1. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW www.vuaskari.com SCHEME OF STUDIES THIS MODULE INCLUDES: TIME VALUE OF MONEY - BASICS TIME VALUE OF MONEY - BASICS DISCOUNTED CASH FLOW VALUATION DISCOUNTED CASH FLOW VALUATION BOND VALUATION BOND VALUATION COMMON STOCK VALUATION COMMON STOCK VALUATION

2. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW TIME VALUE OF MONEY TIME VALUE OF MONEY  FUTURE VALUE  PRESENT VALUE  ANNUITIES  PERPETUITIES

3. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW FUTURE VALUE Depends on three factors – Size of Investment – Time Period – Interest Rate

4. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW FUTURE VALUE TIME VALUE DEFINED – A dollar or Rupee received today is better than a dollar or rupee to be received after a year. Why? – Because the dollar or rupee received today will start earning profit right from today

5. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW FUTURE VALUE FV = (Investment, Time, Interest Rate) This can be written as FV = PV x (1 + r) t (1 + r) t is known as Present Value Investment Factor (PVIF) (1 + r) t is known as Present Value Investment Factor (PVIF) r = Rate of Interest t = Time period

6. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Example You invest Rs. 1000 today and will get Rs. 1100 at the end of one year, if interest rate is 10% p.a. = 1000 X (1 + 0.10)= 1100 = 1000 X (1 + 0.10)= 1100 At the end of second year your investment is worth: 1100 x (1 + 0.10) = 1210 1100 x (1 + 0.10) = 1210 Alternatively: 1000 x (1 + 0.10) 2 = 1210

7. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW COMPOUND INTEREST After One year: After One year: – 1000 X (1.10) = 1100 After two years: After two years: – 1100 X (1.10) = 1210 At the end of 2 nd year total Investment 1210 that means we earned 210 in terms of Interest. 210 = 100+100+10 10 is basically Compound Interest

8. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW COMPOUND INTEREST This 1210 has four parts: – 1000 original investment – 100 interest – 1 year – 100 interest – 2 year – 10 interest on Year 1 interest Earning interest on interest is know as compounding Interest over period is reinvested to earn more interest.

9. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW LONG PERIOD EXAMPLE : (Future Value) An investment opportunity pays 12% pa and a business entity intends to invest 500,000. What will be the worth of this investment in 7 years time? How much interest will the company earn in this period? What portion of total interest represents compound interest?

10. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Solution Worth after 7 years: FV = PV x (1 + r) t FV =500000 x (1.12) 7 =1105350 (1.12) 7 = 2.2107 (1.12) 7 = 2.2107

11. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW 2 nd Question: How much Interest will the Company earn in this period? Total interest earned: 1105350 – 500000 = 605350 Compound Interest: 500000 x 12% x 7 = 420000 =605350 – 420000 = 185350

12. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW PRESENT VALUE You know that you will get 10000 at the end of 3 rd year from now. The interest rate is 10%. What is the PV of 10000 now? FV = PV x (1+r) 3 10000= PV x (1.10) 3 PV = 10000/ (1.10) 3 = 7513.14

13. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW We can find PV the other way too: PV = FV / (1 + r) t 1 / (1.10) 3 = known as PVDF PV = FV X PVDF PV = 10000 X 0.7513* = 7513 = 7513 * From table A-3

14. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Comparison between two options Option 1= Pay 4000 today and 6000 after 2 years to buy a computer Option 2= Pay all today a get a credit of 500. (Net price today is 9500) Interest rate is 10% at present. Interest rate is 10% at present. Which option is better? Which option is better?

15. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Option 1: Finding PV: PV = 4000 + (6000 / (1.10) 2 PV = 4000 + 4958.68 = 8958.68 It means that 4958.68 invested today @ 10% will yield 6000 at the end of year 2, enabling you to pay off your liability.

16. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Option 2: PV = 9500 Option 1 is better because it cost 8958.68 as compared to 9500 of option 2.

17. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW So far we come across four factors of Time Value of Money: So far we come across four factors of Time Value of Money: PV PV FV FV Interest factor or discount factor Interest factor or discount factor Time period Time period Given three we can find the fourth. Given three we can find the fourth.

18. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Finding interest rate An opportunity requires 1000 investment today that will double at the end of 8 th year. What is the implicit interest rate? An opportunity requires 1000 investment today that will double at the end of 8 th year. What is the implicit interest rate? PV = FV / (1 +r) 8 1000 = 2000 / (1 +r) 8 (1 +r) 8 = 2000/1000 (1 +r) 8 = 2 r =9% r =9%

19. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Three Ways to Solve: – Mathematical Equation – Financial Calculator – Time Value of Money Tables Look FV table 8 year row select and move towards right unless under the interest Rate %age you read 2 or nearest to 2. Look FV table 8 year row select and move towards right unless under the interest Rate %age you read 2 or nearest to 2. Implicit Interest Rate = 9% Implicit Interest Rate = 9%

20. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW PERPETUITY Defined: Stream of equal cash payments equally spaced that continues for ever. If you wish to help a welfare trust by providing 100,000/- per annum forever and the interest rate is 10%, how much amount must be set-aside today? Formula: PV of Perpetuity = C/r = 100000/0.10 = 100000/0.10 = 1,000,000/- = 1,000,000/-

21. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW And if you wish to start payments after 3 rd year, then what is the PV of this delayed Perpetuity? And if you wish to start payments after 3 rd year, then what is the PV of this delayed Perpetuity? PV of Perpetuity = 1,000,000 / (1.10) 3 PV of Perpetuity = 1,000,000 / (1.10) 3 = 751315 = 751315

22. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW ANNUITIES Series of equal amount and equally spaced payments for limited period of time but not unlimited. Valuation of Annuities: Using FV/PV tables Using FV/PV tables Using formula Using formula

23. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Example: You want to buy an asset for your business that will cost you 4000 per year for next three years. Assume interest rate of 10%. Find out the PV of this annuity? Using table 4000 x 1/(1.10) 4000 x 1/(1.10) 2 4000 x 1/(1.10) 3 = 9947.41

24. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Using Formula: PV= Annuity x 1/0.1 – 1/ 0.10(1.10) 3 = 4000 x 2.4869 = 9947.60 = 4000 x 2.4869 = 9947.60