# Topic 3 - Financial Maths, Security Valuation – Bills, Bonds & Equity

This article is a topic within the subject Business Finance.

## Contents |

## Required Reading

Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 156-222.

## Valuing A Firm

A firms can be *valued in 2 ways*; the **present value (PV) of cash flows generated by the firms productive assets or the sum of the PV of the cash flows generated by a firms individual securities (debt and equity).** The net cash flows from real assets, after reinvestment costs are known as free cash flows.

**Equity represents an ownership interest**. Shareholders are able to vote but are ranked behind debt in liquidation. The **market price should equal the stocks intrinsic value IF the market is efficient**. The required rate of return is the minimum return on a share for an investor to buy it accounting for alternative investments & risk.

### Developing a Model

If you kept pushing back the selling date, the price of the stock is the PV of all expected future ‘dividends’ payments made to shareholders in the form of cash or shares – dependent on business performance].

### Constant Dividend Model

The firm will pay a constant dividend; this is often the case with preferred stock. Price/value is computed using the perpetuity formula.

### Constant Dividend Growth: (A Growing Perpetuity)

The firm will increase the dividend by a constant percentage every period.
**Dividend (Year t) = Dividend (Year 0) x ( 1 + Growth Rate )^t**, is the relationship between current dividends & future dividends in the constant dividend growth model.

### Variable Dividend Growth

Dividend growth is not consistent initially, but settles down to a constant growth rate eventually. We discount the initial years individually until after the final variable dividend. We than employ the constant growth dividend model & discount that value back the same amount of years as the final variable dividend.

#### Examples: Required Rate of Return = 10%

#### Finding the Required Rate of Return through the Constant Dividend Growth Model

XYZ last traded at $1.50. Next year’s dividend is $0.20 & is expected to grow at 5% forever. Assuming the market is efficient,

## Calculating The Dividend Growth Rate

Assuming the payout ratio & ROE remains stable, the estimated growth in dividends is **Growth = (1 - payout ratio) × Return on Equity**

## P/E Ratios

A simple method of appraising whether a stock is over or under priced. It is Price/(Earnings Per Share) & can be used to compare with other companies, particularly those in its industry. From this we can derive:

## Debt Securities: Bank Bills

## Bond Valuation

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**Bonds** are *debt instruments that are issued & are generally longer than 1 year*. For example, ABC issues 100,000 bonds for $1000 each, with a coupon rate of 5% & maturity in 2 years.

**Par Value**, the principal repaid at maturity - $1000**Coupon Rate**, the interest rate paid by the issuer - 5%**Fixed Coupon**, the interest rate remains fixed over the life of the bond**Zero Coupon**, no coupon is paid, the bond is initially sold at a discount to par value offering capital gain**Floating Rate**, the coupon rate is adjusted periodically to account for changes in the market interest rate**Coupon Payment**, par value × coupon rate = $50, is usually paid semi annually ($25)**Maturity Date**, the date where par value is to be repaid**Yield to Maturity**, rate of return earned on a bond held until maturity. Required interest rate on the bond in market

## Yield To Maturity And The Coupon Rate

Assuming, the YTM or RR remains constant, the value of a premium bond will decrease over time to its par value while a discounted bond will increase over time to its par value. This is because the coupon rate becomes relatively less important as compared to the repayment of face value.

## Interest Rates & Term Structures

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**Interest Rate Risk** is the *chance that interest rates will change in the future, thereby changing the value of an asset*. This is because future streams of cash are discounted differently. This alters reinvestment effects. Interest rate risk is influenced by:

**Term to Maturity**-*The longer the term to maturity, the greater the effect of the new interest rate via compounding*- Longer term bonds are generally more price sensitive to interest rates
- Lower coupon bonds are also more sensitive as they has less cash flow earlier on

- Default Risk -
*The chance that the bond issuer will fail to make a coupon or principal payment*- As default risk rises, the bond value falls

**Term Structure** is the *relationship between term to maturity & the interest rate for securities in the same risk class*. It tells us the pure time value of money. The determinants of term structure are:

**Market Expectations Theory**- Interest rates are set so investors can expect to receive, on average, the same return over any future period, regardless of the security in which they invest
- Long & short term rates are perfect substitutes
*The observed long term rate is a function of today’s short term rate & expected future short term rates*

**Liquidity Premium Theory***Although future interest rates are set by investor expectations, investors need to be given some reward (liquidity premium) for taking the extra risk involved in longer term securities - longer term = larger fluctuations*- Upward bias built into long term rates because of risk premium (upward sloping)
- Forward rates are not equal to expected future short term rates

### Inflation & the Term Structure: Inflation Premium (If increasing inflation - Upward Sloping)

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We would expect lenders to *require the nominal interest rate to compensate them for expected inflation*. A **high inflation rate expectation usually means a high nominal interest rate**. Inflation expectations raise expectations about future interest rates, raise liquidity risk & have an impact on the term structure.

**Fisher Effect - (1 + Nominal Rate) = (1 + Real Rate) x (1 + CPI Rate)**

### Determinants of Yield to Maturity: Default Risk & Interest Rates

While we know the size of the cash flows from debt securities, there is some possibility that the borrower may default. **The higher the markets assessment of default probability the higher required rate of return (or YTM) on the debt**.

### Other Factors Affecting Interest Rate Structures

An investor will only buy a security of low marketability if the yield is greater than that on a higher marketability security. Additionally there is a higher expected rate of return on equity than on debt as shareholders are exposed to greater risk.

## Market Equilibrium

In market equilibrium, security prices are stable& there is no general tendency for people to buy or sell. Price = PV of future cash flows (intrinsic value). If P < IV, buy orders will come in due to ‘bargain’ & price will rise until expected return = required return. (Vice versa)

## End

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## References

**Textbook** refers to Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010.

- ↑ Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 201-211
- ↑ Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 157-159
- ↑ Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 160-172
- ↑ Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 188-199
- ↑ Essentials of Corporate Finance (2nd Australian and New Zealand edition), by Stephen A. Ross, Rowan Traylor, Ron Bird, Randolph W. Westerfield and Bradford D. Jordan, McGraw Hill Irwin, 2010., pp. 186-187