# BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR. John R. Graham Adapted from S. Viswanathan FUQUA SCHOOL OF BUSINESS

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1 BA 351 CORPORATE FINANCE LECTURE 4 TAXES AND THE MARGINAL INVESTOR John R. Gaham Adapted fom S. Viswanathan FUQUA SCHOOL OF BUSINESS DUKE UNIVERSITY 1

2 In this lectue we conside the effect of govenment tax policy on valuing cetain cash flows. In paticula we conside the effect of copoate taxes and pesonal income taxes on the cost of capital. We stat by consideing a wold whee thee is a copoate tax but no pesonal income tax. Such situation leads to the taditional MM fomula which implies that thee is a tax advantage to debt. Let the copoate tax ate be τ C. The value of a leveed fim would then be just the value of the unleveed fim plus the pesent value of the tax shields (this is just the APV fomula which we will study late). Thus: Value of Leveed fim = Value of Unleveed fim + PV of tax shields. To deive this fomula, conside a fim whose only asset is a pepetual cash flow of \$1M and whose copoate tax ate is 40%. Suppose that municipal bonds exist and that these ae tax fee and ean a etun of 10% (i.e. eveyone can boow and lend tax-fee, at the pesonal level, of 10%). One can eplicate a cash flow of \$1M(1-0.4) = \$0.6M evey peiod by investing in \$1M(1-0.4)/0.10 = \$6M woth of pepetual bonds. Equivalently, conside the following table: 2

3 REPLICATING THE UNLEVERED FIRM t = 0 t=1 t=2 and so on Befoe Tax Cash Flow \$1M \$1M Afte Tax Cash Flow \$0.6M \$0.6M Replicating Investment \$0.6M/0.1 = \$6.0M \$0.6M \$0.6M The afte-tax income to the copoation (and to the individual as thee ae no pesonal taxes) in this example is \$0.6M a yea, afte payment of the 40% copoate tax. An investment of \$6M in tax exempt secuities would also yield an afte tax income of \$0.6M a yea. Thus the value of the unleveed cash flows of the fim is \$6M. This could have been diectly obtained as \$1M(1-0.4)/0.1 = \$6M. Now suppose the fim issues \$2M face value in pepetual debt. The inteest ate of the debt must be 10% (if it is less than 10% no one will puchase the debt). At 10%, the inteest payment pe yea is \$0.2M. Redoing the table above, we obtain: 3

4 REPLICATING THE LEVERED FIRM t = 0 t = 1 t = 2 and so on Befoe Tax and Inteest Cash Flow \$1M \$1M Inteest Payment \$0.2M \$0.2M Net Income Afte Inteest Befoe Taxes \$0.8M \$0.8M Taxes \$0.32M \$0.32M Afte Tax Equity Cash Flow \$0.48M \$0.48M Replicating equity investment \$0.48M/0.1 = \$4.8M Replicating debt investment \$0.2M/0.1 = \$2.0M \$0.48M \$0.2M \$0.48M \$0.2M The total value of the fim is thus the value of equity plus the value of debt. Thus the total value of the fim is \$4.8M + \$2.0M = \$6.8M. Thus the additional value fom undetaking \$2M in debt is \$0.8M. An altenative way to calculate this is as follows: 4

5 t = 0 t =1 t=2 and so on Inteest Payment \$0.2M \$0.2M Tax Shield Fom Inteest Payment \$0.08M \$0.08M Replicating equity investment \$0.08/0.1 = \$0.8M \$0.08M \$0.08M fomula: Thus an equity investment of \$0.08M will eplicate the tax shield. Hence we obtain the Value of Leveed fim = Value of Unleveed fim + PV of tax shields In this wold with pepetual debt (with no pesonal taxes) we can also obtain the following fomula: PV of tax shields = τ c D whee D is the amount of debt that is undetaken and τ c is the copoate tax ate. Again, in this example, the debt is \$2M and the tax ate times the debt is \$0.4(\$2M) = \$0.8M which agees with ou answe above. I caution that this additional fomula is coect only in the case of pepetual debt and no pesonal taxes. Bealey and Myes pesent a simila example using Meck's balance sheet. Meck is a fim that has no debt in its balance sheet. The top panel in Table 18-3a (see B&M, page 502) shows Meck's balance sheet (both the book value and the maket value) while panel b shows Meck's balance sheets afte it decides to boow \$1 billion in pepetual debt. The \$1 billion in pepetual debt with a copoate tax ate of 35% is woth \$350M (again we ae assuming 5

