# On the tax incentive for corporate insurance purchase.

On the Tax Incentive for Corporate Insurance Purchase

Abstract

Recognizing that property loss is diversifiable risk, reasons other than risk aversion have been advanced to explain why corporations purchase property insurance. One possibility is the tax benefit from insurance purchases. This study examines the magnitude of this tax benefit and how it varies with the asset's life, the inflation rate, the tax rate, and the speed of depreciation. The tax benefit, computed using reasonable values for the above variables, appears small relative to the typical load in insurance contracts. Hence the tax incentive cannot be the sole reason for corporate purchase of property insurance.

Introduction

Mayers and Smith [4] first pointed out that risk aversion cannot be an obvious reason for corporate purchase of property-liability insurance since any insurable risk could be diversified in the investors' portfolios. They suggested that the insurance-related tax provisions may favor purchase of insurance over self-insurance. Using a single-period model they derived an expression for the tax benefit of insurance. Main [3] extended the analysis to a multi-period model where the corporation either purchases insurance to cover an asset over its entire life or not at all. using numerical examples Main showed that the tax benefit could be substantial.

This study develops a more general multi-period model by viewing the insurance purchase decision as a sequence of interrelated single-period decisions. Numerical examples using the provisions of the current tax code (post-1986 tax reform) show the tax benefit to be small relative to the typical load in insurance contracts and smaller than what was reported by Main.(1)

(1)The load is the portion of the premium that pays for the insurer's expenses and profits.

Tax Treatment of Involuntary Conversions

When a taxpayer's property is destroyed or stolen, an involuntary conversion occurs. If the insurance settlements exceed the adjusted basis of the destroyed property (the book value), the taxpayer has a gain. The following example illustrates the tax treatment of such gains.(2) Consider an asset originally purchased for $100 with a current book value of $40. The asset is insured for $75. If a loss occurs and the asset is not replaced, the $35 gain has to be recognized for tax purposes. If the asset is replaced, as long as the replacement cost exceeds the indemnity, the firm can elect not to recognize this $35 gain. With this election, if the replacement cost was $90, the book value of the replaced asset equals the replacement value less the unrecognized gain, $90 - $35 = $55. If the replacement cost equals the indemnity, $75, the adjusted basis of the replaced asset equals that of the old asset, $40.

In Main [3] any such gain from involuntary conversion was considered taxed at a lower capital gains tax rate. Thus the extra tax shields due to lower capital gains rate made the firm elect to recognize the gain because the firm paid the capital gains tax on the $35 and got a $35 depreciation tax shield in the future. In contrast, under the post 1986 tax code, the gain from involuntary conversion will be taxed entirely at the ordinary income tax rates and hence, the firm will always elect to not recognize the gain. A $35 tax exemption now is preferred to a $35 depreciation spread over future periods if the tax rate is constant. The latter scenario is the basis for the model of the insurance purchase decision in the next section.

The Model

Consider a firm that purchases an asset with N periods of useful life. At the end of each period there is a fixed probability of a property loss. The risk of such a loss is diversifiable. In the beginning of each period, the company may purchase insurance to cover the end-of-period market value of the asset. To model this insurance purchase decision, the following assumptions are made: 1. When the loss occurs it will be a complete loss and the lost asset will be replaced with an asset of identical vintage. 2. The marginal tax rate is constant and is independent of the occurrence of the loss. 3. Both accounting and economic depreciation are on a straight line basis over the asset's life.(3) 4. The inflation rate and the real rate of interest are constant for all periods and the inflation is fully anticipated.(4) The notations used are as follows:

(2)See Section 1033 of the tax code. Mayers and Smith [4] provide a summary of the provisions of this section.

(3)Although the accounting depreciation is identical to the economic depreciation, inflation will cause a divergence between the market value and the book value.

