overview and basic concepts of time value of money

1. Overview of
Time Value
of
Money

2. Time Value of Money
• Time value of money means that the value of money is different in
different time periods. The value of money received today is more
than the value of same amount receivable at some other time in future.
• The difference in the value of money today and tomorrow is referred
as time value of money.
• Therefore, given a choice of receiving a sum of money today or in the
future, a rational person will always choose to receive the money now
as it has more value today than in the future.
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3. • Four reasons may be attributed to the individual’s time preference for
money:
• Investment Opportunities
• Risk (Future is uncertain and risky)
• Personal Consumption Preference
• Inflation (Purchasing power)
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4. Techniques of Time Value of Money
Two most common methods of adjusting cash flows for time value of
money:
Compounding—the process of calculating future values of cash flows
and
Discounting—the process of calculating present values of cash flows.
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5. Valuation concepts
Interest are of two types
a. Simple Interest
b. Compound Interest
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6. Simple Interest
• Simple Interest = Po (I)(n)
• Po= Principle amount at year 0
• I=Interest rate per annum
• N= number of years for which interest is calculated
Formula for calculating Future value
• FVn=Po + Po(I)(n)
• FVn= Future value at the end of “n” years.
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7. Q.1.What is the simple interest and total amount received of Rs. 8,000 for
4 years at 12% p.a. (3,840 and 11,840)
Q.2.A deposited Rs. 10,000 in a savings bank account today at a 5%
simple interest for a period of 5 years. What is his accumulated interest?
( 2500)
Q.3. At what rate per cent will Rs. 26,435 amount to Rs. 31,722 in 4
years? (5%)
Q.4. Krishna annual savings are Rs 1,000,which is invested in bank saving
account that pays a 5% simple interest. Krishna wants to know his total
future value at the end of 8 years period. (1400)
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8. Compound Interest
1. Compound or Future Value of Single Amount
• CVn or FVn =Po(1+I)n Or Po×CVIFn.i
• CVn or FVn =Compound or Future value at the end of n years
• Po=Principle amount at year 0
• I= Interest rate per annum
• n=number of years for which compounding is done
• CVF= Compound Value Interest Factor
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9. Q.5 Suppose you have Rs 10,00,000 today and you deposit it with a
financial institute, which pay 8% compound interest for a period of 5
years. How much deposit would grow?
(14,69,000)
Q.6 Mr A deposited Rs 50,000 in a Bank for 3 years at 9% per annum.
How much amount would he get at the end of 3 years ? (64,750)
Q.7 Find out compounded interest on Rs. 6,000 for 3 years at 9%
compounded annually.
(7,770)
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10. Generally compounding is done once in year. But it may be semi annually,
quarterly, monthly and daily. It can calculated by following formula
CVn= P0 1+
I
m
m×n
CVn = Compound value at the end of the year n
P0 = Principal amount at the beginning of year n
I = Interest rate per annum
m= number of times per year compounding is done
n= number of years or maturity period
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11. Q.8 Find out compounded interest on Rs. 40,000 for 5 years at 10% compounded
annually. (64440)
Q.9 How much does a deposit of Rs.40,000 grow to at the end of 10 years at the
rate of 6% interest and compounding is done semi-annually. Calculate the
amount at the end of 10 years.
(72,240)
Q.10 Suppose that a firm deposits Rs. 50 lakh at the end of year for 4 year at the
rate of 8% interest and compounding is done on quarterly basis. What is the
compound value at the end of 4th year?
(68,65,000)
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12. When interest is payable half-yearly
CVn = Po (1 + i/2 )2n
When interest is payable quarterly
CVn= Po(1+i/4)4n
When interest is payable monthly
CVn = Po (1+i/12)12n
When interest is payable daily
CVn= Po(1+i/365)365n
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13. Time Line
• When cash flows occur at different points of time, it is easier to deal
with them using a time line.
• A time line shows the timing and the amount of each cash flow in a
cash flow stream.
