unsecured term loan credit facility entered into in April 2015 (2015 Term Loan) which had $600 million outstanding as of December 31, 2016 and $750 million outstanding as of December 31, 2015.
Our revolving credit facility and our term loan facilities require that we maintain certain financial covenants as outlined in Note F— Borrowings and Credit Arrangements to our consolidated financial statements contained in Item 8 of this Annual Report.
As of and through December 31, 2016, we were in compliance with the required covenants.
Any inability to maintain compliance with these covenants could require us to seek to renegotiate the terms of our credit facility or seek waivers from compliance with these covenants, both of which could result in additional borrowing costs.
Further, there can be no assurance that our lenders would agree to such new terms or grant such waivers.
Senior Notes We had senior notes outstanding of $4.650 billion as of December 31, 2016 and as of December 31, 2015.
Our senior notes were issued in public offerings, are redeemable prior to maturity and are not subject to any sinking fund requirements.
Our senior notes are unsecured, unsubordinated obligations and rank on parity with each other.
These notes are effectively junior to borrowings under our credit and security facility, to the extent if borrowed by our subsidiaries, and to liabilities of our subsidiaries.
On January 12, 2017, we used our existing credit facilities to repay the $250 million plus interest of our senior notes due in January 2017.
The debt maturity schedule for the significant components of our debt obligations as of December 31, 2016 is as follows:
## Table 0 ##
Note: The table above does not include unamortized discounts associated with our senior notes, or amounts related to interest rate contracts used to hedge the fair value of certain of our senior notes or debt issuance costs.
Other Arrangements We maintained a $300 million credit and security facility secured by our U. S.  trade receivables maturing on June 9, 2017.
We had borrowings of $60 million outstanding under this facility as of December 31, 2016 and no borrowings outstanding as of December 31, 2015.
On February 7, 2017, we amended the terms of this credit and security facility, including increasing the facility size to $400 million.
This amendment retained a similar maximum leverage ratio requirement and extended the facility maturity to February 2019.
We also have accounts receivable factoring programs in certain European countries that we account for as sales under Financial Accounting Standards Board (FASB) Accounting Standards Codification?
(ASC) Topic 860, Transfers and Servicing.
These agreements provide for the sale of accounts receivable to third parties, without recourse, of up to approximately $391 million as of December 31, 2016.
We de-recognized $152 million of receivables as of December 31, 2016 at an average interest rate of 1.8 percent, and $151 million as of December 31, 2015 at an average interest rate of 2.4 percent.
In addition, we have uncommitted credit facilities with a commercial Japanese bank that provide for borrowings, promissory notes discounting and receivables factoring of up to 21.000 billion Japanese yen (approximately $180 million as of December 31, 2016).
We de-recognized $149 million of notes receivable as of December 31, 2016 at an average interest rate of 1.6 percent and $132 million of notes receivable as of December 31, 2015 at an average interest rate of 1.6 percent.
De-recognized accounts and notes are excluded from trade accounts receivable, net in the accompanying audited consolidated balance sheets.
We had outstanding letters of credit of $44 million as of December 31, 2016 and as of December 31, 2015.
As of December 31, 2016 and 2015, none of the beneficiaries had drawn upon the letters of credit or guarantees.
We believe we will generate sufficient cash from operations to fund these arrangements and intend to fund these arrangements without drawing on the letters of credit.
For additional details related to our debt, including our revolving credit facility, term loans, senior notes and other arrangements, see Note F—Borrowings and Credit Arrangements to our consolidated financial statements included in Item 8 of this Annual Report.
Equity During 2016 we received $111 million in proceeds from stock issuances related to our stock option and employee stock purchase plans, as compared to $114 million in 2015 and $60 million 2014.
Proceeds from the exercise of employee stock options and employee stock purchases vary from period to period based upon, among other factors, fluctuations in the trading price of our common stock and in the exercise and stock purchase patterns of employees.
group purchasing organizations to sell our products to participating hospitals at negotiated prices.
We recognize revenue from these agreements following the same revenue recognition criteria discussed above.
Warranty Obligations We offer warranties on certain of our product offerings.
The majority of our warranty liability relates to implantable devices offered by our CRM business, which include defibrillator and pacemaker systems.
Our CRM products come with a standard limited warranty covering the replacement of these devices.
We offer a full warranty for a portion of the period post-implant, and a partial warranty for a period of time thereafter.
We estimate the costs that we may incur under our warranty programs based on the number of units sold, historical and anticipated rates of warranty claims and cost per claim, and record a liability equal to these estimated costs as cost of products sold at the time the product sale occurs.
