PSU ACCTG 550 - Net of tax returns on real and financial assets

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Smeal College of Business Taxation and Global Management Decisions: ACCTG 550Pennsylvania State University Professor HuddartNet-of-tax returns on real and financial assetsSuppose there is a riskless financial asset that costs one dollar at thebeginning of the period and pays 1 + r dollars at the end of every period.The difference, r,istaxed at rate t.Thus, it is possible to borrow and lendat the after-tax rate of r(1 − t)per period. There is also a real asset costingx>0. The asset produces a riskless pretax cash flow of k in perpetuity atthe end of each period. For tax purposes, the original cost of the asset maybe depreciated straight line at rate 0 ≤ d ≤ 1. Taxable income for any periodis the pretax cash flow less the depreciation. Tax is paid at rate t,sothat atthe end of the first period, the net-of-tax cash flow isk − t(k − dx)=k(1 − t)+dtx.The cash outflow to acquire the asset is not tax deductible. Suppose furtherthat other income is available to offset tax depreciation in excess of cashflows from the asset. Then the net present value of investing in the real assetis− x +1/dn=1k(1 − t)+dtx[1+(1− t)r]n+∞n=1+1/dk(1 − t)[1 + (1 − t)r]n(1)= − x +kr+dtx(1 − t)r1 − [1+(1− t)r]−1/d . (2)In (1),• the first term is the cost of the asset,• the second term is the net-of-tax cash flows over the depreciable life ofthe asset discounted back to time zero at the after-tax rate of return,and• the final term is the net-of-tax cash flows from the asset after the assetis fully depreciated.cSteven Huddart, 1995–2002. All rights reserved. www.smeal.psu.edu/faculty/huddartACCTG 550 Real and financial assetsThis quantity can be rewritten as (2). Each of the three components of thisexpression has a straightforward interpretation.• The first term is the cost of the asset.• The second term is the present value of the perpetual pre-tax cash flowfrom the asset, k, capitalized at the pre-tax rate, r. Note that this isthe same as the after tax cash flow, k(1 − t), capitalized at the after taxdiscount rate, r(1 − t).• The final term is the present value of the reduction in tax paymentsafforded by the depreciation deduction (often called the tax shield).1This is the only term where tax factors d and t play a role.–Ifeither the depreciation rate or the tax rate is zero, then the beforetax and net-of-tax present values of the asset are the same.–Ifd and t are both positive, then the tax shield is also positive. Itsvalue increases with both d and t.– When tax depreciation is immediate, i.e., d =1,then the tax shieldisxt1+(1− t)r.This value can be substantial. Consider an investment that may bededucted fully from taxes in the year it is made, such as advertising.For t = 30% and r = 10%, the tax shield is 28% of the cost of theasset.Figure 1 illustrates the relationship between the depreciation rate andthe value of the tax shield. The importance of the tax shield to projectvaluation is highlighted by the three calculations in table 1.1Notice that this term has the same form as the present value of an annuity of dtxfor 1/d periods discounted at rate r(1 − t).Page 2Real and financial assets ACCTG 550Figure 1. Illustration of the dependence of the value of the taxshield (vertical axis) on the depreciation rate (horizontal axis).Assumptions: r = 10% and t = 30%.Page 3ACCTG 550 Real and financial assetsFigure 2. Illustration of the dependence of the value of the taxshield (vertical axis) on the tax rate (horizontal axis). Assumptions:r = 10% and d = 30%.Page 4Pretax discount rate 10% Time 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Year 8 Year 9 Year 10 BeyondPretax cashflow (1,000) 100 100 100 100 100 100 100 100 100 100 100Tax depreciation 0% 0 0 0 0 0 0 0 0 0 0 0Taxable income 100 100 100 100 100 100 100 100 100 100 100Tax 0 % 0 0 000000000Net of tax cash flow (1,000) 100 100 100 100 100 100 100 100 100 100 100Discount factor 10% 1.0000 .9091 .8264 .7513 .6830 .6209 .5645 .5132 .4665 .4241 .3855 3.8554NPV (0) (1,000) 91 83 75 68 62 56 51 47 42 39 386Pretax cashflow (1,000) 100 100 100 100 100 100 100 100 100 100 100Tax depreciation 10% (100) (100) (100) (100) (100) (100) (100) (100) (100) (100) 0Taxable income 0 0 0 0 0 0 0 0 0 0 100Tax 30% 0 0 00000000(30)Net of tax cash flow (1,000) 100 100 100 100 100 100 100 100 100 100 70Discount factor 7 % 1.0000 .9346 .8734 .8163 .7629 .7130 .6663 .6227 .5820 .5439 .5083 7.2621NPV 2 1 1 (1,000) 93 87 82 76 71 67 62 58 54 51 508Pretax cashflow (1,000) 100 100 100 100 100 100 100 100 100 100 100Tax depreciation 50% (500) (500) 000000000Taxable income (400) (400) 100 100 100 100 100 100 100 100 100Tax 50% 200 200 (50) (50) (50) (50) (50) (50) (50) (50) (50)Net of tax cash flow (1,000) 300 300 50 50 50 50 50 50 50 50 50Discount factor 5 % 1.0000 .9524 .9070 .8638 .8227 .7835 .7462 .7107 .6768 .6446 .6139 12.2783NPV 4 6 5 (1,000) 286 272 43 41 39 37 36 34 32 31 614Real and financial assets ACCTG 550Table 1. Illustration of the dependence of the net present value ofa real project on the income tax rate and depreciation tax shield.In each case, the pretax discount rate is r = 10%, the cost of theasset is x =$1, 000, and the perpetual future cash flow is k = $100.In the first panel, there are no taxes, so t =0and d =0.Inthe second panel, the tax rate is t = 30% and the asset can bedepreciated straight line over ten years. In the third panel, the taxrate is t = 50% and the asset can be depreciated straight line overtwoyears.Page 5ACCTG 550 Real and financial assets1. Questions:One surprising conclusion that might be drawn from this analysis is thatthe net-of-tax present value of an investment is increasing in t. That is, thehigher the tax rate, the more attractive is the investment!(1) The statement above is a striking one. What must be held constant(and probably is not in real life) for it to be true?Answer: Both the price of the real asset and the pre-tax interest rate must be constant when tax rates change.It is likely that these prices would adjust in response tochanges in the rates of depreciation and tax.(2) What condition defines equilibrium prices and returns on financial assetsrelative to real assets?Answer: An arbitrage condition must hold. In equilib-rium, the net-of-tax returns on financial activities and thenet-of-tax returns on real activities must be the same forthe marginal investor.(3) What opportunities would you be able to exploit if you observed


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