intangible assets such as patents , customer-related intangible assets and other intangible assets with finite useful lives are amortized on a straight-line basis over their estimated economic lives . the weighted-average useful lives approximate the following: .
considering the years 2015-2016 , what was the average cash paid for income taxes?
recoverability of intangible assets with finite useful lives is assessed in the same manner as property , plant and equipment as described above . income taxes : for purposes of the company 2019s consolidated financial statements for periods prior to the spin-off , income tax expense has been recorded as if the company filed tax returns on a stand-alone basis separate from ingersoll rand . this separate return methodology applies the accounting guidance for income taxes to the stand-alone financial statements as if the company was a stand-alone enterprise for the periods prior to the spin-off . therefore , cash tax payments and items of current and deferred taxes may not be reflective of the company 2019s actual tax balances prior to or subsequent to the spin-off . cash paid for income taxes , net of refunds for the twelve months ended december 31 , 2016 and 2015 was $ 10.4 million and $ 80.6 million , respectively . the 2016 net cash income taxes paid includes a refund of $ 46.2 million received from the canadian tax authorities . the income tax accounts reflected in the consolidated balance sheet as of december 31 , 2016 and 2015 include income taxes payable and deferred taxes allocated to the company at the time of the spin-off . the calculation of the company 2019s income taxes involves considerable judgment and the use of both estimates and allocations . deferred tax assets and liabilities are determined based on temporary differences between financial reporting and tax bases of assets and liabilities , applying enacted tax rates expected to be in effect for the year in which the differences are expected to reverse . the company recognizes future tax benefits , such as net operating losses and tax credits , to the extent that realizing these benefits is considered in its judgment to be more likely than not . the company regularly reviews the recoverability of its deferred tax assets considering its historic profitability , projected future taxable income , timing of the reversals of existing temporary differences and the feasibility of its tax planning strategies . where appropriate , the company records a valuation allowance with respect to a future tax benefit . product warranties : standard product warranty accruals are recorded at the time of sale and are estimated based upon product warranty terms and historical experience . the company assesses the adequacy of its liabilities and will make adjustments as necessary based on known or anticipated warranty claims , or as new information becomes available . revenue recognition : revenue is recognized and earned when all of the following criteria are satisfied : ( a ) persuasive evidence of a sales arrangement exists ; ( b ) the price is fixed or determinable ; ( c ) collectability is reasonably assured ; and ( d ) delivery has occurred or service has been rendered . delivery generally occurs when the title and the risks and rewards of ownership have transferred to the customer . both the persuasive evidence of a sales arrangement and fixed or determinable price criteria are deemed to be satisfied upon receipt of an executed and legally binding sales agreement or contract that clearly defines the terms and conditions of the transaction including the respective obligations of the parties . if the defined terms and conditions allow variability in all or a component of the price , revenue is not recognized until such time that the price becomes fixed or determinable . at the point of sale , the company validates the existence of an enforceable claim that requires payment within a reasonable amount of time and assesses the collectability of that claim . if collectability is not deemed to be reasonably assured , then revenue recognition is deferred until such time that collectability becomes probable or cash is received . delivery is not considered to have occurred until the customer has taken title and assumed the risks and rewards of ownership . service and installation revenue are recognized when earned . in some instances , customer acceptance provisions are included in sales arrangements to give the buyer the ability to ensure the delivered product or service meets the criteria established in the order . in these instances , revenue recognition is deferred until the acceptance terms specified in the arrangement are fulfilled through customer acceptance or a demonstration that established criteria have been satisfied . if uncertainty exists about customer acceptance , revenue is not recognized until acceptance has occurred . the company offers various sales incentive programs to our customers , dealers , and distributors . sales incentive programs do not preclude revenue recognition , but do require an accrual for the company 2019s best estimate of expected activity . examples of the sales incentives that are accrued for as a contra receivable and sales deduction at the point of sale include , but are not limited to , discounts ( i.e . net 30 type ) , coupons , and rebates where the customer does not have to provide any additional requirements to receive the discount . sales returns and customer disputes involving a question of quantity or price are also accounted for as a .