We assess the adequacy of our recorded warranty liabilities on a quarterly basis and adjust these amounts as necessary.
Changes in our product warranty accrual during 2016, 2015, and 2014 consisted of the following (in millions):
## Table 1 ##
Inventories We state inventories at the lower of first-in, first-out cost or market.
We base our provisions for excess, expired and obsolete inventory primarily on our estimates of forecasted net sales.
A significant change in the timing or level of demand for our products as compared to forecasted amounts may result in recording additional provisions for excess, expired and obsolete inventory in the future.
Further, the industry in which we participate is characterized by rapid product development and frequent new product introductions.
Uncertain timing of next-generation product approvals, variability in product launch strategies, product recalls and variation in product utilization all affect our estimates related to excess, expired and obsolete inventory.
Approximately 40 percent of our finished goods inventory as of December 31, 2016 and December 31, 2015 was at customer locations pursuant to consignment arrangements or held by sales representatives.
Property, Plant and Equipment We state property, plant, equipment, and leasehold improvements at historical cost.
We charge expenditures for maintenance and repairs to expense and capitalize additions and improvements that extend the life of the underlying asset.
We provide for depreciation using the straight-line method at rates that approximate the estimated useful lives of the assets.
We depreciate buildings over a 20 to 40 year life; building improvements over the remaining useful life of the building structure; equipment, furniture and fixtures over a three to ten year life; and leasehold improvements over the shorter of the useful life of the improvement or the term of the related lease.
Depreciation expense was $270 million in 2016, $274 million in 2015 and $287 million in 2014.
Valuation of Business Combinations We allocate the amounts we pay for each acquisition to the assets we acquire and liabilities we assume based on their fair values at the dates of acquisition, including identifiable intangible assets and in-process research and development which either arise from a contractual or legal right or are separable from goodwill.
We base the fair value of identifiable intangible assets acquired in a business combination, including in-process research and development, on detailed valuations that use information and assumptions provided by management, which consider management’s best estimates of inputs and assumptions that a market participant would use.
We allocate any excess purchase price over the fair value of the net tangible and identifiable intangible assets acquired to goodwill.
Transaction costs associated with these acquisitions are expensed as incurred through selling, general and administrative costs.
In those circumstances where an acquisition involves a contingent consideration arrangement, we recognize a liability equal to the fair value of the contingent payments we expect to make as of the acquisition date.
We re-measure this liability each reporting period and record changes in the fair value through a separate line item within our consolidated statements of operations.
Increases or decreases in the fair value of the contingent consideration liability can result from changes in discount periods and rates, as well as changes in the timing and amount of revenue estimates or in the timing or likelihood of achieving regulatory, revenue or commercialization-based milestones.
Indefinite-lived Intangibles, including In-Process Research and Development Our indefinite-lived intangible assets that are not subject to amortization include acquired balloon and other technology, which is
representative.
In October 2016, we notified Preventice of our intent to terminate the commercial agreement and will transition the sales force back to Preventice in 2017 under the terms of the agreement.
On April 13, 2015, we acquired 25 percent of the common stock of Frankenman Medical Equipment Company (Frankenman).
Frankenman is a privately-held company headquartered in Suzhou, China, and is a local market leader in surgical staplers.
Additionally, we entered into co-promotional and co-selling agreements with Frankenman to commercialize selected products jointly in China.
We believe this alliance will enable us to reach more clinicians and treat more patients in China by providing access to training on less invasive endoscopic technologies with clinical and economic benefits.
We are accounting for our investments in Preventice and Frankenman, as well as certain of our other strategic investments, as equity method investments, in accordance with FASB ASC Topic 323.
The aggregate carrying amount of our strategic investments as of December 31, 2016 and December 31, 2015, were comprised of the following categories:
## Table 2 ##
As of December 31, 2016, the book value of our equity method investments exceeded our share of the book value of the investees’ underlying net assets by approximately $200 million, which represents amortizable intangible assets and in-process research and development, corresponding deferred tax liabilities, and goodwill.
The net losses from our equity method adjustments, presented within the Other, net caption of our consolidated statement of operations were $17 million in 2016 and were immaterial in 2015 and 2014.
NOTE C—DIVESTITURES In January 2011, we closed the sale of our Neurovascular business to Stryker Corporation for a purchase price of $1.500 billion in cash.
