# Your firm currently has $56 million in debt outstanding with a 9% interest rate. The terms of the...

## Question:

Your firm currently has $56 million in debt outstanding with a 9% interest rate. The terms of the loan require it to repay $14 million of the balance each year. Suppose the marginal corporate tax rate is 40%, and that the interest tax shields have the same risk as the loan. What is the present value of the interest tax shields from this debt?

## Present Value:

The present value of an amount that it is to be received in the future can be calculated by multiplying the amount with the present value interest factor. The present value interest factor is a table that contains the value of discounting factors of different interest rates and time periods.

## Answer and Explanation: 1

**Info:**

Loan = $56

Annual Repayment = $14

**By Computing:**

{eq}Years \ required \ to \ pay-back \ the \ loan \ = \ \dfrac{Loan}{Annual \ Repayment} \\ Years \ required \ to \ pay-back \ the \ loan \ = \ \dfrac{56}{14} \\ Years \ required \ to \ pay-back \ the \ loan \ = \ 4 \ years {/eq}

Present value of the interest tax shields from this debt is shown below:

Accounts Title | Year 0 | Year 1 | Year 2 | Year 3 | Year 4 | Total Present value |
---|---|---|---|---|---|---|

Debt at the beginning that is year | 56 | |||||

Amount paid annually towards principal | 14 | 14 | 14 | 14 | ||

Debt at the end of the year | 56 | 42 | 28 | 14 | 0 | |

Interest on the debt at the end of the year @ 0.09 | 5.04 | 3.78 | 2.52 | 1.26 | ||

Interest tax shield @40% | 2.016 | 1.512 | 1.008 | 0.504 | ||

Present value for 10% for all the years | 1 | 0.917431193 | 0.841679993 | 0.77218348 | 0.708425211 | |

Present value of interest tax shields | 1.849541284 | 1.27262015 | 0.778360948 | 0.357046306 | 4.257568689 |

Therefore, the present value of the interest tax shields from the debt is $4.2575.

#### Learn more about this topic:

from

Chapter 8 / Lesson 3Learn how to find present value of annuity using the formula and see its derivation. Study its examples and see a difference between Ordinary Annuity and Annuity Due.