CFA Level III · Private Wealth Pathway

Preserving the Wealth: formula sheet

Full chapter guide

Key formulas

Taxable estate: Taxable estate = Gross estate − Deductions (debts, expenses, spousal and charitable transfers where allowed) − Exemption; Use only the deductions and exemptions the question gives. Rules vary by jurisdiction.
Estate tax payable: Estate tax = Taxable estate × Tax rate; Applies to the whole estate. If the question gives progressive bands, tax each band separately.
Inheritance tax by heir: Inheritance tax = (Amount received by heir − Heir's allowance) × Heir's rate; Computed per heir. Allowance and rate may depend on the relationship to the deceased.
Net amount to heirs: Net to heirs = Gross estate − Debts and expenses − Transfer taxes; Gifts made earlier may be added back or taxed separately depending on the rules given.
Future value of a transferred asset: FV = PV × (1 + g)^n; Used when comparing a lifetime gift with a bequest. A gift can move future growth out of the estate.
Core capital: Core capital = PV of after-tax spending needs and liabilities (discounted at a conservative rate, over the client's planning horizon); Include inflation in spending growth. Add any lump-sum liabilities, such as taxes due or planned large purchases. A higher confidence level or lower discount rate raises core capital.
Excess capital: Excess capital = Investable assets − Core capital; Positive means surplus available for gifts or transfer. Negative means a shortfall.
Present value of a growing annuity (real return form): Real rate ≈ (1 + nominal) ÷ (1 + inflation) − 1; PV = Annual spending × [1 − (1 + r)^−n] ÷ r; Use when spending is level in real terms. Compute the real rate exactly if the question gives nominal return and inflation. Use the beginning-of-year version (annuity due) if spending is taken at the start of each year.
Capital sufficiency check: Sufficiency = Investable assets ÷ Core capital; Above 1 means core needs are covered. Below 1 means the plan is not fully funded.
After-tax value of a bequest: FV of bequest = V0 × (1 + r)^n × (1 − t_e); V0 is today's value, r is the annual growth rate, n is years until death, t_e is the estate tax rate. Assumes the whole asset is taxed at death.
Gift with tax deducted from the gift (tax-inclusive): FV of gift = V0 × (1 − t_g) × (1 + r)^n; t_g is the gift tax rate, taken out of the amount given, so the donor's outlay is V0. Use t_g = 0 for a tax-free gift. Assumes growth is not taxed again at the donor's death.
Gift with tax paid by the donor on top (tax-exclusive): Cost to donor = G × (1 + t_g); for equal outlay V0, G = V0 ÷ (1 + t_g); recipient gets G × (1 + r)^n; The donor funds G plus the tax. The tax paid leaves her estate. To compare with a bequest, set her total outlay equal to V0 and solve for G.
Decision rule: Gift now is better if FV of gift > FV of bequest; Compare like with like: the same starting cost to the donor, and the same horizon.
Break-even comparison: Gift better if (1 − t_g) > (1 − t_e), i.e. t_g < t_e, when growth is untaxed in the gift route; Valid for a gift with tax deducted from the gift. For a tax-exclusive gift with equal outlay, compare 1 ÷ (1 + t_g) with (1 − t_e) instead.
Revocable trust rule: Control retained ⇒ assets generally still in settlor's estate; probate avoided; Good for incapacity planning and privacy. Does not by itself reduce transfer tax or give strong creditor protection.
Irrevocable trust rule: Control given up ⇒ assets generally outside settlor's estate; more protection; Tax and legal outcomes depend on the jurisdiction and on any powers retained by the settlor.
Insurance liquidity need: Liquidity need = estate tax + settlement costs + debts + equalisation payments − liquid assets available; Use to size the insurance cover. Compare the result with the policy premium and the owner's ability to pay it.
Tool selection test: Goal (control, tax, privacy, protection, liquidity) → matching tool; Name the client goal first, then the tool, then the trade-off.
Foreign tax credit (limit): Credit allowed = lesser of (foreign tax paid) and (home tax on the foreign-source asset); A common credit design. It prevents double tax but the client still pays at the higher of the two rates. Check the wording of the question.
Total tax with credit: Total tax = home tax on worldwide estate − allowed credit + foreign tax paid; Use when the home country taxes worldwide assets and gives a credit.
Forced heirship share: Free portion = Estate − (forced share % × Estate); Only the free (disposable) portion can be left at will. Apply any marital regime first to find the estate.
Taxing bases: Tax claim may rest on: residence/domicile, citizenship, or asset situs; Overlapping claims cause double taxation. Treaty tie-breaker rules resolve residence conflicts.
Relief methods: Relief = treaty, foreign tax credit, deduction, or exemption; Credit usually gives more relief than a deduction. Exemption gives the most.
Collar payoff logic: Collar = long stock + long put (strike X_L) + short call (strike X_U); Floor at the put strike, cap at the call strike. A zero-cost collar sets the call premium received equal to the put premium paid.
Protective put: Value at expiry = max(S_T, X), before the premium. Profit = max(S_T, X) − S_0 − P, where P is the put premium (time value ignored).; The position is long stock plus a long put. It keeps all upside above the strike and limits downside to the strike. The premium is paid today. The standard profit formula ignores time value. Only if a question asks for a financing-cost adjustment should you compound amounts at the risk-free rate.
Prepaid variable forward: Investor receives upfront cash (a percentage of the current value of the shares) and delivers a variable number of shares at maturity: all shares if S_T ≤ floor price; a decreasing number of shares as S_T rises between the floor and the cap; and a fixed smaller number of shares above the cap, equal to the original shares × (floor ÷ cap); This is mainly a monetization tool. It gives upfront cash, and the floor also gives downside protection. Above the cap the number of shares delivered stays fixed at the floor/cap fraction, so the investor keeps the shares not delivered and gains from any rise above the cap on them. Between the floor and the cap, the investor gives up the gains. Tax treatment depends on jurisdiction.
After-tax proceeds from sale: After-tax proceeds = Shares × Price − Shares × (Price − Basis) × Tax rate; Price and basis are per share. Use it to compare selling now with the cost of holding a hedged position.
Swap hedge of equity exposure: Client pays the stock return and receives another return (such as an index or a fixed rate); Economically converts the stock's return into the index or fixed return received, without selling the shares. If the client receives an index return, basis risk remains because the stock and the index will not move together. The client keeps legal ownership of the stock, its voting rights and its tax basis, so the position is still legally concentrated. Counterparty credit risk applies. In some jurisdictions an equity swap can be treated as a constructive sale and trigger tax, so do not assume tax is deferred.