At the time of divestiture, due to our continuing involvement in the operations of the Neurovascular business following the transaction, the divestiture did not meet the criteria for pre sentation as a discontinued operation.
Our sales related to our divested Neurovascular business have declined as the various transition services and supply agreements have terminated.
We recorded a gain of $12 million during 2014 associated with the transaction and we recorded revenue related to the Neurovascular business following its divestiture of $4 million in 2014.
NOTE D—GOODWILL AND OTHER INTANGIBLE ASSETS The gross carrying amount of goodwill and other intangible assets and the related accumulated amortization for intangible assets subject to amortization and accumulated write-offs of goodwill as of December 31, 2016 and 2015 are as follows:
## Table 3 ##
Our technology-related intangible assets that are not subject to amortization represent technical processes, intellectual property and/or institutional understanding acquired through business combinations that are fundamental to the on-going operations of our business and have no limit to their useful life.
Our technologyrelated intangible assets that are not subject to amortization are comprised primarily of certain acquired balloon and other technology, which is foundational to our continuing operations within the Cardiovascular market and other markets within interventional medicine.
We assess our indefinite-lived intangible assets at least annually for impairment and reassess their classification as indefinite-lived assets.
We assess qualitative factors to determine whether the existence of events and circumstances indicate that it is more likely than not that our indefinite-lived intangible assets are impaired.
If we conclude that it is more likely than not that the asset is impaired, we then determine the fair value of the intangible asset and perform the quantitative impairment test by comparing the fair value with the carrying value in accordance with FASB ASC Topic 350.
In 2016, Arconic also recognized discrete income tax benefits related to the release of valuation allowances on certain net deferred tax assets in Russia and Canada of $19 and $20 respectively.
After weighing all available evidence, management determined that it was more likely than not that the net income tax benefits associated with the underlying deferred tax assets would be realizable based on historic cumulative income and projected taxable income.
Arconic also recorded additional valuation allowances in Australia of $93 related to the Separation Transaction, in Spain of $163 related to a tax law change and in Luxembourg of $280 related to the Separation Transaction as well as a tax law change.
These valuation allowances fully offset current year changes in deferred tax asset balances of each respective jurisdiction, resulting in no net impact to tax expense.
The need for a valuation allowance will be reassessed on a continuous basis in future periods by each jurisdiction and, as a result, the allowances may increase or decrease based on changes in facts and circumstances.
In 2015, Arconic recognized an additional $141 discrete income tax charge for valuation allowances on certain deferred tax assets in Iceland and Suriname.
Of this amount, an $85 valuation allowance was established on the full value of the deferred tax assets in Suriname, which were related mostly to employee benefits and tax loss carryforwards.
These deferred tax assets have an expiration period ranging from 2016 to 2022 (as of December 31, 2015).
The remaining $56 charge relates to a valuation allowance established on a portion of the deferred tax assets recorded in Iceland.
These deferred tax assets have an expiration period ranging from 2017 to 2023.
After weighing all available positive and negative evidence, as described above, management determined that it was no longer more likely than not that Arconic will realize the tax benefit of either of these deferred tax assets.
This was mainly driven by a decline in the outlook of the Primary Metals business, combined with prior year cumulative losses and a short expiration period.
In December 2011, one of Arconic’s former subsidiaries in Brazil applied for a tax holiday related to its expanded mining and refining operations.
During 2013, the application was amended and re-filed and, separately, a similar application was filed for another one of Arconic’s former subsidiaries in Brazil.
The deadline for the Brazilian government to deny the application was July 11, 2014.
Since Arconic did not receive notice that its applications were denied, the tax holiday took effect automatically on July 12, 2014.
As a result, the tax rate applicable to qualified holiday income for these subsidiaries decreased significantly (from 34% to 15.25%), resulting in future cash tax savings over the 10-year holiday period (retroactively effective as of January 1, 2013).
Additionally, a portion of one of the subsidiaries net deferred tax assets that reverses within the holiday period was remeasured at the new tax rate (the net deferred tax asset of the other subsidiary was not remeasured since it could still be utilized against the subsidiary’s future earnings not subject to the tax holiday).
This remeasurement resulted in a decrease to that subsidiary’s net deferred tax assets and a noncash charge to earnings of $52 ($31 after noncontrolling interests).
The following table details the changes in the valuation allowance:
## Table 4 ##
The cumulative amount of Arconic’s foreign undistributed net earnings for which no deferred taxes have been provided was approximately $450 at December 31, 2016.
Arconic has a number of commitments and obligations related to the Company’s growth strategy in foreign jurisdictions.
