Time Value Of Money-B.V.Raghunandan
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Transcript of Time Value Of Money-B.V.Raghunandan
- 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 ofequal 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 atthe 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 ofloan 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
Investors 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 wasnt 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.
51. THANK YOU