Valuation of Long Term Securities

What is a cynic? A man who knows the price of everything and the value of nothing.

Oscar Wilde

Valuation

• Liquidation value

• Book value

• Market value

• Intrinsic value

Discounted Cashflow Model

The value of an asset is the present value of its expected cashflows discounted at a risk adjusted required rate of return.

Discounted Cashflow

V = C1/(1+r) + C2/(1+r)2 + C3/(1+r)3+….+

(Cn+ M) / (1+r)n

Required Rate of Return

• Time

• Inflation

• Risk

All securities in an equivalent risk class are priced to offer the same expected return.

Bond Valuation

• Face value

• Coupon rate

• Maturity

• Future cashflows

Bond Valuation

V = C1/(1+r) + C2/(1+r)2 + C3/(1+r)3+….+

(Cn+ M) / (1+r)n

Where C1…..Cn are the coupon payments, M is the maturity value.

r is the discount rate and V is the value of the bond.

Bond Valuation

V = C* PVIFAr,n + M * PVIFr,n

Rs 100 FV. 10% coupon. 9 years maturity.

12% discount rate.= 10 * PVIFA (12%.9years) + 100 * PVIF(12%.9years)= 10 *5.328 + 100 * 0.361 = 89.38

8% discount rate.= 10 * PVIFA (8%.9years) + 100 * PVIF(8%.9years)= 10* 6.247 + 100 * 0.5 = 112.47

Zero Coupon Bond

• No periodic payment of interest. Sold at discount to face value.

• V = Maturity value * 1/ (1+r)n

= Maturity value * PVIFr,n

• 1000 FV. 10 years. 12% discount rate.

• Value = 1000 * 0.322 = Rs 322

Perpetual Bonds

• A bond that does not mature and hence, pays constant interest forever.

• V = C/ r

Yield to Maturity

• The discount rate that equates the present value of all the future cashflows of the bond to the current market price

• Interest rate risk. Relationship between interest rate and bond prices

Valuation of shares

Value of a share equals the present value of expected future dividends.

Dividend Discount Model

Valuing Common Stocks

Expected Return - The percentage yield that an investor forecasts from a specific investment over a set period of time. Sometimes called the market capitalization rate.

Expected Return

rDiv P P

P1 1 0

0

Valuing Common Stocks

Example: If Fledgling Electronics is selling for $100 per share today and is expected to sell for $110 one year from now, what is the expected return if the dividend one year from now is forecasted to be $5.00?

15.100

1001105Return Expected

Valuing Common Stocks

The formula can be broken into two parts.

Dividend Yield + Capital Appreciation

Expected Return

rDiv

P

P P

P1

0

1 0

0

Valuing Common Stocks

• Price = P0 =(Div1+ P1)/ (1+r)

• Current price based on forecasted dividend, forecasted price and discount rate

Valuing Common Stocks

Dividend Discount Model - Computation of today’s stock price which states that share value equals the present value of all expected future dividends.

H - Time horizon for your investment.

PDiv

r

Div

r

Div P

rH H

H01

12

21 1 1

( ) ( )

...( )

Valuing Common Stocks

Example

Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

Valuing Common Stocks

Example

Current forecasts are for XYZ Company to pay dividends of $3, $3.24, and $3.50 over the next three years, respectively. At the end of three years you anticipate selling your stock at a market price of $94.48. What is the price of the stock given a 12% expected return?

PV

PV

300

1 12

324

1 12

350 94 48

1 12

00

1 2 3

.

( . )

.

( . )

. .

( . )

$75.

Valuing Common Stocks

If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY.

Valuing Common Stocks

If we forecast no growth, and plan to hold out stock indefinitely, we will then value the stock as a PERPETUITY.

Perpetuity PDiv

ror

EPS

r 0

1 1

Assumes all earnings are paid to shareholders.

Valuing Common Stocks

Constant Growth DDM - A version of the dividend growth model in which dividends grow at a constant rate (Gordon Growth Model).

Valuing Common Stocks

If the same stock is selling for $100 in the stock market, what might the market be assuming about the growth in dividends?

$100$3.

.

.

00

12

09

g

g

Answer

The market is assuming the dividend will grow at 9% per year, indefinitely.

Valuing Common Stocks

• If a firm elects to pay a lower dividend, and reinvest the funds, the stock price may increase because future dividends may be higher.

Payout Ratio - Fraction of earnings paid out as dividends

Plowback Ratio - Fraction of earnings retained by the firm.

Valuing Common Stocks

Growth can be derived from applying the return on equity to the percentage of earnings plowed back into operations.

g = return on equity X plowback ratio

Valuing Common Stocks

Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to plow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

Valuing Common Stocks

Our company forecasts to pay a $5.00 dividend next year, which represents 100% of its earnings. This will provide investors with a 12% expected return. Instead, we decide to blow back 40% of the earnings at the firm’s current return on equity of 20%. What is the value of the stock before and after the plowback decision?

P0

5

1267

.$41.

No Growth With Growth

g

P

. . .

. .$75.

20 40 08

3

12 08000

Valuing Common Stocks

Example - continued

If the company did not plowback some earnings, the stock price would remain at $41.67. With the plowback, the price rose to $75.00.

The difference between these two numbers (75.00-41.67=33.33) is called the Present Value of Growth Opportunities (PVGO).

Valuing Common Stocks

Present Value of Growth Opportunities (PVGO) - Net present value of a firm’s future investments.

Sustainable Growth Rate (g) - Steady rate at which a firm can grow: plowback ratio X return on equity.

Price Earnings Ratio

• Relationship of growth with P/E ratio

• Shareholder value created thru investments that yield returns in excess of COC

Growth vs Return

ROIC Growth P/E

• Growth Inc 14% 13% 17

• Returns Inc 35% 5% 17