Quick revision

Core capital is the amount needed to maintain the client's lifestyle with a high degree of confidence; excess capital is the assets above that level.
Only excess capital should be considered for gifting; giving away core capital risks the client's own security.
Compare gifts and bequests on an after-tax basis at the same point in time, with the same growth assumption.
A lifetime gift can remove future growth from the estate; a bequest may allow a tax basis step-up where the rules provide for it.
Taxes on a gift may be paid by the donor or the recipient depending on the rules given; read the vignette carefully.
Trusts separate legal ownership from benefit; revocable and irrevocable trusts differ in control and tax treatment.
Foundations suit long-term or charitable goals; insurance can provide liquidity to pay estate taxes.
Forced heirship rules can restrict who inherits regardless of the client's wishes.
Cross-border cases depend on residence, citizenship and asset location; tax treaties or credits may relieve double taxation.
Concentrated positions carry single-asset risk; options include selling, hedging, monetising, exchange funds and gifting.
Link every recommendation to the client's objectives and constraints, and give the reason in a short sentence.
Type a correct calculated number on its own if needed; only the number of responses asked for is evaluated.

Common mistakes

Mixing up estate tax and inheritance tax. Fix: Ask who is taxed and on what base. Estate tax: the estate's total. Inheritance tax: each heir's share.
Saying a will avoids probate. Fix: A will is what probate validates. To avoid probate, use a trust, joint survivorship or named beneficiaries, subject to local rules.
Using a high expected return to discount core spending Fix: Core capital is meant to be secure. Use the conservative rate the question specifies for funding the lifestyle, and say why.
Ignoring inflation or taxes on spending Fix: Either grow spending at inflation and discount at nominal, or use the real rate on today's spending. Use after-tax figures if the question gives taxes.
Taxing the growth in the gift route as if it stayed in the donor's estate. Fix: Ask where the growth happens. After a completed gift it belongs to the recipient, unless the question says otherwise.
Comparing options with different costs to the donor. Fix: Set the donor's total outlay equal in both routes before comparing.
Saying a revocable trust removes assets from the taxable estate. Fix: Remember that retained control generally keeps the assets in the estate. A revocable trust mainly avoids probate and helps with incapacity and privacy.
Recommending an irrevocable trust without noting loss of control. Fix: Always add the trade-off: the settlor cannot normally take the assets back or change the terms.
Assuming the client's will works in every country. Fix: State that a will may need to be valid or recognised in each jurisdiction, and that separate wills or local advice are often needed.
Applying forced heirship to common law countries by default. Fix: Link forced heirship mainly to civil law (and some religious law) systems. Common law generally gives testamentary freedom, with limited exceptions.

Exam tips

Read the command word in bold. 'Calculate' needs a number only. 'Justify' needs a reason tied to the client.
Show each deduction line so partial credit is possible if one number is wrong, but put the final figure clearly.
Always state who pays: the estate for estate tax, the heir for inheritance tax, the donor or donee for gift tax as the question states.
In cross-border vignettes, mark domicile, citizenship and asset location before any maths.
Recommendations should be short: tool, reason, client objective. Do not list every feature.
Show the real rate, the annuity inputs and the final subtraction on separate lines. A correct number alone earns credit, but shown work protects you if you slip.
Match the command word: calculate asks for numbers; recommend or justify asks for a reason tied to goals and constraints. Keep it short.
Read the timing of withdrawals and the stated discount rate carefully. These are the most common traps in the question.