The book provides a rigorous introduction to corporate finance and the valuation of equity. The first half of the book covers much of the received theory in these areas such as the relationship between the risk of an equity security and the return one can expect from it, the effects of leverage (that is, the borrowing policies of the firm) on the return one can expect from the firm's shares and the role that dividends, operating cash flows and accounting earnings play in the valuation of equity. The second half of the book is more advanced and deals with the important role that "real options" (that is, as yet unexploited investment opportunities) play in the valuation of equity.
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1 The measurement of returns on bonds, equities and other financial instruments
Ā§1-1. The calculation and indeed, the manipulation of returns pervades our everyday lives. When one opens a bank account or line of credit with a financial institution, the rate of interest on surplus funds and/or the rate of interest on the overdraft facilities we expect to use figure highly in the decisions we make about which bank/and or financial institution we will lend our custom to. When it comes to risky assets such as the shares and bonds of publicly listed companies, we make investment decisions by weighing the returns we expect to get from our proposed investments against the risks that are likely to arise from them. Our retirement plans also hinge crucially on the returns earned by the superannuation funds with which we deposit our retirement funds and on the prospective benefits these returns will enable us to enjoy after we retire. All of this presupposes of course that we have a clear understanding of how the returns on a given portfolio or financial instrument ought to be calculated. Hence, the principal brief of this chapter is to identify the pitfalls that may arise from the incorrect calculation and averaging of the returns that accrue on shares, bonds, portfolios and other financial instruments. We begin our analysis with a consideration of the procedures that can be used to compute the returns on bonds.
Ā§1-2. A bond is a written contract by a debtor to pay a creditor a redemption payment V on an indicated date and to pay a pre-specified amount K (normally termed interest) on a periodic basis. The typical bond mentions a borrowed principal H, called the face value or par value of the bond. Bonds typically make interest payments on a semi-annual basis and are redeemable at par ā in which case V = H. Consider, then, the purchaser of a bond who demands that his money be invested at a pre-specified rate r. We call this the investment rate. The price the investor will pay for the bond is given by
the present value of the final redemption payment (V) plus the present value of the remaining interest payments (K)
One can demonstrate how this valuation formula is implemented using the following simple example.
An H = Ā£100 par 6 per cent bond pays interest on a semi-annual basis. This means that interest of K = (0.06/2) Ć H = 0.03 Ć Ā£100 = Ā£3 is paid at the mid-point of the year and also at the end of year until such time as the bond is redeemed. The bond is to be redeemed on 30 June 2012. Determine the price to be paid for the bond if (a) the bond is purchased on 1 July 2009, (b) the investment rate is 2 per cent (per half year); that is, r = 4 per cent (per annum) compounded semi-annually and (c) the bond is redeemable at par; that is V = Ā£100 = H. Now the present value of Ā£100 receivable in three yearsā time, compounded at 4 per cent (per annum) compounded semi-annually, is
Likewise, the present value of the interest payments compounded at 4 per cent (per annum) compounded semi-annually is
Hence, the investor would be prepared to pay no more than (Ā£88.80+Ā£16.80) = Ā£105.60 for the bond.
Ā§1-3. The rate of interest quoted on a bond is normally what is known as the nominal rate of interest. With a given nominal rate r, compounded m times per year, we define the corresponding effective rate of interest to be the rate that would apply if compounding occurred on an annual basis only. One can demonstrate this point by supposing for the example given in Ā§1-2 above that the investment rate is 4.04 per cent compounded annually. We would then have that the present value of Ā£100 receivable in three yearsā time, compounded at an annual rate of 4.04 per cent, would be
Likewise, the present value of the interest payments compounded at an annual rate of 4.04 per cent will be
Hence, the value of the bond is again (Ā£88.80 + Ā£16.80) = Ā£105.60, i.e. the same value as calculated in Ā§1-2 above. This implies that an interest rate of 4 per cent (per annum) compounded semi-annually is equivalent to an interest rate of 4.04 per cent compounded annually. In other words, an effective rate of interest of 4.04 per cent corresponds to a nominal rate of interest of 4 per cent (per annum) compounded semi-annually. The effective rate of interest is often called the Annual Percentage Rate or APR for short. We develop the relationship between the nominal rate of interest and the effective rate of interest (or APR) in further detail in Ā§1-7 below.
Ā§1-4. Suppose I have to repay a loan and I want to confirm the integrity or otherwise of the figures that have been given to me by the lending institution. The principles just enunciated for bond valuation may also be applied here. The present value of the repayments on the loan must be equal to the amount borrowed, or
where P is the principal (or the amount) borrowed, N is the number of repayments that will be made on the loan, R is the periodic repayment and r is the investment rate on the loan. One can demonstrate the application of this formula by considering a person who takes out a loan of Ā£2,000 that is to be repaid in 12 equal monthly instalments. The borrowing (investment) rate is 18 per cent (per annum). It thus follows that P = Ā£2,000, r = 0.18/12 = 0.015 or 1