(4)There is no loss of generality. Insurance contracts are not generally indexed. Therefore the inflation risk exposure is the same in both self insurance and market insurance. n = number of remaining periods of the asset's life Mn = the market value when n periods of life remain Bn = the book value when n periods of life remain pi sub n = insurance premium paid at the beginning of the period (when n periods of life remain) to insure against a possible loss at the end of that period p = the probability of property loss lambda = loading in the insurance contract as a percentage of the premium r = the discount rate (real rate of interest plus inflation) T = the marginal tax rate of the firm alpha = the inflation rate With n - 1 periods of life remaining the market value of the asset will be Mn - 1 = Mn(n - 1 / N)(1 + alpha)N - n + 1 and the insurance premium for this coverage will be pi sub n = pMn - 1/(1 + r)(1 - lambda) where Mn is the original cost of the asset. In the event of loss, if insured, the firm will receive Mn - 1 from the insurance claims which will be used to replace the asset. The unrecognized (tax-free) gain will be Mn - 1 - Bn(n - 1 / n) and the book value of the replaced asset will be Bn(n - 1 / n) with n - 1 periods of remaining life. On the other hand, if there is an uninsured loss, there will be a cash outflow of Mn - 1 to replace the asset. In this case the book value of the replaced asset will be Mn - 1.

The firm will seek to maximize the expected present value of the net cash flows from the following sources: future tax shields from depreciation and write-offs, future replacement expenditures, and current and future insurance premiums paid.(5) In the dynamic programming terminology, this maximand will be the optimal value function, denoted as Fn(Bn).(6)

The expected present value of net cash flows for an asset with book value Bn and n periods of remaining life equals: EPVIn(Bn) = - pi sub n(1 - T) + 1 / 1 + r [ t / n Bn + Fn - 1(n - 1 / n Bn)] if insured and EPVUn(Bn) = 1 / 1 + r{(1 - p)[tan / n Bn + Fn - 1(n - 1 / n Bn)] + p[ tan B sub n - 1 + Fn - 1(Mn - 1)]}

(5)Brealey and Myers [1] have argued that expected present values are meaningful only if all uncertainties about future cash flows are resolved simultaneously. However, since this discussion is limited to diversifiable risk, expected present value can be interpreted as the present value of expected cash flows discounted at the risk-free rate.

(6)For a detailed description of the formulation of a dynamic program see Wagner[7]. if uninsured. Insurance will be purchased only if EPVI sub n (B sub n) is greater than EPVU sub n (B sub n). Thus F sub n (B sub n) = MAX{EPVI sub n (B sub n), EPVU sub n (B sub n)}, which is the recurrence relation for the dynamic program. Since the firm will not buy insurance with n = 1 (the market value goes to zero at n=0) the boundary condition will be F sub 1 (B sub 1) = gamma B sub 1/1+r Now the program can be solved recursively.

Computation of the Tax Benefit

In the absence of tax benefits, the firm will be indifferent to purchasing or not purchasing insurance at actuarially fair rates. With tax benefits such an indifference would occur if the loading in the insurance contract exactly offsets the tax benefit. Hence the tax benefit as a proportion of the premium equals the loading at this indifference point. The latter can be determined by trial and error.

Table 1 presents the results from computation of tax benefits for a range of asset lives using the following assumptions: real interest rate 4 percent, loss probability 0.01, and tax rate 34 percent.(7) The tax benefit is computed for the insurance purchase in the first year of the asset's life.(8) The longer the useful life of the asset the larger is the tax benefit from insurance. Table 2 reports the variation in the tax benefit for a 15-year asset as the inflation and tax rates are allowed to vary while the other parameters are held constant.

(7)In each case the loading was gradually increased from zero until the firm was indifferent between purchasing and not purchasing insurance in the beginning of the first year. It was found that the tax benefit as a proportion of the premium did not vary substantially with a change in the loss probability assumption.

(8)In the following years, unlike the first year, the book value and the market value of the asset may diverge. Computations (not reported here) indicate that such divergence of the book value from the market value does not affect the size of the tax benefit substantially.

The depreciation method is also allowed to change from the straight-line method to an extreme form of accelerated depreciation: full depreciation in the first year. The tax benefit increases with increasing inflation and tax rates. Faster depreciation of the asset also leads to a larger tax benefit. However, over the range of the parameter values considered, the tax benefit is small compared to the typical loading of 20 percent to 30 percent in the insurance industry and smaller than the 36 percent tax benefit reported by Main [3].(9)

All of the above computations have used a constant marginal tax rate, independent of the occurrence of the property loss. With progressive tax rates, an uninsured loss may lower the marginal tax rate of a firm. Consequently, the expected tax shield from write-off for an uninsured loss will be smaller and the tax benefit from insurance will be larger.

