11

THE INTERNAL RATE OF RETURN(IRR )is the discount rate that forces the

NPV of the project to zero

33

ExampleExample::

Original investment (cash outflow): = Original investment (cash outflow): = $35000$35000

-Useful life: five yearsUseful life: five years..

the following table show the following table show AnnualAnnual income income generated from investmentgenerated from investment YearsYearsCash Cash

inflowsinflows

111200012000

221500015000

331600016000

4450005000

5560006000Minimum desired rate of return: 15% . Determine IRRMinimum desired rate of return: 15% . Determine IRR

44

11 – – Assume discount rate = 10%Assume discount rate = 10%

present present valuevalue

PV PV factofactorr

amounamounttyearsyears

--35000.35000.

000011--350003500000

10909.0910909.090.90910.9091120001200011

12396.6912396.690.82640.8264150001500022

12021.0412021.040.75130.7513160001600033

3415.073415.070.68300.68305000500044

3725.533725.530.62090.62096000600055

7467.427467.42      

55

11 – – Assume discount rate = 18%Assume discount rate = 18%

yearsyearsamounamountt

PV PV factofactorr

present present valuevalue

00--350003500011

--3500035000

.00.00

1112000120000.84750.847510170.010170.0

00

2215000150000.71820.718210773.010773.0

00

3316000160000.60860.60869737.609737.60

44500050000.51580.51582579.002579.00

55600060000.43710.43712622.602622.60

      882.20882.20

66

11 – – Assume discount rate = 20%Assume discount rate = 20%

yearsyearsamounamountt

PV PV factfactoror

present present valuevalue

00--350003500011

--35000.35000.

0000

1112000120000.83300.83309996.009996.00

2215000150000.69440.694410416.0010416.00

3316000160000.57870.57879259.209259.20

44500050000.48230.48232411.502411.50

55600060000.40190.40192411.402411.40

      --505.90505.90

IRR= %18+ %2*)882.2/1388.1( =%19.27 , IRR= %18+ %2*)882.2/1388.1( =%19.27 , IRR > minimumIRR > minimum

desired rate of return %15 the should accept the projectdesired rate of return %15 the should accept the project

77

Ch 3An Introduction to

Corporate Debt andEquity

Company financing operation into two broad categories, equity and debt.

Equity is the owners’ initial and subsequent investment in the company.

Debt consists mainly of various forms of short-term and long-term borrowing.

Interest rates on the debt can be either fixed or floating (variable) .

Floating rates change in response to changes in a relevant index of prevailing market rates of interest.

88

CORPORATE BONDS

The holder of a corporate bond has a legal right to long term payment of contractually agreed interest payments and repayments on the bond.

VALUING A CORPORATE BONDThe value of a risk-free corporate bond would equal the present value (PV) of its interest and repayment cash flow discounted at the risk-free rate of interest.A corporate bonds are not risk-free, however.

A corporate bond certifies include the maturity.The maturity is the final date for repayment of the bond.The bond certificate also specifies the interest payments, called coupons. Typically, coupon payments occur every six months until the bond matures.Therefore, the value of a bond must equal the PV of the coupons and of the eventual repayment of its face value:

99

•Bond Value Now= Present Value of Coupons+ Present Value of Face Value

B0 = C1 + C2 + C3 … .+ CN +Bn

( 1+r)1 + (1+r)2 + (1+r)3 ..+(1+r)n (1+r)n OR

B0 = interest x 1- 1 + Face Value x 1/(1+r)

( 1+r)n r

For example, a corporate bond with exactly five years left to maturity pays interest at 10% of face value. This implies that if the face value equals 100$, the bond pays two coupons per year of $5 each for five years.

Suppose that the annualized interest rate on securities of the same risk is currently only 7%.

What is the PV for the bond?

1010

Bond ValuationBond Valuation0 1 2 n

k

INT INTINTValue

...

