# 2 Time Value of Money

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1 2 Time Value of Moey BASIC CONCEPTS AND FORMULAE 1. Time Value of Moey It meas moey has time value. A rupee today is more valuable tha a rupee a year hece. We use rate of iterest to express the time value of moey. 2. Simple Iterest Simple Iterest may be defied as Iterest that is calculated as a simple percetage of the origial pricipal amout. Formula for Simple Iterest SI = P0 (i)() 3. Compoud Iterest Compoud iterest is the iterest calculated o total of previously eared iterest ad the origial pricipal. Formula for Compoud Iterest FV = P 0 (1+i) 4. Preset Value of a Sum of Moey Preset value of a sum of moey to be received at a future date is determied by discoutig the future value at the iterest rate that the moey could ear over the period. Formula for Preset Value of a Sum of Moey FV P0 = (1+ i) Or, P0 = 5. Future Value FV (1 + i) Future Value is the value at some future time of a preset amout of moey, or a The Istitute of Chartered Accoutats of Idia

2 2.2 Fiacial Maagemet series of paymets, evaluated at a give iterest rate. Formula for Future Value 6. Auity FV = P0+ SI = P0 + P0(i)() Or, FV = P0 1 + r k A auity is a series of equal paymets or receipts occurrig over a specified umber of periods. Preset Value of a Ordiary Auity: Cash flows occur at the ed of each period, ad preset value is calculated as of oe period before the first cash flow. Preset Value of a Auity Due: Cash flows occur at the begiig of each period, ad preset value is calculated as of the first cash flow. Formula for Preset Value of A Auity Due PVA = = R (PVIFi,) Future Value of a Ordiary Auity: Cash flows occur at the ed of each period, ad future value is calculated as of the last cash flow. Future Value of a Auity Due: Cash flows occur at the begiig of each period, ad future value is calculated as of oe period after the last cash flow. 7. Sikig Fud Questio 1 Formula for Future Value of a Auity Due FVA = R (FVIFAi,) It is the fud created for a specified purpose by way of sequece of periodic paymets over a time period at a specified iterest rate. Formula for Sikig Fud FVA=R [FVIFA(i,)] Explai the relevace of time value of moey i fiacial decisios. Aswer Time value of moey meas that worth of a rupee received today is differet from the worth of a rupee to be received i future. The preferece of moey ow as compared to future moey is kow as time preferece for moey. The Istitute of Chartered Accoutats of Idia

3 Time Value of Moey 2.3 A rupee today is more valuable tha rupee after a year due to several reasos: Risk there is ucertaity about the receipt of moey i future. Preferece for preset cosumptio Most of the persos ad compaies i geeral, prefer curret cosumptio over future cosumptio. Iflatio I a iflatioary period a rupee today represets a greater real purchasig power tha a rupee a year hece. Ivestmet opportuities Most of the persos ad compaies have a preferece for preset moey because of availabilities of opportuities of ivestmet for earig additioal cash flow. May fiacial problems ivolve cash flow accruig at differet poits of time for evaluatig such cash flow a explicit cosideratio of time value of moey is required. Questio 2 A perso is required to pay four equal aual paymets of ` 4,000 each i his Deposit accout that pays 10 per cet iterest per year. Fid out the future value of auity at the ed of 4 years. Aswer (1+ i) FVA = A i (1+.10) 4, , = ` 18,564 Future Value of Auity at the ed of 4 years = ` 18,564 Questio 3 A compay offers a Fixed deposit scheme whereby ` 10,000 matures to ` 12,625 after 2 years, o a half-yearly compoudig basis. If the compay wishes to amed the scheme by compoudig iterest every quarter, what will be the revised maturity value? Aswer Computatio of Rate of Iterest ad Revised Maturity Value Pricipal = ` 10,000 Amout = ` 12,625 The Istitute of Chartered Accoutats of Idia