As such, management has no plans to distribute such earnings in the foreseeable future, and, therefore, has determined it is not practicable to determine the related deferred tax liability.

Tables referenced above, in order (Table 0 first):
<table><tr><td>(in millions)</td><td>2017</td><td>2018</td><td>2019</td><td>2020</td><td>2021</td><td>Thereafter</td><td>Total</td></tr><tr><td>Senior Notes</td><td>$250</td><td>$600</td><td>$—</td><td>$1,450</td><td>$—</td><td>$2,350</td><td>$4,650</td></tr><tr><td>Term Loans</td><td>—</td><td>225</td><td>150</td><td>375</td><td>—</td><td>—</td><td>750</td></tr><tr><td></td><td>$250</td><td>$825</td><td>$150</td><td>$1,825</td><td>$—</td><td>$2,350</td><td>$5,400</td></tr></table>
<table><tr><td></td><td colspan="3">Year Ended December 31,</td></tr><tr><td></td><td>2016</td><td>2015</td><td>2014</td></tr><tr><td>Beginning balance</td><td>$23</td><td>$25</td><td>$28</td></tr><tr><td>Provision</td><td>25</td><td>15</td><td>9</td></tr><tr><td>Settlements/ reversals</td><td>-26</td><td>-17</td><td>-12</td></tr><tr><td>Ending balance</td><td>$22</td><td>$23</td><td>$25</td></tr></table>
<table><tr><td></td><td colspan="2">As of</td></tr><tr><td></td><td>December 31, 2016</td><td>December 31, 2015</td></tr><tr><td>Equity method investments</td><td>$265</td><td>$173</td></tr><tr><td>Cost method investments</td><td>20</td><td>45</td></tr><tr><td>Available-for-sale securities</td><td>20</td><td>—</td></tr><tr><td>Notes receivable</td><td>42</td><td>30</td></tr><tr><td></td><td>$347</td><td>$248</td></tr></table>
<table><tr><td></td><td colspan="2">As of December 31, 2016</td><td colspan="2">As of December 31, 2015</td></tr><tr><td>(in millions)</td><td>Gross Carrying Amount</td><td>AccumulatedAmortization/ Write-offs</td><td>Gross Carrying Amount</td><td>AccumulatedAmortization/ Write-offs</td></tr><tr><td>Amortizable intangible assets</td><td></td><td></td><td></td><td></td></tr><tr><td>Technology-related</td><td>$9,123</td><td>$-4,468</td><td>$8,948</td><td>$-4,054</td></tr><tr><td>Patents</td><td>529</td><td>-374</td><td>520</td><td>-358</td></tr><tr><td>Other intangible assets</td><td>1,583</td><td>-722</td><td>1,529</td><td>-610</td></tr><tr><td></td><td>$11,235</td><td>$-5,564</td><td>$10,997</td><td>$-5,022</td></tr><tr><td>Unamortizable intangible assets</td><td></td><td></td><td></td><td></td></tr><tr><td>Goodwill</td><td>$16,578</td><td>$-9,900</td><td>$16,373</td><td>$-9,900</td></tr><tr><td>In-process research and development (IPR&D)</td><td>92</td><td>—</td><td>99</td><td>—</td></tr><tr><td>Technology-related</td><td>120</td><td>—</td><td>120</td><td>—</td></tr><tr><td></td><td>$16,790</td><td>$-9,900</td><td>$16,592</td><td>$-9,900</td></tr></table>
<table><tr><td>December 31,</td><td>2016</td><td>2015</td><td>2014</td></tr><tr><td>Balance at beginning of year</td><td>$1,291</td><td>$1,151</td><td>$1,252</td></tr><tr><td>Increase to allowance</td><td>772</td><td>180</td><td>102</td></tr><tr><td>Release of allowance</td><td>-209</td><td>-42</td><td>-70</td></tr><tr><td>Acquisitions and divestitures (F)</td><td>-1</td><td>29</td><td>-36</td></tr><tr><td>Tax apportionment, tax rate and tax law changes</td><td>106</td><td>-15</td><td>-67</td></tr><tr><td>Foreign currency translation</td><td>-19</td><td>-12</td><td>-30</td></tr><tr><td>Balance at end of year</td><td>$1,940</td><td>$1,291</td><td>$1,151</td></tr></table>

Question: what was the increase in the balance at end of the year from 2015 to 2016?
Answer: 0.50271
Reasoning program: divide(1940,1291), subtract(#0,const_1)