24. Fair value estimate

Due to the short‑term cycle, it is assumed that the fair value of cash and cash equivalents balances, financial investments, accounts receivable and accounts payable approximate their book values. For the measurement and determination of fair value, the Company uses various methods including market, income or cost approaches, in order to estimate the value that market participants would use when pricing the asset or liability. The financial assets and liabilities recorded at fair value are classified and disclosed in accordance with the following levels:

Level 1 – Unadjusted quoted prices on an active, liquid and visible market for identical assets or liabilities that are accessible at the measurement date;

Level 2 - Quoted prices (adjusted or unadjusted) for identical or similar assets or liabilities on active markets; and

Level 3 - Assets and liabilities, for which quoted prices, do not exist, or where prices or valuation techniques are supported by little or no market activity, unobservable or illiquid.

a) Assets and liabilities measured and recognized at fair value:


	December 31, 2018				December 31, 2017
	Level 1	Level 2	Level 3	Total	Level 2	Level 3	Total
Financial assets
Financial investments	32	—	—	32	—	—	—
Derivative financial instruments	—	136	295	431	289	270	559
Accounts receivable	—	(108)	—	(108)	170	—	170
Investments in equity securities	987	—	—	987	—	—	—
Total	1,019	28	295	1,342	459	270	729
Financial liabilities
Derivative financial instruments	—	636	178	814	581	209	790
Participative stockholders' debentures	—	1,407	—	1,407	1,233	—	1,233
Total	—	2,043	178	2,221	1,814	209	2,023

The Company changed its accounting estimate on the calculation of the participative stockholders' debentures from January 1, 2018. The Company has replaced in the calculation the assumption of spot price at the reporting date to the weighted average price traded on the market within the last month of the quarter.

There were no transfers between Level 1 and Level 2, or between Level 2 and Level 3 in the year ended December 31, 2018.

The following table presents the changes in Level 3 assets and liabilities for the year ended December 31, 2018:


	Derivative financial instruments
	Financial assets	Financial liabilities
Balance at December 31, 2017	270	209
Gain and losses recognized in income statement	25	(31)
Balance at December 31, 2018	295	178

Methods and valuation techniques

i) Derivative financial instruments

Derivative financial instruments are evaluated through the use of market curves and prices impacting each instrument at the closing dates, detailed in the item "market curves” (note 34).

For the pricing of options, the Company often uses the Black & Scholes model. In this model, the fair value of the derivative is determined basically as a function of the volatility and the price of the underlying asset, the strike price of the option, the risk free interest rate and the option maturity. In the case of options where payoff is a function of the average price of the underlying asset over a certain period during the life of the option, the Company uses Turnbull & Wakeman model. In this model, in addition to the factors that influence the option price in the Black-Scholes model, the formation period of the average price is also considered.

In the case of swaps, both the present value of the long and short positions are estimated by discounting their cash flows by the interest rate in the related currency. The fair value is determined by the difference between the present value of the long and short positions of the swap in the reference currency.

For the swaps indexed to TJLP, the calculation of the fair value assumes that TJLP is constant, that is, the projections of future cash flows in Brazilian Reais are made considering the last TJLP disclosed.

Forward and future contracts are priced using the future curves of their corresponding underlying assets. Typically, these curves are obtained on the stock exchanges where these assets are traded, such as the London Metals Exchange (“LME”), the Commodity Exchange (“COMEX”) or other providers of market prices. When there is no price for the desired maturity, Vale uses an interpolation between the available maturities.

The fair value of derivatives within level 3 is estimated using discounted cash flows and option model valuation techniques with unobservable inputs of discount rates, stock prices and commodities prices.

ii) Participative stockholders’ debentures - Consist of the debentures issued during the privatization process (note 13), for which fair values are measured based on the market approach. Reference prices are available on the secondary market.

Critical accounting estimates and judgments

The fair values of financial instruments that are not traded in active markets are determined using valuation techniques. Vale uses its own judgment to choose between the various methods. Assumptions are based on the market conditions, at the end of the year.

An analysis of the impact if actual results are different from management’s estimates is present on note 34 (sensitivity analysis).

b) Fair value of financial instruments not measured at fair value

The fair value estimate for level 1 is based on market approach considering the secondary market contracts. For loans allocated to level 2, the income approach is adopted and the fair value for both fixed‑indexed rate debt and floating rate debt is determined on a discounted cash flow basis using LIBOR future values and Vale’s bonds curve.

The fair values and carrying amounts of loans and borrowings are as follows:


Financial liabilities	Balance	Fair value	Level 1	Level 2
December 31, 2018
Debt principal	15,228	16,262	10,686	5,576
December 31, 2017
Debt principal	21,955	23,088	14,935	8,153