(shield) = Tc × rd × D ÷ rd = Tc × D

Discount at the cost of debt, since the shield is as certain as the interest payments.

Net gain from gearing (Miller)

Gain = [1 − (1 − Tc)(1 − Te) ÷ (1 − Td)] × D

Te is the personal tax rate on equity income and Td the personal tax rate on debt income. If (1 − Tc)(1 − Te) = (1 − Td), the gain is zero.

Quick revision

• Direct tax is levied on income or wealth of the person who pays it; indirect tax is levied on spending and passed on.
• Progressive tax takes a rising share as income rises; proportional takes a constant share; regressive takes a falling share.
• Good tax principles include certainty, fairness, convenience and economy of collection.
• Taxable income = gross income − allowable deductions and reliefs.
• Capital gain = sale proceeds − cost (after allowable costs); apply the gains rules given in the question.
• Taxable profit differs from accounting profit because tax law treats depreciation and some expenses differently.
• Interest is generally tax deductible for companies; dividends are paid from profit after tax.
• Debt tax shield = interest × corporate tax rate, assuming the company has enough profit to use it.
• After-tax cost of debt = pre-tax cost of debt × (1 − tax rate).
• Use after-tax cash flows in project appraisal.
• Tax can favour debt, but financial distress costs limit how much debt is sensible.
• Always state your assumptions, such as the tax rate and timing of tax payment.

Common mistakes

• Calling a tax progressive because richer people pay more rupees. Fix: Always compute tax ÷ income. A flat 10% tax takes more rupees from the rich but is still proportional.
• Saying indirect taxes are always regressive. Fix: Say they are often regressive because poorer households spend more of their income on taxed goods. Luxury taxes can be progressive.
• Applying the top slab rate to the whole income Fix: Tax only the part of income inside each band at that band's rate. Use the marginal rate only for extra income.
• Using the wrong holding period or rate for a gain Fix: Check the holding period against the threshold in the question. Use only the rates the question gives.
• Deducting both accounting depreciation and capital allowances. Fix: Add back accounting depreciation first. Then deduct only the capital allowance.
• Applying the tax rate to accounting profit. Fix: Always finish the adjustments to reach taxable profit before applying the rate.
• Using the pre-tax cost of debt in WACC. Fix: Always write kd × (1 − Tc) in WACC unless the question says interest is not deductible.
• Discounting a perpetual tax shield again at a high rate, such as the cost of equity. Fix: The shield depends on interest payments, which are as risky as debt. Use the cost of debt, which gives Tc × D.

Exam tips

• Show the average-rate calculation even in short answers. Method marks are usually given for it.
• Use the exact words direct, indirect, progressive, proportional and regressive. Examiners look for them.
• In discussion questions, name the canon you are applying and tie it to the tax in the question.
• In MCQs, watch for options that use tax amounts instead of tax rates. Those are usually the traps.
• Revise this topic with personal income tax and corporate taxation, since later questions assume these terms.
• Write your assumptions at the top: regime, rates, holding period threshold. Examiners give marks for clear method even if a figure slips.
• Show the slab table line by line. A tidy table earns method marks and makes errors easy to spot.
• In MCQs, check the answer options for the typical wrong values: whole income at the top rate, or the exemption left out.