1. 1 THE INTERNAL RATE OF RETURN (IRR) is the discount rate that forces the NPV of the project to zero

2. 2 Internal Rate of Return Model The IRR determines the interest rate at which the NPV equals zero. If IRR > minimum desired rate of return, then NPV > 0 and accept the project. If IRR < minimum desired rate of return, then NPV < 0 and accept the project.

3. 3Example: Original investment (cash outflow): = $35000 - Useful life: five years. the following table show Annual income generated from investment Cash inflows Years120001 150002 160003 50004 60005 Minimum desired rate of return: 15%. Determine IRR

4. 4 1 – Assume discount rate = 10% yearsamount PV facto r present value 0-350001 - 35000. 00 1120000.909110909.09 2150000.826412396.69 3160000.751312021.04 450000.68303415.07 560000.62093725.53 7467.42

5. 5 1 – Assume discount rate = 18% present value PV facto r amountyears - 35000.00 1-350000 10170.0 0 0.8475120001 10773.0 0 0.7182150002 9737.600.6086160003 2579.000.515850004 2622.600.437160005 882.20

6. 6 1 – Assume discount rate = 20% present value PV facto r amountyears - 35000. 00 1-350000 9996.000.8330120001 10416.000.6944150002 9259.200.5787160003 2411.500.482350004 2411.400.401960005 -505.90 IRR= %18+ %2*(882.2/1388.1) =%19.27, IRR > minimum desired rate of return %15 the should accept the project

7. 7 Ch 3 An Introduction to Corporate Debt and Equity 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.

8. 8 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 BOND The 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:

9. 9 Bond Value Now= Present Value of Coupons+ Present Value of Face Value B 0 = C1 + C2 + C3 ….+ CN +Bn (1+r)1 + (1+r)2 + (1+r)3..+(1+r)n (1+r)n OR B 0 = 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?

10. 10 Bond Valuation 012n k INT Value... M  VBVB = INT 1+k... + 1+k 12 1 k n ++ +  + M 1+k n.  VBVB = 1+k tn 1 M k + +  n t=1

11. 11 PV B 0 = interest x 1- 1 + Face Value x 1/(1+r) (1+r)n r = 113$. = 50 x 1- 1 + 100 = 113$.. ( 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.

12. 12 HOW MUCH SHOULD AN INVESTOR PAY FOR SHARES IN A COMPANY ’ S EQUITY? LENDING TO PARTNERSHIPS The 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 shareholders 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.

13. 13 DIVIDENDS companies 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 it Consequently, the value of a share equals the PV of its expected dividends: Share Value Now = Present Value of Expected Dividends S 0 = 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,

14. 14 GROWTH AND THE VALUE OF EQUITY Expected 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 percentage For 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 other information, 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%

15. 15 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

16. 16 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 C ¼ 10 million to Company A. The PV of Company B ’ s debt is C ¼ 5 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

17. 17 EXECUTIVE STOCK OPTIONS Executive 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