Question

2. The Birmingham Road Company (BRC) has won a tender to build a highway extension. The project will last 10 years and will generate free cash flows (FCFs) of £100 million per year for 10-years. These FCFs are after-tax but before financing costs. The unlevered (i.e., all equity) cost of capital for the project is 10% and BRC’s tax rate is 40%.

   BRC will finance the project with a combination of debt and equity and is considering three alternatives as regards borrowing. The (pre-tax) interest rate in each case would be 5%. (Note: there are no tax consequences when the firm repays principal – as opposed to interest – on a loan).

   1. “ConstantD/V”:Adjustingtheamountofborrowingeachyearsothattheratio of the amount of debt to the total value of the project is maintained at 40%; OR

   2. “Constantamountofdebt”:Takingoutaconventional10-yearloan(i.e.,theloan will be repaid in year 10) with the amount of the loan equal to 40% of the unlevered value of the project; OR

   3. “Amortizing Loan”: Taking out a 10-year amortizing loan, i.e., one in which equal payments are made each year so that the loan – including interest – is finally repaid in year 10. The amount of the loan will be equal to 40% of the unlevered value of the project.

   Questions

   1. What is the PV of the FCFs if the project is all equity financed?

   2. What is the present value of the tax shields for borrowing scenario #1 (Constant D/V)?

   3. What is the present value of the tax shields for borrowing scenario#2 (Constant amount of debt)?

   4. What is the present value of the tax shields for borrowing scenario #3 (Amortizing Loan)?

   5. Are these tax shields the same? If not, why not?

   6. Suppose that BRC plans that all after-tax project cash flows each year, net of any loan interest payments and loan repayments due to lenders in that year, will be paid out to shareholders as a dividend. If you were a bank considering lending to BRC for this project, how would BRC’s dividend plan affect your view of each of the three borrowing alternatives?

Answer 1

PV of the FCFs if Project is all Equity Financed	Amount in GBP Millions
Free Cash Flows for 10 years	100 Million GBP Per Year
Cost of Equity	10%
Tax Rate	40%
Present Value of Cash Flows	=	PV(rate,nper,pmt)
	=	PV(0.1,10,-100)
	=	614.46 GBP Million
Present Value of Tax Sheilds in Scenario #2 Constant Amount of Debt
Year	1	2	3	4	5	6	7	8	9	10
Free Cash Flows Before Finance Cost	100	100	100	100	100	100	100	100	100	100
Amount Borrowed	245.78	245.78	245.78	245.78	245.78	245.78	245.78	245.78	245.78	245.78
	(614.46*40%)
Interest @ 5%	12.289	12.289	12.289	12.289	12.289	12.289	12.289	12.289	12.289	12.289
Tax Saving @ 40%	4.9156	4.9156	4.9156	4.9156	4.9156	4.9156	4.9156	4.9156	4.9156	4.9156
	(12.289*40%)
WACC	=	Cost of debt * weight of Debt + Cost of Equity * Weight of Equity
	=	5*0.4+10*0.6
	=	8%
Present Value of Tax Sheild	=	PV(rate,nper,pmt)
	=	PV(0.08,10,-4.9156)
	=	32.98 GBP Million