4 2.4 Fiacial Maagemet 10,000 = 12,625 4 (1+ i) P = A (PVF, i ) 10,000 = 12,625 (PVF 4, i ) = (PVF 4, i ) Accordig to the Table o Preset Value Factor (PVF 4,i ) of a lump sum of Re. 1, a PVF of for half year at iterest (i) = 6 percet. Therefore, the aual iterest rate is = 12 percet. i = 6% for half year i = 12% for full year. Therefore, Rate of Iterest = 12% per aum Revised Maturity Value = 10, = 10, = 10,000 (1.03) Revised Maturity Value = 12,670. Questio = 10, [Cosiderig (CVF 8,3 ) = 1.267] A doctor is plaig to buy a X-Ray machie for his hospital. He has two optios. He ca either purchase it by makig a cash paymet of ` 5 lakhs or ` 6,15,000 are to be paid i six equal aual istallmets. Which optio do you suggest to the doctor assumig the rate of retur is 12 percet? Preset value of auity of Re. 1 at 12 percet rate of discout for six years is Aswer Advise to the Maagemet Optio I: Cash Dow Paymet Cash dow paymet= ` 5,00,000 Optio II: Aual Istallmet Basis Aual istallmet = 6,15, = ` 1,02,500 Preset Value of 1 to 6 = 1,02, = ` 4,21,378 8 The Istitute of Chartered Accoutats of Idia

5 Time Value of Moey 2.5 Advise: The doctor should buy X-Ray machie o istallmet basis because the preset value of cash out flows is lower tha cash dow paymet. This meas Optio II is better tha Optio I. Questio 5 Ascertai the compoud value ad compoud iterest of a amout of ` 75,000 at 8 percet compouded semiaually for 5 years. Aswer Computatio of Compoud Value ad Compoud Iterest Semiaual Rate of Iterest (i) = 8/2 = 4 % = 5 x 2 = 10, P = ` 75,000 Compoud Value = P (1+i) = 75,000 (1+4 %) 10 = 75,000 x = ` 1,11,015 Compoud Iterest = ` 1,11,015 ` 75,000 = ` 36,015 Questio 6 X is ivested ` 2,40,000 at aual rate of iterest of 10 percet. What is the amout after 3 years if the compoudig is doe? (i) Aually (ii) Semi-aually. Aswer Computatio of Future Value Pricipal (P) = ` 2,40,000 Rate of Iterest (ĭ) = 10% p.a. Time period ()= 3 years Amout if compoudig is doe: (i) Aually Future Value = P (1 + ĭ ) 10 = 2,40,000 ( = 2,40,000 ( ) 3 3 The Istitute of Chartered Accoutats of Idia

6 2.6 Fiacial Maagemet (ii) = 2,40,000 x = ` 3,19,440 Semi-Aually Future Value = 2,40,000 = 2,40,000 ( ) 6 = 2,40,000 x ( 1.05) 6 = 2,40,000 x = ` 3,21, x 2 3x2 EXERCISES 1. Ram has deposited ` 55,650 i a bak, which is payig 15 per cet rate of iterest o a te-year time deposit. Calculate the amout at the ed of te years? (Aswer: ` 2,25,159.90) 2. Calculate the amout which Mr. Shyam should deposit ow to receive ` 50,000 after 15 years. The iterest rate is 9 per cet. (Aswer: ` 13,750) 3. Mr. Pito borrowed ` 1,00,000 from a bak o a oe-year 8% term loa, with iterest compouded quarterly. Determie the effective aual iterest o the loa? (Aswer: 8.24%) 4. Suppose Adit has borrowed a 3-year loa of ` 10,000 at 9 per cet from his employer to buy a motorcycle. If his employer requires three equal ed-of-year repaymets, the calculate the aual istalmet. (Aswer: ` 3,951) 5. The cost of a ew mobile phoe is ` 10,000. If the iterest rate is 5 percet, how much would you have to set aside ow to provide this sum i five years? (Aswer: ` 7,840) The Istitute of Chartered Accoutats of Idia

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