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The Dart Company is financed entirely with equity. The company is considering a loan of $1.83 million. The loan will be repaid in equal principal installments over the next two years, and it has an interest rate of 8 percent. The company’s tax rate is 35 percent. According to MM Proposition I with taxes, what would be the increase in the value of the company after the loan? (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Respuesta :

TomShelby

Answer:

PV of tax shield 52276.75

Δ52276.75 in the company's value

Explanation:

Modigliani Miller proposition1 with taxes:

[tex]V_u + PV_{taxshield} = V_l[/tex]

We have to calculate the interest expense for the loan, then apply the tax shield and calculate the present value

beginning   Principal payment   Interest   ending

1,830,000   228,750   36,600   1,601,250

1,601,250   228,750   32,025   1,372,500

1,372,500   228,750   27,450   1,143,750

1,143,750   228,750   22,875   915,000

915,000   228,750   18,300   686,250

686,250   228,750   13,725   457,500

457,500   228,750   9,150   228,750

228,750   228,750   4,575   -  

                                164,700  

Next we calculate the tax shields:

Interest tax shield

36600 12810

32025 11208.75

27450 9607.5

22875 8006.25

18300 6405

13725 4803.75

9150 3202.5

4575 1601.25

Next the present value of the tax shield

the first for are for the first year

and the next for, for the second year.

                      year 1 year 2

Q1                    12810 6405

Q2               11208.75 4803.75

Q3                9607.5 3202.5

Q4               8006.25      1601.25

Total            41632.5 16012.5

Finally we calculate the present value of the tax shield

[tex]\frac{Principal}{(1 + rate)^{time} } = PV[/tex]

[tex]\frac{41632.5}{(1 + 0.08)} = PV[/tex]

[tex]\frac{16012.5}{(1 + 0.08)^{2} } = PV[/tex]

Y1 38549.61

Y2 13728.14

PV of tax shield 52276.75

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