After completing its capital spending for the year, Carlson Manufacturing has $2

ID: 2776838 • Letter: A

Question

After completing its capital spending for the year, Carlson Manufacturing has $2,600 extra cash. Carlson’s managers must choose between investing the cash in Treasury bonds that yield 7 percent or paying the cash out to investors who would invest in the bonds themselves.

A. If the corporate tax rate is 40 percent, what personal tax rate would make the investors equally willing to receive the dividend or to let Carlson invest the money? (Do not round intermediate calculations.)

B. Is the answer to (a) reasonable (yes or no)?

C. Suppose the only investment choice is a preferred stock that yields 12 percent. The corporate dividend exclusion of 70 percent applies. What personal tax rate will make the stockholders indifferent to the outcome of Carlson’s dividend decision? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

D. Is this a compelling argument for a low dividend payout ratio (yes or no)?

Explanation / Answer

A) let T be the personal tax rate on the income of investors.40 percent is the corporate tax rate on the Bond yield.

The after tax cash received by investors, after payment of dividends= 2600*(1-T ). this as a Investment the investors invest in the Treasury bonds themselves at 7%, thus the income received by them from investment = 7%*Investment=7%*2600*(1-T ), the after tax income(after paying personal tax T) of investors =7%*2600*(1-T )*(1-T)= 7%*2600*(1-T )2....(1)

If the corporate themselves invest in Treasury bonds at 7%,the income earned by them=7%*2600, after tax Income= 7%*2600*(1-.4) ...(2)

Now for the investors equally willing to receive the dividend or to let Carlson invest the money the after tax income made by them must equal the after tax income made by corporate on 2600 therefore ,equate 1 and 2

=> 7%*2600*(1-T )2=7%*2600*(1-.4)

=>(1-T )2=(1-.4)=.6 =>1-T=sqrt(.6)=> T=1-sqrt(.6)=.225 or 22.5%

Thus the personal tax rate of 22.5% would make the investors equally willing to receive the dividend or to let Carlson invest the money.

B) Yes the answer seems reasonable enough the personal income tax rate is justified at 22.5%

C) Now corporation can exclude 70% of preferred stock income and thus the income on which taxes are paid by corporate= .3*12%*2600,the total tax paid by corporate on income is .3*12%*2600*(.4) ...(1)

Also total tax paid by(after paying personal tax T) investors =2600*T+(1-T)*12%*2600*T= 2600T*(1+.12(1-T))...(2)

Now for the investors equally willing to receive the dividend or to let Carlson invest the money the taxes on income made by them must equal taxes on income made by corporate on 2600 therefore ,equate 1 and 2

.3*12%*2600*(.4)=2600T*(1+.12(1-T))

=>.3*12%*(.4)=T*(1+.12(1-T))

=>.12*.12=T(1.12-.12T)

=>.12*.12=1.12T-.12T2

=>.12T2-1.12T+.0144=0 => we solve to get T=(1.12+/-sqrt(1.122-4*.12*.0144))/.24

=> T=(1.12+/-sqrt(1.247488))/.24

=> T=(1.12+/-1.117)/.24 => T=(1.12+1.117)/.24=932% is rejected to be a feasible tax rate or T= (1.12-1.117)/.24=.003/.24=0.0125 or 1.25% we accept, therefore personal tax rate of 1.25% will make the stockholders indifferent to the outcome of Carlson’s dividend decision.

D) Yes its a compelling argument for a low dividend payout ratio as personal income tax rate is usually high around 20% is much higher than the above calculated value of 1.25% this makes the argument for no dividends payout as investors are better off financially when no dividends are paid out due to very low taxes paid by the corporate due to 70% rule as compared to when dividends are paid.At high tax rate personal income tax rate the investors receives much lower income after tax.If T=22.5% then taxes paid by investors=2600*.225*(1+.12(1-.225))=639.405 while tax paid by corporate is .3*.12*2600*(.4)=37.44 are much lower than taxes paid by the investors so better off with low dividend payout ratio policy.

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After completing its capital spending for the year, Carlson Manufacturing has $2

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After completing its capital spending for the year, Carlson Manufacturing has $2

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