# The Finance Decision

## Equity Valuation and the Cost of Capital

### Introduction

Part Two provided a detailed explanation of the investment decision with only oblique reference to the finance decision, which determines a company's cost of capital (discount rate) designed to maximise shareholder wealth. But if wealth is to be maximised, management must determine what return their shareholders require from an investment and then only accept projects that have a positive NPV when discounted at that rate.

There is also the question as to what cut-off rate should apply to investment proposals if corporate finance were obtained from a variety of sources, other than ordinary shares? Each stakeholder requires a rate of return that may differ from the equity market and may be unique. In this newly leveraged situation, the company's overall cost of capital (rather than its cost of equity) measured by its weighted, average cost of capital (WACC) would seem to be the appropriate investment acceptance criterion.

Given the normative assumption of financial management, the purpose of Part Three is straightforward. How does a firm maximise corporate wealth by securing funds at minimum cost that not only provides shareholders with their desired rate of return, once investment takes place, but also satisfies the expectations of all capital providers?

To set the scene, Chapter Five provides an explanation of the most significant explicit, opportunity cost of external funding available to management. The cost of ordinary shares measured by their rate of return, often termed the equity capitalization rate or yield.

### The Capitalisation Concept

In Chapter Two we defined an investment's present value (PV) as its relevant periodic cash flows (Ct) discounted at a constant cost of capital (r) over time (n). Expressed algebraically: The equation has a convenient property. If the investment's annual cash receipts are also constant and tend to infinity, (Ct = C = C2 = C3 = Cw) their PV simplifies to the formula for the capitalisation of a constant perpetual annuity: The term r is called the capitalisation rate because the transformation of a cash flow series to value (i.e. capital) is termed "capitalisation". With data on PVw and r, or PVw and Ct, we can also determine values for Ct or r respectively. Rearranging Equation (2) with one unknown: These PV equations are vital to your understanding of various share valuation models, which define the possible cost of equity as a managerial cut-off rate for investment. So, let us define the models beginning with dividend valuation.

### Single-Period Dividend Valuation

Assume you hold a share for one year, at the end of which a dividend is paid. You then sell the share ex-div, which means the new investor does not receive the dividend (you do) as opposed to cum-div, where the dividend is incorporated into price. Your current ex-div price, (P0) is defined by the expected year-end dividend (D1) plus the expected year-end share price (P1) discounted at the appropriate rate of return for shares in that risk class, the cost of equity (Ke). Thus, we have the single-period dividend valuation model: Sequentially, if the new investor holds the share for a further year, then their ex-div price on acquisition (i.e. dated when you sold it) is also given by the single- period model. Note however that if you held the share for two years, its current ex-div price would be the discounted sum of two dividends and the ex-div price at the end of year two, as follows: ### Finite Dividend Valuation

Assuming the cost of equity Ke is constant; the current ex-div price of a share held for any finite number of years (n) and then sold equals: Rewritten, this defines the finite-period, dividend valuation model: where Pn equals the ex-div value at time period n, determined by the discounted sum of subsequent dividends. Activity 1

A potential shareholder anticipates a dividend per share of 10 pence and 11 pence in years one and two respectively, whereupon the shares are expected to be sold ex div for £3.00 each. If the equity capitalisation rate is 20 percent per annum, confirm that the maximum current ex-div price at which the shares should be purchased is £2.24.