gives an exposure to interest, annuity and perpetuity

1. Time Value of Money Module 2

2. Meaning of Time Value of Money Time Value of Money=Interest/Discount Interest/Discount- The cost the user of funds pays to the owner of funds Interest arises when it is calculated on the Principal i.e future value is calculated from the present value Discount arises when it is calculated on the future value of the amount lent i.e., present value is calculated from the future value

3. Determinants of Interest Sum lent called Principal – P Period of Lending – n (always in terms of Years) Rate of Interest – R (always expressed as a Percentage meaning the interest payable for every Rs.100 per year)

4. Types of Lending/Investment I. Compound Interest: Future Value of Single Cash Flow (F), Present Value of Single Cash Flow (P) II. Perpetuity III. Future Value of Annuity IV. Present Value of Annuity

5. I Compound Interest A single sum is lent The repayment is made in a single instalment Principal is the present value Repayment amount is the Future Value

6. Formula for Calculation of Future Value

7. Problem No.2.1 Ashoka (P) Ltd. purchased Rs. 60,000 worth of Mortgage Bonds of 5-year tenure. If the bonds carry 12% interest, calculate the maturity value of the bonds.

8. Problem No.2.2 Canara Bank offered an educational loan to Rahul, an Engineering student. Amount lent was Rs. 6,00,000 carrying a compound interest of 8% per annum. Rahul repaid the entire amount after 7 years along with interest in one lumpsum. Calculate the total amount paid by Rahul to Canara Bank.

9. Problem No.2.3 Raviraj invested Rs. 75,000 into HDFC Top 100 Funds- Growth Option. Over a period of 5 years, the fund achieved a growth of 21% on an average. Calculate the value of the investment after 5 years.

10. Problem No 2.4 Sweekar deposited Rs. 23,000 into the cash certificate of Teachers’ Co-op. Bank Ltd. for a period of 2 years at a compound interest of 9% per annum. Calculate how much Sweekar would receive after 2 years. What will be the future value after 3 years?

11. Problem No 2.5 Gautam wants to have Rs. 45,000, 4 years from now. For this purpose, he wants to invest in a mutual fund, which is expected to give a compound interest of 16% per annum. Calculate how much he should invest now.

12. II Perpetuity (Perpetual Annuity) Annuity is a series of equal annual payments (A) When the annuity is payable forever, it is called perpetual annuity or perpetuity Perpetuity has neither n nor the future value. It has only present value

13. Contracts of Perpetuity Determination of Life Membership Fee Creation of an Endowment Fund Freehold Estate Loan on which only the interest is paid

14. Perpetuity Due & Immediate In Perpetuity Immediate, the annuity is payable at the end of every year like the prizes awarded out of an Endowment Fund In Perpetuity Due, the annuity is payable at the beginning of every year as in Life Membership Fund Due and immediate exist for Contracts of Annuity also

15. Present Value of Perpetuity Present Value of Perpetuity Immediate: P= Present Value of Perpetuity Due P=

16. Problem No 2.6 An Endowment Fund is proposed to give a gold medal for the I Rank holder in MBA of Mangalore University examinations. The value of the gold medal is estimated to be Rs.35,000 each year. Reckon interest rate at 9% per annum and calculate the size of the fund.

17. Problem No 2.7 Mangalore University Commerce Teachers’ Association collects Rs.250 as annual membership. It wants to offer one-time payment in the form of Life Membership Fee considering rate of interest at 8%. Calculate what should be the Life Membership Fee.

18. Problem No 2.8 Swadesh is a tenant living in the house owned by Videsh at an annual rent of Rs.25,000. Videsh is in need of money and agrees to give the house as a freehold estate to Swadesh. Calculate how much he should demand from Swadesh assuming the going rate of interest at 7% per annum.

19. Problem No 2.9 Jack borrows money from his close friend Jill at an interest rate of 16% per annum. Jack can pay a maximum of Rs.40,000 as interest per year. Jill agrees that Jack need not repay the loan as long as Jill pays the interest every year. Calculate the amount of loan Jack can borrow.