6 that thee ae no pesonal taxes). Thus Meck's total value inceases by \$350M to \$134,506M. Its equity value captues the entie incease and inceases to \$125,877M. In the above appoach we ignoed the pesonal tax status of investos. But pesonal taxes do affect the tax advantage to debt elative to equity because they affect the befoe-tax yields that investos demand on these instuments. If debt at the pesonal level is taxed at a highe ate than equity at the pesonal level, investos demand a highe befoe-tax yield on debt. This highe befoe-tax yield on debt will educe the tax advantage of debt. In what follows, we quantify the effect of pesonal taxes on the tax advantage (o disadvantage) fom leveing up the fim. To emphasize the dependence of the tax advantage to leveage, conside an investo who has a tax ate of τ p on debt income and τ e on equity income. These two tax ates need not be the same fo a vaiety of easons. Fist, capital gains ae often taxed at a diffeent ate than dividend and inteest income. This was tue befoe the 1986 Tax Refom Act. A lowe capital gains tax is again the law unde the 1991 and 1997 tax packages. Thus fo such individuals, the maginal tax ate on inteest income is highe than that on capital gains income. Also, even with the same ate of taxation on capital gains, dividends and inteest income, the effective ate on capital gains would still be lowe because the capital gains tax is paid only when gains ae ealized; that is, capital gains taxation can be delayed, so the "value" of capital gains taxation is the pesent value of the taxes that will be paid in the futue. Futhe, capital gains can be avoided altogethe at death (even fo one's heis). Finally, thee ae investos like copoations who have specific deductions that make the tax ates on dividends and inteest income diffeent. Thus, it is easonable to assume that thee ae diffeent tax ates fo inteest income and equity income. 6

7 Now, conside a fim that has a cash flow befoe tax and inteest of C. Suppose the fim is unleveed. Then the cash flow afte taxes is C (1 - τ c ). If the shaeholde has access to boowing and lending at the tax fee ate of, then we have the following table: REPLICATING THE UNLEVERED FIRM t = 0 t = 1 t = 2 and so on Opeating Cash Flow C C Afte Copoate Tax Cash Flow C(1 τ c ) C(1 τ c ) Afte Copoate And Pesonal Taxes Cash Flow C(1 τ c )(1 τ e ) C(1 τ c )(1 τ e ) Replicating investment C(1 τ c )(1 τ e )/ C(1 τ c )(1 τ e ) C(1 τ c )(1 τ e ) Thus the value of the unleveed fim is C( 1 τ )(1 τ c e ) Conside now a leveed fim that has debt of maket value D and inteest D ( D is not independent of the distibution of pesonal tax ates and, but we ignoe that fo now). Then we can eplicate the debt and equity cash flows of the leveed fim as follows: 7

8 REPLICATING THE LEVERED FIRM t = 0 t = 1 t = 2 and so on Opeating Cash Flow C C Inteest D D D D Befoe Tax, Afte Inteest CF C D D C D D Afte Tax Copoate Equity CF (C D D)(1 τ c ) (C D D)(1 τ c ) Afte Copoate and Pesonal Taxes Cash Flow (C - D D)(1 τ c )(1 τ e ) (C - D D)(1 τ c )(1 τ e ) Replicating Investment (Equity) (C- D D)(1 τ c )(1 τ e ) / (C - D D)(1 τ c )(1 τ e ) (C - D D)(1 τ c )(1 τ e ) Afte Pesonal Tax Debt CF D D(1 τ p ) D D(1 τ p ) Replicating Investment (Debt) D D(1 τ p )/ D D(1 τ p ) D D(1 τ p ) 8

9 Thus the value of the leveed fim is: C(1 τ c )(1 τ = ( C D )(1 τ D D (1 c )(1 τ e ) τ + D p ) e ) D D + [(1 τ ) (1 τ )(1 τ )] p c e Since the fist tem epesents the value of the unleveed fim, the gain to leveage is: D D [ 1 τ ) (1 τ )(1 τ )] ( p c e We can simplify this futhe if the individual who has pesonal tax ates of τ e and τ p detemines the yield (and coupon ate) on debt. Fo then D = ( 1 τ ) p and thus the gains to leveage is: (*) D 1 (1 τ c )(1 τ 1 τ p e ) Bealey and Myes (page 505) develop a diagammatic deivation of this fomula and you may want to take a look at this. 9

10 Suppose the individual that we ae consideing is taxed at the same ate of inteest and dividend income, i.e., τ p = τ e. Then the gains to leveage would be just τ c D, the same fomula that we got when thee wee no pesonal taxes. Thus the taditional MM appoach is coect when the tax ate on equity income and debt income is identical. The gains to leveage fomula above (Equation * above) depends on the pesonal tax ates of the investo unde consideation. Since diffeent investos have diffeent tax ates on debt and equity income, on whose pesonal tax ates should we focus? Those of the maginal investo, a fundamentally impotant notion. The maginal investo is the investo who detemines the maket pices of the secuities unde consideation. This statement by itself is not a vey illuminating one. In what follows we will explain this concept by using diffeent examples. Let us etun to the discussion above whee we computed the gains to leveage. Suppose the equilibium petax etun on equity is E and that on debt is D. Then investos will specialize in holding debt and equity instuments as follows: Goup I: Pefe Debt (1 - τ p ) D > (1 - τ e ) E Goup II: Pefe Equity (1 - τ p ) D < (1 - τ e ) E Goup III: Indiffeent (1 - τ p ) D = (1 - τ e ) E The fist goup obtains a highe afte-tax yield fom debt and hence will buy debt. The second goup obtains a highe afte-tax yield fom equity and hence will buy equity. The thid goup obtains the same yield fom debt and equity and so is indiffeent. 10

