Question

The Bellwood Company is financed entirely with equity. The company is considering a loan of $4.7 million. The loan will be repaid in equal principal installments over the next two years and has an interest rate of 9 percent. The company’s tax rate is 21 percent.

  

According to MM Proposition I with taxes, what would be the increase in the value of the company after the loan? (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

Given,

Loan amount = $4.7 million or $4700000

Interest rate = 9% or 0.09

Tax rate = 21%

Solution :-

Interest for year 1 = Loan amount x interest rate

= $4700000 x 9% = $423000

Tax shield for year 1 = Interest for year 1 x tax rate

= $423000 x 21% = $88830

Repayment in year 1 = $4700000/2 = $2350000

Loan balance after year 1 = $4700000 - $2350000 = $2350000

Interest for year 2 = Loan balance after year 1 x interest rate

= $2350000 x 9% = $211500

Tax shield for year 2 = Interest for year 2 x tax rate

= $211500 x 21% = $44415

Now,

Increase in the value of the company after the loan

= [Tax shield for year 1/(1 + interest rate)] + [Tax shield for year 2/(1 + interest rate)²]

= [$88830/(1 + 0.09)] + [$44415/(1 + 0.09)²]

= [$88830/(1.09)] + [$44415/(1.09)²]

= [$88830/1.09] + [$44415/1.1881]

= $81495.412844 + $37383.2169009

= $118878.63