Project Evaluation

Company XYZ Ltd. is located in a country where companies are taxed on their corporate income, but individuals are not taxed on their personal income. Mr. A is toying with the idea of buying this company. He is also thinking of how to finance the purchase if he decides to buy it. To arrive at an answer to these questions) of whether to buy, and how to finance the purchase), Mr. A analyses the different alternatives. He starts by assuming that XYZ Ltd. is purchased with debt only.

Buying XYZ Ltd. using only equity

XYZ Ltd. has an expected annual free cash flow (FCF) of Rs. 1,000 per year; this FCF is anticipated to recur, year after year, at the same level.

Mr. A has computed the cost of capital for the purchase as rU = 20%. The symbol "U" as a subscript for the discount rate (rU) stands for "unlevered" and is meant to indicate that in this case rU is the discount rate appropriate for the case where Mr. A buys XYZ Ltd. with only equity (meaning: his own money, without borrowing).

This rU = 20% is a cost of capital that reflects only the business risks of XYZ Ltd. If purchased only with equity, therefore, the company is thus worth 1, 000/(20%) = 5, 000.

Let the symbol VU stand for the "unlevered value of the firm". That is, VU is what a company is worth if it is financed only with equity.

In this case,

VU =

Buying XYZ Ltd. using debt

The source of borrowing to Mr. A is one of his relatives, Ms. R. This relative is in fact his business partner, but their joint deals are structured so that she's always the lender and Mr. A the equity owner. There's another unusual feature to the lady's lending--she gives out perpetual debt--her loans require only an annual payment of interest, but no repayment of principal.

The cost of debt to Mr. A, denoted by rD, is the interest rate charged by his mother on her loans to him. In this case rD = 8%. Together, Mr. A and Ms. R are exploring two alternative financing arrangements:

* Alternative 1: Mr. A buys XYZ Ltd. for cash; immediately thereafter, the company borrows Rs. 3,000 from Ms. R and repays it to Mr. A. In this case XYZ Ltd. is a levered company. ("Leverage" in this context means that the company has debt on its balance sheets.)

* Alternative 2: Mr. A borrows Rs. 3,000 from Ms. R, and then buys XYZ Ltd. for cash. In this case, XYZ Ltd. is an unlevered "all-equity" company (no debt on its balance sheets) and Mr. A is levered.

The fundamental difference between these two alternatives is that the country's tax code has a corporate income tax but no personal