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14. Compound Value when Multiple series of
cash inflow
a. If cash inflow is uneven
1. At the end of year:
CVn= P1(1+I)n-1+P2(1+I)n-2+………+CFn
2. At the beginning of year:
CVn=P0(1+I)n+P1(1+I)n-1+………..+CFn
CVn=Compound value at the end of year “n”
P0= Principle amount at the year 0
P1= Principle amount at the end of year 1
P2= Principle amount at the end of year 2
I= Interest rate per annum
n= Maturity period Dr. Ankit Jain 14

15. b. If cash inflow is even (Annuity)
• Annuity is a series of even cash flows for a specified duration. It involves a
regular cash outflow or inflow. For e.g. recurring deposit, systematic
investment plan, life insurance premium etc.
• If cash flows happen at the beginning of the year, it is called annuity due,
whereas when the cash flows happen at the end it is called as a regular or
ordinary or deferred annuity.
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16. 1.If cash flow happens at end of the year-
CVn = P
(1+𝐼) 𝑛−1
𝐼
Or CVn = P (CVIFAI.n)
2. If cash flow happens at beginning of the year-
CVn=P
1+𝐼 𝑛−1
𝐼
1 + 𝐼 Or CVn = P (CVIFAI.n) ( 1+I)
CVn= Compound Value
P= Fixed Periodic cash inflow or outflow
I= Interest rate per annum
n=number of years to maturity
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17. Q.11.Mr X deposits 5000 at the end of each year at 8% per year. What
amount will he received at the end of 6years?
(36687.5 or 36680)
Q.12.What will a deposit of 4,500 at 10% compounded semiannually be
worth if left in the bank for six years?
(8082)
Q.13.Given an annual opportunity cost of 10%, what is the future value
of a Rs.1,000 ordinary annuity for 10 years?
(15937)
Q.14.How long does it take for Rs 856 to grow into Rs 1,122 at an
annual interest rate of 7%? (4 years)
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18. Q.15.How much will an ordinary annuity of Rs 650 per year be worth in eight years at an
annual interest rate of 6 percent? (6433)
Q.16.What annual interest rate would you need in order to have an ordinary annuity of Rs
7,500 per year accumulate to Rs 2,79,600 in 15 years? (12%)
Q.17.What annual interest rate is implied if you lend someone Rs 1,850 and are repaid Rs
2,078.66 in two years? (6%)
Q.18.Mr A deposits at the end of each year Rs.2,000,3,000,4,000,5,000 and 6,000 for years 1
to 5 respectively. He wants to know his series of deposits value at the end of 5 years with 6%
rate of compound interest.
(21,893)
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19. • Suppose A invest Rs 100000 and he wants to double
the amount at 8 % per annum. How much time require
to double the amount ?
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20. Rule of 72
Rule of 72 is a shortcut to estimate the number of years
required to double your investment at a given annual
rate of return.
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21. Doubling Period
Rule of 72 Dp =
72
Interest rate
Rule of 69 Dp= .35+
69
Interest rate
Dp = Doubling Period
I=Interest rate (not in %)
Q.19. If you deposit Rs 500 today at 10% rate of interest, in how many years will
this amount double? (7.25 years)
Q.20.How long will it take to double your money if it grows at 12% annually?(6
years)
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22. Present Value
a. Present value of single amount
PV=FV
1
(1+I)
n
or FV (PVIFI.n)
Where PV = Present value at beginning of the year
FV = Future value receivable at the end of ‘n’ years
I = Interest rate or discounting factor or cost of capital
n = Duration of the cash flow.
PVIFI.n = Present value interest factor at ‘I’ interest and for
‘n’ years
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23. Q.21An investors wants to find the present value of Rs.40000 received
after 3 years. His interest rate is 10%.
(30040)
Q.22 What is the present value of Rs. 2,67,600 which will received
after 5 years at 6% rate of interest?
(1,99,897)
Q.23 Calculate the present value of each of the following cash flows
using a discount rate of 14%
a. Rs 2,000 cash outflow immediately
b. Rs 6,000 cash inflow one year from now
c. Rs.6,000 cash inflow two years from now
d. Rs 7,000 cash inflow four years from now
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24. b. Present value of a series of cash flows
1.Present value of uneven cash flows
PV=
𝐹𝑉1
(1+𝑖)1 +
𝐹𝑉2
(1+𝑖)2 +. . .
