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CORPORATE FINANCE VALUATION OF FUTURE CASH FLOW SCHEME OF STUDIES THIS MODULE INCLUDES: • TIME VALUE OF MONEY - BASICS • DISCOUNTED CASH FLOW VALUATION • BOND VALUATION • COMMON STOCK VALUATION CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW TIME VALUE OF MONEY FUTURE VALUE PRESENT VALUE ANNUITIES PERPETUITIES CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW FUTURE VALUE Depends on three factors – Size of Investment – Time Period – Interest Rate 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 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 Future Value Interest Factor (FVIF) r = Rate of Interest t = Time period 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 At the end of second year your investment is worth: 1100 x (1 + 0.10) = 1210 Alternatively: 1000 x (1 + 0.10)2 = 1210 CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW COMPOUND INTEREST • After One year: – 1000 X (1.10) = 1100 • After two years: – 1100 X (1.10) = 1210 At the end of 2nd year total Investment 1210 that means we earned 210 in terms of Interest. 210 = 100+100+10 10 is basically Compound Interest 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. 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? 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 CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW 2nd 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 CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW PRESENT VALUE You know that you will get 10000 at the end of 3rd 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 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 * From table A-3 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 and get a credit of 500. (Net price today is 9500) • Interest rate is 10% at present. • Which option is better? 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. 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. CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW • So far we come across four factors of Time • • • • Value of Money: PV FV Interest factor or discount factor Time period • Given three we can find the fourth. 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 8th 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 CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Finding interest rate (1 +r)8 = 2 1+ r = (2)1/8 1+r = (2)0.125 1+r = 1.09 r = 1.09 – 1 r = 0.09 or 9% 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. • Implicit Interest Rate = 9% 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 = 1,000,000/- CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW • And if you wish to start payments after 3rd year, then what is the PV of this delayed Perpetuity? • PV of Delayed Perpetuity = C/r (1+r)^t =100,000 / 0.1(1.10)3 = 751,315 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 formula 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 CORPORATE FINANCE - MODULE # 2 VALUATION OF FUTURE CASH FLOW Using Formula: PV= Annuity x 1/0.1 – 1/ 0.10(1.10)3 PV = 4000 x {10 – 1/0.1331} PV = 4000 x {10 – 7.513} = 4000 x 2.4869 = 9947.60