20. Problem No 2.10 The flat-owners in a locality created a fund of Rs.9,00,000 for the maintenance of their building. If the fund generates interest at 7.5% per annum, how much they can spend per year on maintenance?

21. Problem No 2.11 A hotel is rented out at an annual sum of Rs.1,00,000 as rent. The proprietor wants to sell it to the lessee. What price he should demand assuming interest at 11% per annum.

22. Problem No 2.12 Srivastava intends to sell a house for Rs.8,00,000. As he is not able to find a buyer, he decides to lease it out on yearly rent. Reckoning interest @ 9%, calculate the yearly rent Srivastava can expect.

23. III Future Value of Annuity A series of equal annual payments are made by the investor to the borrower Investor’s money in the hands of the borrower keeps increasing due to the continued payment of annuity and also due to the interest accruing on the money in the hands of the borrower E.g., Recurring Deposit, SIP of a mutual fund, creation of sinking fund Annuity Due and Annuity Immediate

24. Computation of Future Value Annuity Immediate F = Annuity Due F =

25. Problem No 2.13 A deposit of Rs.30,000 is made every year into the bank for a period of 4 years at 8% interest. Calculate the maturity value assuming the annual compounding of interest.

26. Problem No 2.14 A joint stock company has the capacity to set aside Rs. 40,000 for the redemption of debentures for 4 years. If the amount invested fetches 9% compound interest, calculate the value of debentures the company can issue.

27. Problem No.2.15 A company plans to replace the existing machinery after 6 years at a cost of Rs. 11,00,000. If the investments fetch 10% rate of compound interest, calculate the amount that should be transferred to the Sinking Fund at the end of every year.

28. Problem No 2.16 A firm requires Rs. 5,00,000, seven years from now. For this purpose, it is creating a Reserve Fund by transferring equal annual instalments to this Fund, and investing it in outside securities at 6% compound interest per annum. Calculate the annuity. a) if the transfer is made from the end of the current year. b) if the transfer is made from the beginning of the current year.

29. Problem No 2.17 For his son doing MBBS, Nagesh wants to accumulate Rs.13,00,000 over a period of 5 years. For this, he plans o make equal annual deposits in the bank at a compound interest of 11% at the beginning of each year. Calculate how much he must deposit per year.

30. Problem No 2.18 The scrap value of a machine purchased at a cost of Rs. 15,00,000 after an effective life of 6 years is nil. The cost of the machine is expected to go up by 50 % in 6 years’ time. Calculate the amount to be transferred to a Sinking Fund assuming the interest rate to be 5% compounded annually.

31. Problem No 2.19 Terrestrial Alien.Com issued debentures worth Rs.9,00,000 redeemable at a premium of 10%. It decided to create a sinking fund at 12% compound interest per annum. If debentures have a tenure of 5 years, calculate the amount to be transferred to Sinking Fund every year.

32. Problem No 2.20 Vanishing Tar Road Ltd., purchased a machine costing Rs. 9,50,000. Its effective life was expected to be 8 years after which it would realise a scrap value at Rs. 90,000. However, by that time, the new machine would cost 20% more. Assuming a compound interest rate of 8% per annum, calculate the sum to be set aside to the sinking fund every year. Approximate the sum to the nearest thousand.

33. IV Present Value of Annuity Lending or Investment in one lumpsum Repayment is in Instalment Principal in the hands of the borrower comes down with the payment of instalment, but increases due to the interest factor Present Value contracts are far more than Future Value contracts

34. Examples of Present Value Contracts Repayment of Loan in Equal Instalments Commutation of Pension Cash Value of Future Royalty Hire Purchase Annuity Method of Depreciation Settlement of Amount due to a Retiring Partner Leasehold Estate Annuity Policy of Insurance Companies Annuity Method of Valuation of Goodwill Lumpsum Deposit made and equal amounts withdrawn

35. Computation of Present Value Present Value of Annuity Immediate P= Present Value of Annuity Due P=

36. Problem No. 2.21 Arunodaya Textiles borrowed Rs.4 lakh from IDBI at a compound interest of 15% per annum. The repayment was agreed to be by way of 9 equal annual instalments. Calculate the amount of instalment.

