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.)

Question

23-07-2019
Business

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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.)

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TomShelby TomShelby · Answer 1 · 2019-08-03T00:24:49+02:00

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