Financial Valuation: Loan Structures and Equity Cost Models

Loan Types and Capital Cost Analysis

Understanding Loan Structures

American Loans Explained

In American loans, all intermediate payments only include interest expenses. The principal is paid back at maturity.

C − Fees = I = ∑T_i · C_o + C_o

_{o o j=1} (1+R_B)^j (1+R_B)^T

French Loans Explained

The loan is repaid with equal payments (P), which include both interest and partial repayment of the principal. The process requires three steps:

1. Calculate the constant payment per period ‘P’.
2. With the computed value ‘P’, calculate the cost of debt.
3. Compute the effective annual rate.

The Cost of Equity Capital

Firms with excess cash can either pay a dividend or make a capital investment. Because stockholders can reinvest the dividend in risky financial assets, the expected return on a capital-budgeting project should be at least as great as the expected return on a financial asset of comparable risk.

The discount rate of a project should be the expected return on a financial asset of comparable risk.

Dividend Discount Model (DDM)

The DDM approach is used to forecast the expected return on the market as a whole, leading to an estimate of this risk premium. We now use the DDM to estimate the expected return on an individual stock directly (for perpetual growing dividends):

R = Div/P + g

Where P is the price per share of a stock, Div is the dividend per share to be received next year, R_S is the discount rate, and g is the expected annual growth rate in dividends per share (computed as the retention ratio, which is retained earnings to earnings, times ROE). The equation tells us that the discount rate on a stock is equal to the sum of the stock’s dividend yield and its expected growth of dividends. So, to apply the DDM, we must estimate both the dividend yield and the expected growth rate.

Capital Asset Pricing Model (CAPM)

From the firm’s perspective, the investor’s expected return is the Cost of Equity Capital:

R_S = R_F + β·(R_M − R_F)

Determining the Risk-Free Rate (R_F)

Treasury securities are close proxies for the risk-free rate. The CAPM is a period model; however, projects are long-lived, so average period (short-term) rates need to be used. The historical premium of long-term (20-year) rates over short-term rates for government securities is 2%. Therefore, the risk-free rate to be used in the CAPM could be estimated as 2% below the prevailing rate on 20-year treasury securities.

Calculating the Market Risk Premium (R_M - R_F)

There are two primary methods for calculating the market risk premium:

1. Method 1: Using historical data.
2. Method 2: Using the Dividend Discount Model (DDM). Market data and analyst forecasts can be used to implement the DDM approach on a market-wide basis.