# A local firm has debt worth $200,000, with a yield of 11%, and equity worth$300,000. It is...

## Question:

A local firm has debt worth $200,000, with a yield of 11%, and equity worth$300,000. It is growing at a 6% rate, and its tax rate is 40%. A similar firm with no debt has a cost of equity of 15%. Under the MM extension with growth, what is the value of your firm's tax shield, i.e., how much value does the use of debt add? Show your work.

a. $97,778 b.$102,857

c. $113,143 d.$124,457

e. \$136,903

## Tax Shield:

There are some expenses that are deducted from the taxable income. Their expenses reduce the taxable income which results in lesser income tax. These expenses provide tax shield to the company.

Under mm approach with growth,

{eq}Value \ of \ firm \ tax \ shield \ = \ \dfrac{\left ( Value \ of \ debt \ \times \ Tax \ rate \ \times \ Interest \ rate \right )}{\left ( Unlevered \ cost \ of \ capital \ - \ Growth \ rate \right )} \\ Value \ of \ firm \ tax \ shield \ = \ \dfrac{\left ( 200,000 \ \times \ 0.40 \ \times \ 0.11 \right )}{\left ( 0.15 \ - \ 0.06 \right )} \\ Value \ of \ firm \ tax \ shield \ = \ \dfrac{8,800}{0.09} \\ Value \ of \ firm \ tax \ shield \ = \ 97,778 {/eq}

Hence, option a is correct. 