Time value of Money - MBA Online Presentation

Time Value Of Money

1. Financial Management T ime Value of Money

2. People prefer current consumption over future consumption There is inflation in the economy – prices of goods/services increase with time Hence, A Rupee Today is worth more than a Rupee Tomorrow This is called as Time Value of Money. The value of money reduces with time.

3. What is compound interest? Investment amount: Principal So How Does Compounding work? Year Investment Interest 2017 1000 2018 2019 2020 2021 Interest rate, r = 7%

4. When working from Present to Future Compounding Compounding 2017 Rs 1,000 2021 Rs 1,311

5. Can we also work from Future to Present? Discounting Discounting 2017 Rs 1,000 2021 Rs 1,311

6. What happens if we increase the interest rate? Back to Compounding Year Investment Interest r = 7% Investment Interest r = 10% 2017 1000 70 1000 2018 1070 74.9 2019 1144.9 80.1 2020 1225.0 85.8 2021 1310.8 91.8

7. What happens if we increase the interest rate? How Does Compounding work? Year Investment Interest r = 7% Investment Interest r = 10% 2017 1000 70 1000 100 2018 1070 74.9 1100 110 2019 1144.9 80.1 1210.0 121 2020 1225.0 85.8 1331.0 133.1 2021 1310.8 91.8 1464.1 146.4

8. Compounding effect is greater with increasing time Compounding effect is greater with increasing interest rate What do we Observe? Fundamental Investment Rules 2. Invest in higher interest rates 1. Invest for a longer time

9. Time Value of a Lump Sum FV n = PV*(1+i) n FV n = future value at time n PV = present value right now i = interest rate n = time duration

10. Suppose you invest Rs. 100,000 @12% for 4 years. How much money would you have after each of these 4 years? FV = 100000 x (1.12) 4 = Rs 157351.9 Year Investment (Rs) 2017 100000 2018 2019 2020 2021

11. We know: FV = PV*(1+i) n FV=PV*CVF Rearranging, we get PV=FV/PVF Present Value

12. Suppose you want Rs. 100,000 in the year 2021. How much money should you invest in each of these 4 years? PV = 100000 / (1.12) 4 = 63351.8 Year Investment (Rs) 2017 2018 2019 2020 2021 100000

13. Your sister has asked for a loan of Rs 12,500. She has promised to repay the loan at the end of her education after 5 years. You would normally get an interest of 6% in the market. How much would you expect her to pay you after 5 years? Yash Chopra wants to invest some amount for his child’s MBA scheduled to start 10 years from now which will cost Rs 10,00,000. Suppose the bank is giving him an interest of 8.3%pa. How much should he invest now to have that amount? Abbas Mustan wants to earn money in the market. He finds a mutual fund that has given a constant return of 15.6% since past 5 years. He wants to invest Rs 15,00,000 in the fund. How much money will he get after 4 years from now? Practice Questions Answers: 1) Rs 16,727.8; 2) Rs 450,521.4; 3) Rs 2,678,690.8

14. Let’s go a bit deep

15. Birla Sun Life Equity Fund is one of the top rated Mutual Funds in its category industry. It has generated over 15% annual returns year on year. If you start putting Rs 10,000 every year (in SIP mode) starting from 2017, how much money would you have at the end of the year 2020? Series of Cash Flows Jan 2 17 Dec 31 17 Dec 31 18 10000 10000 10000 10000 Dec 31 19 Dec 31 20

16. Series of Cash Flows contd. Jan 1 17 Dec 31 17 Dec 31 18 10000 10000 10000 10000 Dec 31 19 Dec 31 20 10000 10000 (1.15) 10000 (1.15) 2 10000 (1.15) 3 ∑ Rs 49,933.8

17. If you invests the same amount till the year 2035, how much would you get? Such computations are cumbersome and are handled by considering cash flows as “annuities” Annuity is a stream of constant cash flows occurring at uniform intervals of time Examples: Insurance premium, EMIs When cash flows occur at the end of each period it is termed as regular or ordinary annuity. Annuities

18. FV of Annuity is given as FV = A(1+i) n-1 + A(1+i) n-2 + …. + A Future Value of an Annuity FV annuity = A x (1+i) n - 1 i A = equal installments i = interest rate n = no of periods FVA=A*CVFA FV Annuity Factor FVIFA

19. Yash Chopra wants to invest some amount for his child’s MBA to start 10 years from now which will cost Rs 10,00,000. Suppose the bank is giving him an interest of 9%pa. How much should he invest each year for the next 10 years to have that amount? (Ans: 65,820) Let’s Solve a Problem

20. PVAn =A*PVFA (Present value Factor of an Annuity) Present Value of an Annuity PV annuity = A x (1+i) n - 1 i (1+i) n PV Annuity Factor A = equal installments i = interest rate n = no of periods