The underestimation of tax benefit can not be ascertained without specifying the taxable income and the size of the possible loss. However, the constant marginal tax rate assumption appears to be a reasonable approximation to the post-1986 tax rate schedule in a wide variety of cases tested.(10)

Conclusion

A dynamic programming model is used to compute the tax benefit from property insurance purchase by corporations under the post-1986 tax code. The size of the tax benefit is found to be small compared to the typical loading in the insurance contract and smaller than what was reported by Main [3]. If other factors, eg., real-service efficiencies (Mayers and Smith [4]), bankruptcy and agency cost considerations (Mayers and Smith [5] and MacMinn [2]), provide incentives for corporate purchase of insurance, the tax benefit could still affect the insurance decisions at the margin. For example, if the effects of the other factors remain constant, longer-lived assets are more likely to be insured. Also, an increase in the inflation rate or the marginal tax rate, or a change in the tax code speeding up the depreciation schedule may induce firms to insure more of their assets.

(9)Main's computations are for a three year asset based on 46 percent tax rate, zero inflation, and full depreciation in one year.

(10)For example, if a $500,000 total taxable income can be offset by a possible loss of $500,000, the difference in the expected tax shield from an uninsured loss, between the constant marginal tax rate of 34 percent and the marginal tax rate schedule in the post-1986 tax code, was less than 1 percent of the premium. Therefore, the difference in the tax benefit is also likely to be less than 1 percent of the premium. As the income and loss figures are scaled up, the difference becomes smaller.

TABLE : Tax Benefit of Insurance Purchase(*)(*)

TABLE : The Effect of Inflation and Taxes on the Tax Benefit of Insurance Purchase(*)

Abstract

Recognizing that property loss is diversifiable risk, reasons other than risk aversion have been advanced to explain why corporations purchase property insurance. One possibility is the tax benefit from insurance purchases. This study examines the magnitude of this tax benefit and how it varies with the asset's life, the inflation rate, the tax rate, and the speed of depreciation. The tax benefit, computed using reasonable values for the above variables, appears small relative to the typical load in insurance contracts. Hence the tax incentive cannot be the sole reason for corporate purchase of property insurance.

Introduction

Mayers and Smith [4] first pointed out that risk aversion cannot be an obvious reason for corporate purchase of property-liability insurance since any insurable risk could be diversified in the investors' portfolios. They suggested that the insurance-related tax provisions may favor purchase of insurance over self-insurance. Using a single-period model they derived an expression for the tax benefit of insurance. Main [3] extended the analysis to a multi-period model where the corporation either purchases insurance to cover an asset over its entire life or not at all. using numerical examples Main showed that the tax benefit could be substantial.

This study develops a more general multi-period model by viewing the insurance purchase decision as a sequence of interrelated single-period decisions. Numerical examples using the provisions of the current tax code (post-1986 tax reform) show the tax benefit to be small relative to the typical load in insurance contracts and smaller than what was reported by Main.(1)

(1)The load is the portion of the premium that pays for the insurer's expenses and profits.

Tax Treatment of Involuntary Conversions

When a taxpayer's property is destroyed or stolen, an involuntary conversion occurs. If the insurance settlements exceed the adjusted basis of the destroyed property (the book value), the taxpayer has a gain. The following example illustrates the tax treatment of such gains.(2) Consider an asset originally purchased for $100 with a current book value of $40. The asset is insured for $75. If a loss occurs and the asset is not replaced, the $35 gain has to be recognized for tax purposes. If the asset is replaced, as long as the replacement cost exceeds the indemnity, the firm can elect not to recognize this $35 gain. With this election, if the replacement cost was $90, the book value of the replaced asset equals the replacement value less the unrecognized gain, $90 - $35 = $55. If the replacement cost equals the indemnity, $75, the adjusted basis of the replaced asset equals that of the old asset, $40.

