Valuation of Assets and Liabilities: formula sheet

Key formulas

Value vs price

Value = estimated worth for a purpose and date; Price = amount actually paid

Price can differ from value because of urgency, negotiation, or special buyer motives.

Fair market value test

FMV = price between hypothetical willing, informed buyer and seller, neither under compulsion

It is a hypothetical, not a real, transaction. Buyer-specific synergies are excluded.

Fair value (Ind AS 113)

Fair value = exit price in an orderly transaction between market participants at the measurement date

It is market-based, not entity-specific. Transaction costs are not deducted from the fair value.

Investment value

Investment value = worth to a specific investor given its own requirements and synergies

It can be higher than fair market value. It is not a market-participant view.

Premise link

Going concern ≥ orderly liquidation ≥ forced liquidation (usual order of value)

This is a general tendency for an asset, not a guaranteed rule. For a loss-making business, liquidation value can exceed going-concern value.

Adjusted net asset value

Adjusted net assets = Fair value of assets − Fair value of liabilities (including contingent liabilities that are likely)

Add unrecorded assets such as brands if they can be valued. Value per share = adjusted net assets ÷ number of equity shares, after deducting preference capital if any.

Market multiple valuation

Value = Comparable multiple × Subject's metric (e.g. P/E × EPS, or EV/EBITDA × EBITDA)

With an EV multiple you get enterprise value. Deduct net debt to reach equity value.

Present value of a cash flow

PV = CF ÷ (1 + r)^n

r is the discount rate and n the year. Discount each year's cash flow separately.

Terminal value (constant growth)

TV at end of year n = CFₙ × (1 + g) ÷ (r − g)

Valid only when r > g. Discount TV back using the year-n factor.

Enterprise to equity value

Equity value = Enterprise value − Debt + Cash and surplus assets

Use FCFF discounted at WACC to get enterprise value.

Depreciated replacement cost (DRC)

DRC = Replacement cost new − Physical deterioration − Functional obsolescence − Economic obsolescence

Use for plant, machinery and specialised buildings. If a question gives a total depreciation percentage, apply it to replacement cost new.

Straight-line physical depreciation

Depreciation % = Age ÷ Total useful life × 100

Use effective age (condition-based) if the question gives it instead of actual age.

Cost of replacement with price index

Replacement cost new = Historical cost × (Current index ÷ Index at purchase)

Use when no current quote is given. Index trending is only an estimate.

Net realisable value (NRV)

NRV = Estimated selling price − Cost to complete − Selling costs

Compare with cost item by item or group by group, not on the grand total of unrelated items.

Inventory carrying value

Lower of cost and NRV

This is the usual accounting rule under Ind AS 2. For fair value purposes, follow the basis stated in the question.

Building value (cost method)

Value = Land value + (Replacement cost of building − Depreciation)

Value land separately by market comparison. Do not depreciate land.

Capitalised rental value

Value = Net annual income ÷ Capitalisation rate

Net income is after outgoings such as property tax and maintenance.

Scaling by capacity (cost approach)

Cost of new asset = Cost of known asset × (New capacity ÷ Known capacity)^n

Use only if the question gives the exponent n. Often n is given as 0.6.

Relief-from-royalty value

Value = Σ [Revenue_t × Royalty rate × (1 − Tax rate)] ÷ (1 + r)^t

Use only the revenue attributable to the asset. Add terminal value if life is indefinite.

Excess earnings

Excess cash flow = After-tax operating profit from the asset − Contributory asset charges

Contributory charge = fair value of asset × required return on that asset. Discount excess cash flow at the rate for the intangible being valued.

Contributory asset charge

Charge = Fair value (or carrying value) of contributory asset × Required return

Charge is pre-tax or post-tax consistently with the profit it is deducted from.

Goodwill under Ind AS 103

Goodwill = Consideration + NCI + Fair value of previously held interest − Fair value of identifiable net assets

A negative figure is a bargain purchase gain, recognised in other comprehensive income and accumulated in equity as capital reserve after reassessment.

Cost method

Value = Replacement or reproduction cost − Obsolescence

Ignores future profit. Suits assembled workforce or internally developed software.

Present value of annuity-type flows

PV = CF ÷ (1 + r)^t, summed over useful life

Limit the sum to the remaining useful life, for example customer attrition period.

Bond value

V = Σ [C ÷ (1 + r)^t] + M ÷ (1 + r)^n

C is the periodic coupon, r the periodic YTM, M the redemption value, n the number of periods. Use half-yearly r and n for half-yearly coupons.

Approximate YTM

YTM ≈ [C + (M − P) ÷ n] ÷ [(M + P) ÷ 2]

P is the current price. This is an estimate. Use trial and error with interpolation for an exact figure.

Perpetual preference share or irredeemable debt

V = D ÷ r

D is the fixed annual dividend or interest. Applies only when the payments are perpetual and constant.

Redeemable preference share

V = Σ [D ÷ (1 + r)^t] + M ÷ (1 + r)^n

Same structure as a bond, with the dividend in place of the coupon.

Constant growth (Gordon) model

P0 = D1 ÷ (r − g)

D1 = D0 × (1 + g). Valid only when r > g and growth is constant forever.

CAPM cost of equity

r = Rf + β × (Rm − Rf)

Rf is the risk-free rate, Rm the market return.

Ind AS 113 hierarchy

Level 1: quoted prices, identical items. Level 2: other observable inputs. Level 3: unobservable inputs

Highest priority goes to Level 1. Classify by the lowest-level significant input.

