Corporate Finance, Module 17

Homework Assignment

(The attached PDF file has better formatting.)

A project with an indefinite life has an initial investment is $10 million.

The opportunity cost of capital is 12% with all-equity financing, the borrowing rate is 8%, and the firm borrows $4 million against the project.

●    The debt is perpetual; it is refinanced each year.
●    The corporate tax rate is 35%.

A.    What is the interest paid in each year?
B.    What is the present value of the debt tax shields if the debt is fixed at $4 million?
C.    If the debt is re-balanced each year to a fixed percentage of the project’s value, is the present value of the debt tax shield higher or lower? Explain why.

I get the following answer, please correct me if I am wrong...

Part A: $ 320,000

Part B: $ 1.4 million

For Part C, I am not very sure on how to answering, I get $ 112,000/[12% x (1-35%)] = $ 1,435,897, is this answer correct?

For the discounting interest rate in Part C, I take opportunity cost of capital after tax,[12% x (1-35%)], is this correct?

Or I shall use 8% x (1-35%)= 5.2%?

Please advice.

[NEAS: Part C asks if the debt tax shield is higher or lower. For the exact figure, work out the weighted average cost of capital for the project, and use this rate (not tax adjusted) as the capitalization rate. This rate is higher than the cost of debt capital, which gives the answer to Part C. You don’t have to work through all the mathematics for the homework assignment.]

 

 

The weighted average cost of capital for the project is 10.86% which is higher than the cost of debt capital.

Thus, I will get lower debt shield. Is this correct?

Can you please explain Part C in more detail? 

The question seems to imply there is one answer, but intuitively the answer seems to depend on two things:

1) The fixed percentage that you want to re-balance to

2) How the project's value is changing (if it's static why do you need to re-balance every year?)

 

Thanks!

Nevermind: the reading for module 19 took care of this

I tried to solve part C based on the practice problem 17.1G (where equity is converted to debt to keep the debt-equity ratio constant).

Project Value = Equity Financed Value + PV (Tax Shield),

                   = 10 + PV(Tax Shield)

then since 40% of the Project Value = debt value D,

then D = .4(10+ 0.35D)

Solving: D=4.65.

Since the Project Value also is = D + E, the E must be reduced from the original $6M to $5.348M.

(the financing itself does not change the project value)

Therefore, rebalancing the debt will increasing the debt, which will increase the PV of the tax shield.

Is this the correct reasoning?  I don't understand the NEAS comment to use the 3 step WACC calc...

Can anyone help?

-Heather

The 3 step WACC process is referenced in the next module. Page 543 for the ninth edition.

[NEAS: Yes]