In Main [3] any such gain from involuntary conversion was considered taxed at a lower capital gains tax rate. Thus the extra tax shields due to lower capital gains rate made the firm elect to recognize the gain because the firm paid the capital gains tax on the $35 and got a $35 depreciation tax shield in the future. In contrast, under the post 1986 tax code, the gain from involuntary conversion will be taxed entirely at the ordinary income tax rates and hence, the firm will always elect to not recognize the gain. A $35 tax exemption now is preferred to a $35 depreciation spread over future periods if the tax rate is constant. The latter scenario is the basis for the model of the insurance purchase decision in the next section.

The Model

Consider a firm that purchases an asset with N periods of useful life. At the end of each period there is a fixed probability of a property loss. The risk of such a loss is diversifiable. In the beginning of each period, the company may purchase insurance to cover the end-of-period market value of the asset. To model this insurance purchase decision, the following assumptions are made: 1. When the loss occurs it will be a complete loss and the lost asset will be replaced with an asset of identical vintage. 2. The marginal tax rate is constant and is independent of the occurrence of the loss. 3. Both accounting and economic depreciation are on a straight line basis over the asset's life.(3) 4. The inflation rate and the real rate of interest are constant for all periods and the inflation is fully anticipated.(4) The notations used are as follows:

(2)See Section 1033 of the tax code. Mayers and Smith [4] provide a summary of the provisions of this section.

(3)Although the accounting depreciation is identical to the economic depreciation, inflation will cause a divergence between the market value and the book value.

(4)There is no loss of generality. Insurance contracts are not generally indexed. Therefore the inflation risk exposure is the same in both self insurance and market insurance. n = number of remaining periods of the asset's life Mn = the market value when n periods of life remain Bn = the book value when n periods of life remain pi sub n = insurance premium paid at the beginning of the period (when n periods of life remain) to insure against a possible loss at the end of that period p = the probability of property loss lambda = loading in the insurance contract as a percentage of the premium r = the discount rate (real rate of interest plus inflation) T = the marginal tax rate of the firm alpha = the inflation rate With n - 1 periods of life remaining the market value of the asset will be Mn - 1 = Mn(n - 1 / N)(1 + alpha)N - n + 1 and the insurance premium for this coverage will be pi sub n = pMn - 1/(1 + r)(1 - lambda) where Mn is the original cost of the asset. In the event of loss, if insured, the firm will receive Mn - 1 from the insurance claims which will be used to replace the asset. The unrecognized (tax-free) gain will be Mn - 1 - Bn(n - 1 / n) and the book value of the replaced asset will be Bn(n - 1 / n) with n - 1 periods of remaining life. On the other hand, if there is an uninsured loss, there will be a cash outflow of Mn - 1 to replace the asset. In this case the book value of the replaced asset will be Mn - 1.

The firm will seek to maximize the expected present value of the net cash flows from the following sources: future tax shields from depreciation and write-offs, future replacement expenditures, and current and future insurance premiums paid.(5) In the dynamic programming terminology, this maximand will be the optimal value function, denoted as Fn(Bn).(6)

The expected present value of net cash flows for an asset with book value Bn and n periods of remaining life equals: EPVIn(Bn) = - pi sub n(1 - T) + 1 / 1 + r [ t / n Bn + Fn - 1(n - 1 / n Bn)] if insured and EPVUn(Bn) = 1 / 1 + r{(1 - p)[tan / n Bn + Fn - 1(n - 1 / n Bn)] + p[ tan B sub n - 1 + Fn - 1(Mn - 1)]}

(5)Brealey and Myers [1] have argued that expected present values are meaningful only if all uncertainties about future cash flows are resolved simultaneously. However, since this discussion is limited to diversifiable risk, expected present value can be interpreted as the present value of expected cash flows discounted at the risk-free rate.