37. Problem No 2.22 A newly established industrial unit is planning to raise a loan from a financial institution. However, the forecasted cash flow allows the payment of Rs. 1,00,000 per year for 7 years. If the going rate of interest is 14% compound, calculate the amount of loan that can be raised by the industrial unit.

38. Problem No. 2.23 Mohitlal retired from service at the age of 58 years drawing a pension of Rs. 90,000 p.a. If he could commute 1/3 of his pension, calculate the amount he would be paid immediately in a lumpsum amount, assuming expectation of life to be 14 years more and a compound interest at 7.5%.

39. Problem 2.24 Prakash retires from Stellar Shinewell (P) Ltd., and is eligible to receive a pension of Rs.1,50,000 per year. The pension is payable for a period of 12 years. The company has an alternative retirement plan, whereby Prakash is eligible to receive a lumpsum amount instead of the pension. Assuming a compound interest at 9% per annum, calculate the amount that will be paid immediately as per the alternative plan.

40. Problem No. 2.25 An author of a book is to receive a royalty at Rs. 11,000 per year from the publisher for nine years. Instead, the author wants the cash value of royalties to be paid immediately. Considering a compound interest of 10.5% per annum, calculate the amount payable by the publisher immediately.

41. Problem No 2.26 A small scale industrial unit purchases for its manager a house on instalment basis by agreeing to pay Rs. 2,00,000 at the end of each year for 7 years. Assuming an interest rate of 11%, calculate the cash price of the house.

42. Problem No. 2.27 A second hand car is purchased on hire-purchase basis by paying Rs. 50,000 down and five more annual instalment of Rs. 16,000. The instalments included interest at 18% compound interest per annum. Calculate the cash value of the car.

43. Problem No 2.28 A company purchased machinery costing Rs.5,30,000 and spent Rs.75,000 on its installation. The effective life is estimated to be 6 years. Assuming interest at 8% compound per annum, determine the yearly depreciation amount under Annuity Method of Depreciation.

44. Problem No 2.29 Brandon retired from his firm with effect from April 1, 2009. His dues from the firm were calculated and amounted to Rs.4,75,800. The firm agreed to pay the amount in four equal instalments. The instalments included interest @ 8% per annum. Calculate the amount of each instalment.

45. Problem no 2.30 Trickster Co. owed Rs.3,50,000 to the legal heirs of its deceased partner. However, as there wasn’t enough funds, the firm agreed to pay it in 4 equal instalments. The instalments included interest at 15% per annum. Calculate the amount of each instalment.

46. Problem No 2.31 X is planning to take a shop on lease for an annual rent at Rs.96,000 per year for 6 years. However, Y, the lessor wants to lease it out so as to recover the present value of the rental in 6 years. Calculate how much X should pay to Y for the leasehold estate reckoning the interest rate @ 12%.

47. Problem No 2.32 A company values its goodwill on the annuity method. The super profit for the next 8 years are estimated to be Rs.29,000 per year. Consider a compound interest of 12% per annum. Calculate the value of goodwill of the firm.

48. Problem No 2.33 A company wants to create a labour welfare fund out of which it plans to draw out Rs.85,000 per year for 10 years. If the going rate of interest is 8%, calculate how much the company should deposit in the fund now.

49. Problem No 2.34 Suresh borrows from a moneylender Rs.30,000 at a compound interest of 16% per annum. The moneylender stipulates that the loan should be repaid in 5 equal instalments, but the first instalment is payable on the date of loan disbursement. Calculate the instalment payable annually.

50. Problem No 2.35 ShainiGrahambel invented a new type of pen and allowed ABC Pens Ltd., to produce the pen. The company was prepared to pay her Rs.25,000 annual royalty payable at the beginning of each year with the I Instalment payable on signing the contract. However, Shaini wanted to sell the patent to the company for immediate payment of the total value. If the rate of interest was 12% p.a. compound and the patent had a life of 9 years, calculate the price to be demanded by Shaini.

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