M

VB =

INT

1+ k ... +

INT

1+k1 2

1

INT

kn+ +

+ +

M

1+kn .

VB =

INT

1+ kt n

1

M

k+

+n

t=1

1111

PV B0 = interest x 1- 1 + Face Value x 1/(1+r)

( 1+r)n r

=50 x 1- 1 + 100 = 113$ = 113$..

. ( 1+7%/2)10( 1+7%)5

( 7%/2)

Suppose the following information about the bond

The face value = 5000$, the maturity date after 8 years , at 8% interest face value, the bond pays two coupon per year , and the

current market rate = 12% .

Calculate the bond market value?

INTEREST RATES AND BOND PRICES•When the market rates of interest fall( down) , many

fixed-rate bonds like this sell for more than their face value. When the rates rise, many such bonds sell for less than face value.

1212

HOW MUCH SHOULD AN INVESTOR PAY FORSHARES IN A COMPANY’S EQUITY?

LENDING TO PARTNERSHIPSThe unlimited liability of partners is an advantage for lenders .If a partnership is in financial difficulty,the individual partners have to help pay the interest and repayments on the partnership’s debts.This provides the lenders extra security for their loans.

LENDING TO LIMITED LIABILITY COMPANIES

LENDING TO LIMITED LIABILITY COMPANIESshareholders in a limited liability do not have to help pay the company’s debts.

An implication is that a limited liability company can default on loans without involving the shareholders.Smart bankers charge for this valuable option to default, usually with higher interest rates on loans.

1313

DIVIDENDScompanies make regular dividend payments to shareholders, usually once or twice a year. The company’s board decides whether to pay each dividend, how much to pay, and when to pay itConsequently, the value of a share equals the PV of its expected dividends:

Share Value Now = Present Value of Expected Dividends

S0 = E(d1) + E(d2) + E(d3).… +

( 1+RE)1 (1+ER)2 + (1+ER)3

this equations the same as we used to value a bond.The difference is that dividend payments to hareholders and the eventual price of the share are uncertain,

1414

GROWTH AND THE VALUE OF EQUITYExpected Annual Dividend = Current Annual Dividend x Compound Growth Factor

the value of the share is=:

the company dividend (1+g) the rate of discounting- g

G : growth percentageFor example, an investor expects a company to enjoy 10%compound annual growth for ever, and she thinks that the appropriate rate for discounting the company’s dividends would be 12%. She knows that the company’s most recent annual dividend was 2 cents. If she had no otherinformation, she still could use the Gordon–Williams formula to estimate a value for the share. That is:

= 2 x (1+10%) = 1.10$per share 12%- 10%

1515

•ASSET VALUE, DEBT, AND THE VALUE OF EQUITY

Assets = Equity + debt

And Equity = assets – debt

Present Value of Equity = Present Value of Assets -Present Value of Debt

Thus,

Share Value Now = Present Value of Equity Number of Shares Issued

=

Present Value of Assets- Present Value of Debt

Number of Shares Issued

1616

For example, Company A would like to buy Company B and needs to know how much it should be willing to pay. Company A has potential uses for Company B’s assets that would make the assets worth C¼10 million to Company A. The PV of Company B’s debt is C¼5 million. The number of issued shares in B is 2 million. How much should Company A be willing to pay per share for Company B?Share Value Now=

Present Value of Assets - Present Value of Debt Number of Shares Issued

=10 ;000000 -5000000 = 2.50$2 ;000 ;000

Credit Rating the bank makes its lending decision, it must consider the probability that it might take such a loss. The bank uses the borrower’s credit rating as an direct measure of this probability. Value of Equity = Asset Value - Debt

1717

EXECUTIVE STOCK OPTIONSExecutive stock options are especially important.

Executive stock options represent a type of bonus for managers.

The purpose of these options is to reward managers when their actions increase the company’s share price, thereby benefiting shareholders. Show example p. 66