(6)For a detailed description of the formulation of a dynamic program see Wagner[7]. if uninsured. Insurance will be purchased only if EPVI sub n (B sub n) is greater than EPVU sub n (B sub n). Thus F sub n (B sub n) = MAX{EPVI sub n (B sub n), EPVU sub n (B sub n)}, which is the recurrence relation for the dynamic program. Since the firm will not buy insurance with n = 1 (the market value goes to zero at n=0) the boundary condition will be F sub 1 (B sub 1) = gamma B sub 1/1+r Now the program can be solved recursively.

Computation of the Tax Benefit

In the absence of tax benefits, the firm will be indifferent to purchasing or not purchasing insurance at actuarially fair rates. With tax benefits such an indifference would occur if the loading in the insurance contract exactly offsets the tax benefit. Hence the tax benefit as a proportion of the premium equals the loading at this indifference point. The latter can be determined by trial and error.

Table 1 presents the results from computation of tax benefits for a range of asset lives using the following assumptions: real interest rate 4 percent, loss probability 0.01, and tax rate 34 percent.(7) The tax benefit is computed for the insurance purchase in the first year of the asset's life.(8) The longer the useful life of the asset the larger is the tax benefit from insurance. Table 2 reports the variation in the tax benefit for a 15-year asset as the inflation and tax rates are allowed to vary while the other parameters are held constant.

(7)In each case the loading was gradually increased from zero until the firm was indifferent between purchasing and not purchasing insurance in the beginning of the first year. It was found that the tax benefit as a proportion of the premium did not vary substantially with a change in the loss probability assumption.

(8)In the following years, unlike the first year, the book value and the market value of the asset may diverge. Computations (not reported here) indicate that such divergence of the book value from the market value does not affect the size of the tax benefit substantially.

The depreciation method is also allowed to change from the straight-line method to an extreme form of accelerated depreciation: full depreciation in the first year. The tax benefit increases with increasing inflation and tax rates. Faster depreciation of the asset also leads to a larger tax benefit. However, over the range of the parameter values considered, the tax benefit is small compared to the typical loading of 20 percent to 30 percent in the insurance industry and smaller than the 36 percent tax benefit reported by Main [3].(9)

All of the above computations have used a constant marginal tax rate, independent of the occurrence of the property loss. With progressive tax rates, an uninsured loss may lower the marginal tax rate of a firm. Consequently, the expected tax shield from write-off for an uninsured loss will be smaller and the tax benefit from insurance will be larger.

The underestimation of tax benefit can not be ascertained without specifying the taxable income and the size of the possible loss. However, the constant marginal tax rate assumption appears to be a reasonable approximation to the post-1986 tax rate schedule in a wide variety of cases tested.(10)

Conclusion

A dynamic programming model is used to compute the tax benefit from property insurance purchase by corporations under the post-1986 tax code. The size of the tax benefit is found to be small compared to the typical loading in the insurance contract and smaller than what was reported by Main [3]. If other factors, eg., real-service efficiencies (Mayers and Smith [4]), bankruptcy and agency cost considerations (Mayers and Smith [5] and MacMinn [2]), provide incentives for corporate purchase of insurance, the tax benefit could still affect the insurance decisions at the margin. For example, if the effects of the other factors remain constant, longer-lived assets are more likely to be insured. Also, an increase in the inflation rate or the marginal tax rate, or a change in the tax code speeding up the depreciation schedule may induce firms to insure more of their assets.

(9)Main's computations are for a three year asset based on 46 percent tax rate, zero inflation, and full depreciation in one year.

(10)For example, if a $500,000 total taxable income can be offset by a possible loss of $500,000, the difference in the expected tax shield from an uninsured loss, between the constant marginal tax rate of 34 percent and the marginal tax rate schedule in the post-1986 tax code, was less than 1 percent of the premium. Therefore, the difference in the tax benefit is also likely to be less than 1 percent of the premium. As the income and loss figures are scaled up, the difference becomes smaller.

TABLE : Tax Benefit of Insurance Purchase(*)(*)

TABLE : The Effect of Inflation and Taxes on the Tax Benefit of Insurance Purchase(*)

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Author: | Chen, Charng Yi; PonArul, Richard |
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Publication: | Journal of Risk and Insurance |

Date: | Jun 1, 1989 |

Words: | 2081 |

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