(15) Fair value is defined as the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date. To determine fair value, the Company uses various methods including market and income approaches. The Company utilizes valuation models and techniques that maximize the use of observable inputs. The models are industry-standard models that consider various assumptions including time values and yield curves as well as other economic measures. These valuation techniques are consistently applied.

Level 1 measurements consist of quoted prices in active markets for identical assets or liabilities. Level 2 measurements include significant other observable inputs such as quoted prices for similar assets or liabilities in active markets; identical assets or liabilities in inactive markets; observable inputs such as interest rates and yield curves; and other market-corroborated inputs. Level 3 measurements include significant unobservable inputs.

The fair values of financial instruments that do not approximate the carrying values in millions of dollars follow:


	April 29, 2018				October 29, 2017				April 30, 2017
	Carrying Value		Fair Value *		Carrying Value		Fair Value *		Carrying Value		Fair Value *
Financing receivables – net:
Equipment operations **	$	76	$	74
Financial services		24,200		23,997	$	25,104	$	24,946	$	23,301	$	23,141
Total	$	24,276	$	24,071	$	25,104	$	24,946	$	23,301	$	23,141

Financing receivables securitized – net:
Equipment operations **	$	113	$	110
Financial services		4,323		4,273	$	4,159	$	4,130	$	4,282	$	4,253
Total	$	4,436	$	4,383	$	4,159	$	4,130	$	4,282	$	4,253

Short-term securitization borrowings:
Equipment operations **	$	113	$	113
Financial services		4,288		4,274	$	4,119	$	4,118	$	4,225	$	4,225
Total	$	4,401	$	4,387	$	4,119	$	4,118	$	4,225	$	4,225

Long-term borrowings due within one year:
Equipment operations **	$	274	$	273	$	154	$	154	$	120	$	119
Financial services		6,566		6,559		6,064		6,079		5,339		5,345
Total	$	6,840	$	6,832	$	6,218	$	6,233	$	5,459	$	5,464

Long-term borrowings:
Equipment operations **	$	5,537	$	5,850	$	5,491	$	6,026	$	4,520	$	5,020
Financial services		20,742		20,769		20,400		20,606		18,733		18,864
Total	$	26,279	$	26,619	$	25,891	$	26,632	$	23,253	$	23,884

* Fair value measurements above were Level 3 for all financing receivables, Level 3 for equipment operations short-term securitization borrowings, and Level 2 for all other borrowings.

** See Note 18.

Fair values of the financing receivables that were issued long-term were based on the discounted values of their related cash flows at interest rates currently being offered by the Company for similar financing receivables. The fair values of the remaining financing receivables approximated the carrying amounts.

Fair values of long-term borrowings and short-term securitization borrowings were based on current market quotes for identical or similar borrowings and credit risk, or on the discounted values of their related cash flows at current market interest rates. Certain long-term borrowings have been swapped to current variable interest rates. The carrying values of these long-term borrowings included adjustments related to fair value hedges.

Assets and liabilities measured at fair value on a recurring basis in millions of dollars follow:


	April 29		October 29		April 30
	2018*		2017*		2017*
Marketable securities
Equity fund	$	46	$	48	$	135
Fixed income fund		14		15		15
U.S. government debt securities		86		77		79
Municipal debt securities		46		39		39
Corporate debt securities		137		135		132
International debt securities		17		20		28
Mortgage-backed securities **		133		118		118
Total marketable securities		479		452		546
Other assets
Derivatives:
Interest rate contracts		87		116		142
Foreign exchange contracts		101		108		60
Cross-currency interest rate contracts		6		11		14
Total assets ***	$	673	$	687	$	762
Accounts payable and accrued expenses
Derivatives:
Interest rate contracts	$	341	$	131	$	79
Foreign exchange contracts		28		26		50
Cross-currency interest rate contracts		2		1		2
Total liabilities	$	371	$	158	$	131

* All measurements above were Level 2 measurements except for Level 1 measurements of the equity fund of $46 million, $48 million, and $135 million at April 29, 2018, October 29, 2017, and April 30, 2017, respectively; the fixed income fund of $14 million, $15 million, and $15 million at April 29, 2018, October 29, 2017, and April 30, 2017, respectively; and U.S. government debt securities of $42 million, $44 million, and $46 million at April 29, 2018, October 29, 2017, and April 30, 2017, respectively. In addition, $14 million, $17 million, and $23 million of the international debt securities were Level 3 measurements at April 29, 2018, October 29, 2017, and April 30, 2017, respectively. There were no transfers between Level 1 and Level 2 during the first six months of 2018 or 2017.

** Primarily issued by U.S. government sponsored enterprises.

*** Excluded from this table were the Company’s cash equivalents, which were carried at cost that approximates fair value. The cash equivalents consist primarily of money market funds that were Level 1 measurements.

The contractual maturities of debt securities at April 29, 2018 in millions of dollars are shown below. Actual maturities may differ from those scheduled as a result of prepayments by the issuers. Because of the potential for prepayment on mortgage-backed securities, they are not categorized by contractual maturity.


	Amortized		Fair
	Cost		Value
Due in one year or less	$	29	$	28
Due after one through five years		107		105
Due after five through 10 years		95		91
Due after 10 years		62		62
Mortgage-backed securities		139		133
Debt securities	$	432	$	419

Fair value, recurring Level 3 measurements from available-for-sale marketable securities in millions of dollars follow:


	Three Months Ended				Six Months Ended
	April 29		April 30		April 29		April 30
	2018		2017		2018		2017
Beginning of period balance	$	15	$	23	$	17	$	28
Principal payments		(1)		(1)		(3)		(6)
Change in unrealized gain				1				1
End of period balance	$	14	$	23	$	14	$	23

Fair value, nonrecurring Level 1 measurements from impairments in millions of dollars follow:


	Fair Value *				Losses
					Three Months Ended		Six Months Ended
	April 29	October 29		April 30	April 29	April 30	April 29	April 30
	2018	2017		2017	2018	2017	2018	2017
Investments in unconsolidated affiliates		$	28

* See financing receivables with specific allowances in Note 10. Losses were not significant.

The following is a description of the valuation methodologies the Company uses to measure certain financial instruments on the balance sheet at fair value:

Marketable Securities – The portfolio of investments, except for the Level 3 measurement international debt securities, is primarily valued on a market approach (matrix pricing model) in which all significant inputs are observable or can be derived from or corroborated by observable market data such as interest rates, yield curves, volatilities, credit risk, and prepayment speeds. Funds are primarily valued using the fund’s net asset value, based on the fair value of the underlying securities. The Level 3 measurement international debt securities are primarily valued using an income approach based on discounted cash flows using yield curves derived from limited, observable market data.

Derivatives – The Company’s derivative financial instruments consist of interest rate swaps and caps, foreign currency futures, forwards and swaps, and cross-currency interest rate swaps. The portfolio is valued based on an income approach (discounted cash flow) using market observable inputs, including swap curves and both forward and spot exchange rates for currencies.

Financing Receivables – Specific reserve impairments are based on the fair value of the collateral, which is measured using a market approach (appraisal values or realizable values). Inputs include a selection of realizable values.

Investment in Unconsolidated Affiliates – Other than temporary impairments for investments are measured as the difference between the implied fair value and the carrying value of the investments. The fair value for publicly traded entities is the share price multiplied by the shares owned.