11 If both debt and equity coexist in the economy, thee will be investos in all thee goups. We claim that investos in Goup III ae the maginal investos since they hold both debt and equity and thus detemine the elative pices of debt and equity. MILLER'S EQUILIBRIUM Mille's equilibium efes to Meton Mille's (1977) agument that individuals in Goups I (and Goup III) will demand debt while individuals in goup II (and Goup III) will demand equity. Copoations will compete to supply debt to investos in Goup I until copoations as a goup have exhausted all the gains to leveage, i.e., the capital available with investos in Goup I is exhausted. Thus, given the maginal investos (Goup III), it should be the case that the gains to futhe leveage must be zeo, i.e., (1 - τ p ) = (1 - τ c )(1 - τ e ) If we substitute the above in the gains to leveage fomula above (Equation *), it tuns out that the gains to leveage is zeo and the value of the fim is independent to the debt-equity atio! This in tun implies that D E = 1 τ c Essentially, fo Mille's equilibium to occu, we need at least some investos who ae tax disadvantaged towad debt income at the pesonal level and thus demand a highe petax yield fo debt instuments. Hence, even though thee is a copoate tax advantage to debt, the 11

12 pesonal tax disadvantage to debt may outweigh the copoate tax advantage to debt (it does fo Goup II investos who hold equity but not fo Goup I investos who hold debt). Fo the maginal investo in Goup III who holds both debt and equity the pesonal tax disadvantage to debt just offsets the copoate tax advantage to debt. Mille's equilibium thus implies that the petax yield on debt is highe than the petax etun on equity. Most of us would complain that this is inconsistent with the eal wold. We need to emembe that in Mille's appoach we ae compaing iskless debt and iskless equity. The yields that we obseve in the eal wold howeve ae those fo iskless debt (o less isky debt) and isky equity and thus ae not diectly infomative on whethe debt is taxdisadvantaged elative to equity. ON THE REASONABLENESS OF MILLER'S EQUILIBRIUM To undestand how ealistic Mille's ideas ae, we conside the following thee examples fom Bealey and Myes. The fist example looks at a situation consistent with the tax policy befoe the 1986 Tax Refom Act when the copoate ate was 46%, the top inteest and dividend tax ate was 50% and the capital gains ate was 20%. In addition, this example assumes that one effectively pay a tax ate of 10% on ealized capital gains and could convet dividends into capital gains. The table on page 506 shows the calculations in this case. In this table, we see that debt is tax disadvantaged at the pesonal level and the net tax advantage to equity is 0.4%. The next example consides a moe ecent peiod, when the copoate ate was 34% and inteest income was taxed at 39.6%. Again, the assumption is made that capital gains ae 12

13 effectively taxed at half the statutoy ate, o 14% in this case. The fist table on page 507 shows the calculations in this case. Hee, the net tax advantage to debt is 4.5%. The last example looks at a situation whee investos have to pay tax on dividends (half thei equity income) at a ate of 39.6%, and ae taxed effectively at 15% on the capital gains potion of thei equity income. The bottom table on page 507 shows these calculations. The net tax advantage to debt is 12.8%. As such, Mille's conclusions that thee is no tax advantage to leveage because of the offsetting pesonal tax disadvantage to debt is not coect. On the othe hand, the taditional MM position ovestates the tax advantage to debt. Thus, a tax advantage to debt does exist, though it is less than what it is commonly believed to be. On Wall Steet, many analysts blindly assume that the tax advantage of debt is equal to the top statutoy tax ate of 35%. We see hee that this may be a faulty assumption. THE MARGINAL INVESTOR AGAIN The maginal investo is the investo who detemines the pices of the secuities that fims issue. In a majoity of cases, it is clea as to who is the maginal investo. If I own the fim, I am the maginal investo. On othe occasions, it is moe difficult to assess who the maginal investo is. In the case of municipal bonds, which ae tax exempt, the maginal investo is likely to be someone with a high tax backet (though pehaps not the highest). Fo example, a couple yeas ago thee wee shap inceases in the pices of municipal bonds. In paticula, municipal bond yields fell moe than Teasuy yields. An aticle in the Wall Steet Jounal 13

14 intepeted these lage pice inceases in municipal bonds as evidence that the maginal investo had shifted: suddenly, individuals in the highest tax ate wee the maginal investos. If we ae consideing pefeed stock, it is likely that the maginal investo is a copoation that has shot tem suplus cash (emembe that copoations get a deduction fo dividend income educing thei effective ate of taxation on dividend income). 14

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