𝐹𝑉𝑛
(1+𝑖) 𝑛
PV= Present value of cash inflow
FV =Future value of cash inflow
I= Interest rate per annum
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25. 2. Present Value of Even Cash Inflow
a. Present value of Ordinary Annuity
PVAn = FV (PVIFAI.n)
b. Present value of Annuity Due
PVAn = FV (PVIFAI.n) (1+I)
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26. Q.24 Mr. X has to receive Rs. 500 at the beginning of
each year for 4 years. Calculate present value of annuity
due assuming 10% rate of interest.
(1743.5)
Q.25 Mr. X has to receive Rs. 4000 at the end of each
year for 6 years. Calculate present value of ordinary
annuity assuming 10% rate of interest.
(17,420)
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27. Meaning of Perpetuity
• An indefinite series of payment of equal amounts at regular
intervals on a fixed date is known as Perpetuity.
• The word ‘Perpetuity’ is a combination of two terms
perpetual annuity, i.e. a form of annuity which goes on
forever and therefore its future value cannot be calculated.
Hence, it is a continuous stream of consistent cash flows over
the years.
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28. Key Differences Between Annuity and
Perpetuity
• A series of continuous cash flows of an equal amount over a limited
period is known as Annuity. Perpetuity is a type of annuity which
continues forever.
• The annuity is for a fixed period, but Perpetuity is everlasting.
• Future Value of annuity can be easily calculated which is not possible
in case of Perpetuity.
• Perpetuity is an annuity, but an annuity is not perpetuity.
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29. Present Value of Perpetuity
PV=
A
I
PV= Present value of Perpetuity
A= Constant annual cash inflow
I= Interest rate
Q26 Mr. A an investor expects a perpetual amount of Rs 1000 annually from
his investment. What is his present value of perpetuity if the interest rate is
8%?
(12,500)
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30. Effective Rate of Interest
ERI= 1+
I
m
m
− 1
Q.27 Mr. X deposited Rs 1,000 in a bank at 10% of rate
of interest with quarterly compounding . He wants to
know the effective rate of interest.
(10.38%)
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31. Application
of
Time Value of Money
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32. Application of Time Value of Money
• Sinking Fund
• Loan Amortisation
• Equated Monthly Investment
• CAGR
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33. Meaning of Sinking Fund
A sinking fund is an account that is used to deposit and save money to
repay a debt or replace a wasting asset in the future.
In other words, it’s like a savings account that you deposit money in
regularly and can only be used for a set purpose.
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34. Sinking Fund
AP =
𝐹𝑉𝐴 𝑛
1
𝐼
(1+𝐼) 𝑛−1
AP = Annual Payment
FVAn = Future value after n number of years
I= Interest rate
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35. Q.28 A financial manager of a company wants to pay a debt of Rs
2,00,000 at the end of 5 years . He requests to find out the annual
payment required . If his savings earn an interest rate of 10%perannum.
(32,670 OR 32,733)
Q.29 Finance Manager of a company wants to buy an assets costing Rs.
1,00,000 at the end of 10 years. He required to find out the annual
payment required , if the saving earns an interest of 12% per annum.
(5,698)
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36. Meaning of Loan Amortisation
• Loan is an amount raised from outsiders at an interest and repayable at
a specified period (Lumpsum or Installments).
• Payment of loan is known as amortization.
• Financial manager may take loan and he/she may be interested to
know the amount of equal instalment to be paid every year to repay
the complete loan
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37. Loan Amortisation
LI=P
I (1+I
n
)
(1+I)
n
−1
Or
LI=
P
PVIFAI.n
LI= Loan instalment
P= Loan amount
I = Interest rate
N= Loan repayment period Dr. Ankit Jain 37

38. Q.30 A company has raised a loan of Rs 50 lakh from an industrial
finance bank at 9% per annum. The amount has to be paid back in 5
equal yearly instalments. Calculate the instalment amount. (12,85,347
or 12,84,879)
Q.31 A firm takes a loan of Rs 25,00,000. If the compounding rate of
interest is 12%. Find out the amount of each installment if it is repaid
in 5 equal installments.
(6,93,481)
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39. Equated Monthly Installments (EMI)
EMI= P×𝐼
(1+𝐼) 𝑛
1+𝐼 𝑛−1
P= Loan amount
I= Interest rate per month
n=Loan period in months
Q.32 Assuming a loan as Rs.1,00,000, at 12% repay in 1 years . Calculate EMI
? (8874)
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40. Compound Annual Growth Rate
• The compound annual growth rate, also called CAGR, is the return on
investment over a period of time. It measures a true return on an
investment by calculating the year over year returns, compounding
them, and considering the investment values.