21. As winner of a spot the alphabet on Coke bottle cap competition, you can choose one of the following: 100,000 now 200,000 at the end of five years 21,000 each year for 10 years If the interest rate is 10% which alternative will you choose? Ans: C Let’s Try Multiple Choice

22. Recall that the Annuity we are studying also called Regular or Ordinary Annuity Now we will study another type of Annuity known as Annuity Due Annuity Types

23. 1 2 100 100 100 100 3 4 Ordinary Annuity 1 2 100 100 100 100 3 4 Annuity Due

24. Annuity Due Since now the money is coming one year before, the Annuity can be invested earlier and hence will get more interest.

25. Assume today is 1 Jan 2012 and Mr Aftab Shivdasani deposits Rs 10,000 in a bank account on 1st January every year for four years, till 2015. How much money will he get at the beginning of year five if he gets 10% return on an annual basis. Series of Cash Flows Jan 1 12 Jan 1 13 Jan 1 14 10000 10000 10000 Jan 1 15 Jan 1 16 10000

26. Series of Cash Flows contd. Jan 1 12 Dec 31 12 Dec 31 13 10000 10000 10000 Dec 31 14 Dec 31 15 10000 10000 (1.1) 10000 (1.1) 2 10000 (1.1) 3 ∑ 51,051 10000 (1.1) 4

27. Since cash flow occur one period before, FV and PV are increased by a factor of (1+i). We observe that: FV and PV in Annuity Due Ordinary Annuity Annuity Due Future Value A[(1+i) n – 1]/i A{[(1+i) n – 1]/i}.(1+i) A*FVIFA*(1+i) Present Value A[(1+i) n – 1]/i.(1+i) n A{ [(1+i) n – 1]/i(1+i) n }.(1+i) A*PVIFA*(1+i)

28. You feel that you have grown up and want to save money for your child’s education to start 10 years from now. You save Rs 12,000 every year starting from today. How much will you get after 10 years if you get 9% on your saving? 2 step process: Calculate the PV or FV as though it were an ordinary annuity Multiply your answer by (1+i) Ans: 198,723/- Annuity Due Example

29. A perpetuity is a stream of regular payments that goes on forever An infinite annuity Future value of a perpetuity There can be no future value since annuity goes on forever Present value of a perpetuity A Government bond, if purchased, promises to pay Rs 10,000 every year indefinitely to the buyer. At what price will the bond sell if government bonds trade at 5% pa. Perpetuity

30. Till now we have seen the case of an Annuity which is constant throughout the payment period Now let’s see what happens if the annuity grows each year at a constant rate Growing Annuity

31. We get, Growing Annuity 1 2 A(1+g) A(1+g) 2 A(1+g) 3 A(1+g) 4 3 4

32. After completion of your PGDM two years from now, you expect to get a job of Rs 600,000 per year with an annual increment of 10% for the next 10 years. How much should you pay for your PGDM if you can invest the same amount in the market and get a return of 15% per year? Ans:-(Rs 47,25,600) Cost of Education

33. You want to buy a farm which grows Oranges. The farm grows 10,000 oranges every year and you are going to sell the oranges for the next 10 years to the local Market. The cost of an orange is Rs 15 which is growing at 5% per year. The discount rate is 15%. How much should you pay for the farm if nothing else can be grown at the farm? Ans : Rs 9,40,845.4 Solve This

34. What is the PV for a Perpetuity? PV for a perpetuity which is growing at g% per year is given as You want to buy an office building for giving it on rent and earning money every year. The rental amount is Rs 120,000 per year which is expected to grow forever at a constant rate of 4%. If the discount rate is 10%, what is the amount you should pay for the building right now? Ans : Rs 20,00,000 Growing Perpetuity

35. Equal installment payment of a loan on a monthly basis. How is EMI calculated? EMI= P×r×(1+r) n /(1+r) n – 1 Where, r= monthly interest rate and n= number of months. You have taken education loan of Rs 600,000. Let’s say the bank is charging an interest of 10% pa and has kept a repayment period of 5 years after completion of your MBA (which will last for 2 years). How much EMI are you paying? (Ans= Rs12748) Equated Monthly Installments (EMIs)

36. Equal installment payment of a loan on a monthly basis The cost of iPhone 7 is Rs 56,000. If you buy the iPhone 7 at EMI of 12 months, what would be the EMI you will be paying? Amazon is giving you the EMI at 12% interest. Compute the monthly Principal repayment and Interest that you will be paying on the EMI. How much interest have you paid at the end of 12 months? ( Ans= Rs 5008) Equated Monthly Installments (EMIs)