For the exclusive use of M. Nowiszewski

9-210-037
NOVEMBER 20, 2009

TIMOTHY A. LUEHRMAN

Business Valuation and the Cost of Capital
A common approach to valuing a business is to discount its expected future cash flows at its cost of capital. This note explains how to compute the cost of capital for such an analysis. It consists of three sections: the first is focused on the financial economics of the problem; the second on practical considerations related to calculations; and the third concludes with some cautionary advice.

Financial Economics of the Cost of Capital
In the context of a discounted cash flow (DCF) valuation, the term “cost of capital” refers to the discount rate being applied. More specifically, it denotes the opportunity cost of funds associated with the subject business or project. The opportunity cost of funds is the expected return on an alternative investment with the same risk. That this is the correct discount rate follows from the assumption of value maximization: a value-maximizer will demand the same expected return on a given project that he or she could earn on an alternative investment with identical risk.
Having defined the cost of capital as an opportunity cost, we may now note that it is not necessarily the same as a treasurer’s “all-in cost of funds” used for comparing alternative funding sources. For example, suppose an investment project’s opportunity cost of funds is 10%, but the corporate treasurer has found a bargain and can actually raise the needed funds at a cost of 8%.
Which should be used as a discount rate? The correct discount rate is still 10%. If we discount the project’s cash flows at 8%, we will over-value it compared to alternative investments. If we overvalue it, we may over-pay for it compared to alternative investments, which would not be valuemaximizing. The fact that the treasurer can raise cheaper funds is indeed valuable, but the difference between 8% and 10% represents value created by skillful treasury operations, not by the investment project. The two should not be confused.
A further implication of defining the cost of capital as an opportunity cost is that therefore capital markets matter, always. Not because the treasurer uses them to source new funding – some firms are self-financing and seldom if ever raise new external capital. Rather, it is because the capital markets are where we find the “alternative investment with identical risk.” The capital markets represent, in large part, investors’ opportunity set for competing investments. This is so even if a corporation is private rather than public, even if it is self-financing, and even if managers and/or investors privately believe the market is “wrong” about the value it assigns to particular investments. In short, the market matters because it embodies genuine opportunities to buy and sell all kinds of assets.
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Senior Lecturer Timothy A. Luehrman prepared this note as the basis for class discussion.
Copyright © 2009 President and Fellows of Harvard College. To order copies or request permission to reproduce materials, call 1-800-545-7685, write Harvard Business School Publishing, Boston, MA 02163, or go to www.hbsp.harvard.edu/educators. This publication may not be digitized, photocopied, or otherwise reproduced, posted, or transmitted, without the permission of Harvard Business School.

This document is authorized for use only by Michael Nowiszewski in Investment Banking Fall 2014 taught by Viney Sawhney Harvard University from September 2014 to December 2014.

For the exclusive use of M. Nowiszewski
210-037

Business Valuation and the Cost of Capital

The opportunity cost of funds is comprised of two fundamental parts: time value and a risk premium. Time value represents the return investors earn for being patient, but not taking any risk.
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