Question

n September​ 2008, the IRS changed tax laws to allow banks to utilize the tax loss carryforwards of banks they acquire to shield up to​ 100% of their future income from taxes​ (prior law restricted the ability of acquirers to use these​ credits). Suppose Fargo Bank acquired Covia Bank and with it acquired $ 88 billion in tax loss carryforwards. If Fargo Bank was expected to generate taxable income of $ 12 billion per year in the​ future, and its tax rate was 30 %​, what was the present value of these acquired tax loss carryforwards given a cost of capital of 8 %​? How would the present value change under current law which restricts the amount of the deduction to 80 % of​ pre-tax income? If Fargo Bank was expected to generate taxable income of $ 12 billion per year in the​ future, and its tax rate was 30 %​, what was the present value of these acquired tax loss carry forwards given a cost of capital of 8 %​? The present value of these acquired tax loss carryforwards is ​$ nothing billion. ​ (Round to two decimal​ places.)

Answer 1

Given that,

tax loss =$ 88 billion

taxable income = $ 12 billion per year

tax rate = 30 %​

cost of capital r = 8 % =0.08

Determination of present value:

Tax amount A=30% * 12= $ 3.6 billion

utilize the tax loss carryforwards of banks they acquire to shield up to​ 100%:

with 100% utilisation, $ 88 billion can be used for 88/3.6= 24.44 years

$ 3.6 billions used for 24 years.

PV of an annuity of $ 3.6 billion= PV of first 24 years (n=24)

PV =A*(1-(1+r)^(-n))/r

Substitute required values

= 3.6*(1-(1+0.08)^(-24))/0.08

= 3.6(1-0.1577)/0.08

= 3.6*0.8423/0.08

= 3.03228/0.08

PV=$ 37.9 billion

for 25th year =(88-(3.6*24))= $ 1.6 billion

PV for 25th year=1.6/(1+0.08)^25

= 1.6/6.8485

= $ 0.23 billion

Total PV =37.9 + 0.23 = $38.13 billion

amount of the deduction to 80 % of​ pre-tax income:

Tax deduction each year=80%*3.6=$ 2.88 billion

$ 88 billion can be used for 88/2.88= $ 30.55 years

$ 2.88 billions used for 30 years.

PV of first 30 years will be PV of an annuity of $ 2.88 billion

PV =A*(1-(1+r)^(-n))/r

Substitute required values

= 2.88*(1-(1+0.08)^(-30))/0.08

= 2.88(1-0.0994)/0.08

= 2.88*0.9/0.08

= 2.592/0.08

PV= $ 32.4 billion

for 31th year =(88-(2.88*30))= $ 1.6 billion

PV for 31st year=1.6/(1+0.08)^31

= 1.6/10.868

=$ 0.147 billion

Total PV =32.4 + 0.147 = $ 32.547 billion