• In other words, it’s a far more accurate way to measure the overall
return on an investment than using an average returns method.
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41. Compound Annual Growth Rate
Formula for calculating compound annual growth rate:
V0(1+r)n=Vn
V0 = Variable value at the end of year 1
(1+r)n = Growth rate
Vn = Variable value at the end of year n
Q.33 From the following dividend data of a company, calculate compound growth
rate of growth for period (2012-2017).
Year 2012 2013 2014 2015 2016 2017
DPS 21 22 25 26 28 31
(gr=8%)
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42. Test Yourself
Q.1 Your mother is planning to retire this year. Her firm has
offered her a lump sum retirement payment of Rs.50,000 or a
Rs.6,000 lifetime ordinary annuity-whichever she chooses.
Your mother is in reasonably good health and expects to live
for at least 15 more years. Which option should she choose,
assuming that an 8 percent annual interest rate is appropriate to
evaluate the annuity?
Ans. Present value of annuity 51,360 , because the lifetime
annuity has a higher expected present value than the 50,000
lump sum payment, she should take the annuity.
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43. Q.2 A ltd. has issued a Rs. 10,00,000, 10-year bond
issue. The bonds require A ltd. to establish a sinking
fund and make 10 equal, end-of-year deposits into the
fund. These deposits will earn 8 percent annually, and
the sinking fund should have enough accumulated in it
at the end of 10 years to retire the bonds. What are the
annual sinking fund payments?
(69,025)
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44. Q.3 If you wish to accumulate Rs.1,40,000 in 13 years, how much must you
deposit today in an account that pays an annual interest rate of 14%?
(25480 or 25491)
Q.4 Calculate the present value of a perpetuity bond that is expected to pay Rs
5000 of interest per year forever if the investor requires an annual return of 8
percent.
(62500)
Q.5 Mr. A are planning ahead for their son's education. He's eight now and will
start college in 10 years. How much will they have to set aside at the end of each
year to have Rs. 65,000 in 10 years if the annual interest rate is 7%?
(4,704.55)
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45. Q.6 The Tried and True Corporation had earnings of Rs 0.20 per share in 1998.
By 2015, a period of 17 years, its earnings had grown to Rs 1.01 per share.
What was the compound annual rate of growth in the company's earnings?
(10%)
Q.7 You are planning to retire in twenty years. You'll live ten years after
retirement. You want to be able to draw out of your savings at the rate of Rs.
10,000 per year. How much would you have to pay in equal annual deposits
until retirement to meet your objectives? Assume interest remains at 9%.
[1254]
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46. Q.8 You can deposit Rs.4000 per year into an account that pays 12% interest. If
you deposit such amounts for 15 years and start drawing money out of the
account in equal annual installments, how much could you draw out each year
for 20 years? (19965)
Q.9 If you want a Rs.10,00,000 for retirement in 30 years, how much would
you have to save by the end of each year if you could make 12% per year? How
much would you have to set aside each year if you could put money away
starting now?
(4144)
Q.10) How much will Rs.1,000 deposited in a savings account earning an
annual interest rate of 6 percent be worth at the end of 5 years? (1,338)
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47. In Microsoft Excel: Use FV function
FV(rate,nper,pmt,pv,type)
Use PV function
PV(rate,nper,pmt,fv,type)
Use PMT function for calculation Loan instalment annually and EMI
PMT(rate,nper,pv,fv,type)
Where: FV= Future Value
rate= interest rate.
nper= n periods,
pmt= annuity value,
pv= present value,
type= 1 for beginning of the period and 0 for end for end of period.
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48. Solve through Excel
• How much will Rs.1,000 deposited in a savings account earning an
annual interest rate of 6 percent be worth at the end of 5 years?
(1,338)
• An investors wants to find the present value of Rs.40000 received after
3 years. His interest rate is 10%. (30052)
• Assuming a loan as Rs.1,00,000, at 12% repay in 1 years . Calculate
EMI. (8884)
• A firm takes a loan of Rs 25,00,000. If the compounding rate of
interest is 12%. Find out the amount of each installment if it is repaid
in 5 equal installments.
(6,93,524)
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