Convertible debenture split

Liability component = PV of cash flows at the market rate for similar non-convertible debt; equity component = issue price − liability component

Done at initial recognition. Equity part is not remeasured later.

Present value of a single future payment

PV = FV ÷ (1 + r)^n

r is the discount rate per period and n the number of periods. Use the rate matching the liability's risk.

Value of debt with periodic interest

Value = Σ [Interest ÷ (1 + r)^t] + Redemption amount ÷ (1 + r)^n

Interest is coupon rate × face value. r is the current market yield, not the coupon rate.

Present value of an annuity

PV = A × [1 − (1 + r)^−n] ÷ r

Use for equal instalments at the end of each period (ordinary annuity).

Expected value of a provision

Expected value = Σ (Outflow × Probability)

Suits a large population of items, such as warranties. For a single obligation, the most likely outcome may be the better estimate.

Unwinding of discount

Finance cost for the year = Opening provision × discount rate

The discounted provision grows each year and the increase is charged as a finance cost.

Equity value after liabilities

Equity value = Enterprise value − Debt − Other debt-like items (provisions, guarantees likely to be called)

Add cash and non-operating assets where relevant. Do not deduct the same item twice.

Ind AS 37 treatment rule

Probable + reliable estimate → Provision; Possible, or probable but not reliably measurable → Disclose; Remote → Ignore

Apply it to every item in a case before computing anything.

Recoverable amount

Recoverable amount = Higher of (FVLCD, Value in use)

If either one is above the carrying amount, the asset is not impaired and you need not estimate the other.

Fair value less costs of disposal

FVLCD = Fair value − Direct costs of disposal

Costs include legal costs and transaction costs of sale. Finance costs and tax expense are not disposal costs.

Value in use

VIU = Σ [Cash flow in year t ÷ (1 + r)^t], including net disposal proceeds at end of life

Use pre-tax cash flows and a pre-tax discount rate. Exclude financing cash flows, tax receipts or payments, and enhancement of the asset's performance not yet committed.

Impairment loss

Impairment loss = Carrying amount − Recoverable amount (only if positive)

Recognise in profit or loss, or against revaluation surplus for a revalued asset.

Allocation of CGU loss

Step 1: reduce goodwill. Step 2: reduce other assets pro rata to carrying amounts.

No asset is reduced below the highest of its FVLCD, its VIU (if determinable) and zero.

Reversal limit

Reversal ≤ Carrying amount that would have existed (net of depreciation) had no impairment been recognised

Reversal is allowed for assets other than goodwill. Impairment of goodwill is never reversed.

Quick revision

• Value depends on purpose, date and the basis chosen; always state them first.
• Cost approach: what it would cost to replace or reproduce the asset, less obsolescence.
• Market approach: use prices of comparable assets or transactions, adjusted for differences.
• Income approach: present value of expected future benefits at a suitable discount rate.
• Present value = cash flow ÷ (1 + r)^n for a single cash flow in year n.
• Intangibles are usually valued by income methods when no market prices exist.
• Financial assets with active market prices are valued at those quoted prices.
• A provision is a present obligation with a reliable estimate; a contingent liability is only disclosed.
• Impairment loss = carrying amount − recoverable amount, when carrying amount is higher.
• Recoverable amount is the higher of fair value less costs of disposal and value in use.
• Always end with a clear final value and the assumptions behind it.

Common mistakes

• Treating value and price as the same thing. Fix: Write one line each: value is an estimate for a purpose and date; price is the amount actually paid. Show the gap if the question gives both.
• Adding buyer-specific synergies to fair market value. Fix: Include synergies only under investment value. Fair market value uses a hypothetical buyer and excludes them.
• Using book values in the adjusted net asset method. Fix: Restate every asset and liability to fair value first. Add unrecorded items and remove assets or liabilities that do not exist.
• Applying an EV multiple and stopping there. Fix: Always subtract debt and add cash to reach equity value before dividing by shares.
• Depreciating land along with the building. Fix: Split the property. Land stays at market value. Only the building is depreciated.
• Applying depreciation to historical cost instead of replacement cost new. Fix: In the cost approach, first update to today's cost of a new equivalent asset. Then deduct depreciation from that figure.
• Treating goodwill as an asset valued by royalty or excess earnings. Fix: Goodwill is a residual under Ind AS 103. Value identifiable assets first, then compute goodwill by subtraction.
• Applying the royalty rate to total company revenue. Fix: Apply the royalty only to revenue that uses the brand or patent.
• Using the annual rate and annual periods for a half-yearly coupon bond. Fix: Halve the coupon and the YTM, and double the number of periods before looking up any factor.
• Applying D ÷ r to a share whose dividend is growing, or using D0 instead of D1 in the Gordon model. Fix: Check the growth wording. If there is growth, compute D1 = D0 × (1 + g) first, then divide by (r − g).

Exam tips

• Open every theory answer with purpose, date, standard and premise. Examiners reward this framing.
• In MCQs, watch the keywords: 'exit price' means fair value, 'hypothetical' means fair market value, 'specific investor' means investment value.
• When a question gives both a price and a valuation, comment on the gap. Do not treat them as the same number.
• Be careful with absolute words such as 'always'. Liquidation value can exceed going-concern value for weak businesses.
• For case scenarios, name the standard you chose and give one line of reasoning. A clear recommendation earns more than a long list of definitions.
• Read the data first. Questions usually supply only what the intended approach needs.
• Show the equity bridge (EV less debt plus cash) on its own line. Examiners look for it.
• In MCQs, check the premise: liquidation points to net realisable asset values, going concern to income or market.