this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
TVM, Future Value Interest Factor (FVIF), Present Value Interest Factor (PVIF), present value interest factor of an annuity (PVIFA)
Using estimated rates of return, you can compare the value of the annuity payments to the lump sum.
The present value interest factor may only be calculated if the annuity payments are for a predetermined amount spanning a predetermined range of time.
Time Value of Money Formula
FV = PV x [ 1 + (i / n) ] (n x t)
Formula for Future Value Interest factor:
FVIF = (1+r)n
Formula for PVIF
PVIF = 1 / (1 + r)n
Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2]
Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4]
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
Basic Time Value of Money Formula and Example
Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
TVM, Future Value Interest Factor (FVIF), Present Value Interest Factor (PVIF), present value interest factor of an annuity (PVIFA)
Using estimated rates of return, you can compare the value of the annuity payments to the lump sum.
The present value interest factor may only be calculated if the annuity payments are for a predetermined amount spanning a predetermined range of time.
Time Value of Money Formula
FV = PV x [ 1 + (i / n) ] (n x t)
Formula for Future Value Interest factor:
FVIF = (1+r)n
Formula for PVIF
PVIF = 1 / (1 + r)n
Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2]
Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4]
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
Basic Time Value of Money Formula and Example
Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
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Potassium is the principal cation of the intracellular fl uid
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2. Why Money has Time Value?
Because it involves;
Risks and uncertainties.
The purchasing power of the money varies over time because of
inflation.
Money can be employed productively to generate returns.
Returns are in the form of Interest rate and the interest is
categorized into two types.
4. Real Interest Rate:
The compensation that is paid by the borrower for the
postponement of consumption in the Interest Rate is
Real Interest Rate.
Nominal Interest Rate:
The Interest Rate that includes inflation value to the
Real Interest Rate. Real Interest Rate + Expected Rate of
inflation + Risk premium to compensate uncertainty.
5. Time value can be done in two ways:
Compounding
Discounting
Compounding:
It is the process of converting cash flows today or future into even
further future and the resulting value is future value.
Discounting:
The process of converting cash flows in the future into cash flows
today. And cash flows in the into cash flows today. And cash flows of
the future converted today eilds a value phenomenon is called as
discounting.
6. Basic types of compounding problem :
Future value of lump sum or a single flow.
The future value of uneven multiple flows.
The future value of Annuity or Series of identical payments.
7. Finding future value of lump sum or single flow:
If the Interest Rate of future value of a single flow is calculated per
annum:
FV n = PV0 (1+R)n
Ex: The Fixed Deposit scheme of Andhra Bank offers 11% interest per
annum. What will be the value of 10,000 rupees after three years?
Sol: n = 3years
PV0=10,000
Rate of Interest (R)= 0.11
8. Cont.…….
FV= PV0 (1+R)n
= 10,000 (1+0.11)3
= 10,000 (1.11)3
= 10,000 (1.368)
= 13,680.
Hence.,
The value of 10,000rupees after three years becomes 13,680rupees
9. Future value of money of a single flow with
payments made quarterly and half yearly:
If the Rate of Interest is paid more than once in a year, it
means the Rate of Interest frequency has got increased.
The rate of interest can be paid on Quarterly basis and Semi
Annual basis.
FVn = PVO(1+R⁄m)m*n
If the Rate of Interest paid quarterly m = 4
If it is paid semi annually m = 2
10. Ex: Under the Vijay cash certificate scheme Interest Is paid
quarterly the ROI is 10% per annum. Calculate the value of
1000 rupees invested after two years?
sol: PV0=1000
ROI (R)=0.1
n= 2
m=4
FVn = PV0(1+R/m)m*n
= 1000 (1+0.1/4)4*2
= 1000(0.025)8
= 1000(1.218)
= 1218
11. Future value of multiple flows:
FVn = FV1+FV2+FV3+……. FVn
Here, we are finding the future value of uneven flows, some time
multiple flow value might be identical and it is said to be Annuity.
Ex: If 1000 rupees invested at the beginning of 1st year, 2000 rupees
at the beginning of 2nd year and 3000 rupees at third year at 12% Rate
of Interest per annum. What will be the value of investment after
3years?
Sol: (1) future value of 1st years flow:
FV1=1000 (1+0.12)3 =1000 (1.12)3 =1000 (1.404) =1404
12. Contd…….
(2) Future value of second years flow:
FV2 =2000 (1+0.12)2 =2000 (1.12)2 =2000 (1.254) =2508.8
(3) Future value of 3rd years flow
FV3 =3000 (1+0.12)1= 3000 (1.12)1= 3360
Hence, The future cash flow value of uneven multiple flow is
FVn =FV1 +FV2 +FV3
=1404 +2508.8 +3360 = 7272.8
13. Annuity:
It is the term used to describe a series of periodic flows of equal
amounts this flows can be either receipts or payments.
Regular/differed/ordinary Annuity:
A series of equal payments made at the end of each period over a fixed
amount of time.
Annuity Due:
When the cash flows occur at the beginning of each period.
14. Future value of an Annuity:
FVAn =A [ (1+R)t -1 /R]
Ex: Suppose 5000rupees is set aside at the end of each year for the next
10yers at 6% Rate of Interest. Calculate the future value of an Annuity?
sol: A=5000
R=0.06
T=10
FVA = A[ (1+r)t -1/r]
=5000 [ (1+0.06)10 -1/0.06]
=5000 [ (1.06)10 -1/0.06]
16. Discounting:
The process of converting cash flows in the future into the cash flows
today. And the cash flows future converted today eilds a value
=>Present value of a single flow or lump sum:
PV =FVn /(1+R)n
Ex: Pragathi Cash Certificate Scheme of Syndicate Bank issued a cash
certificate of 1lakh rupees to be received after 10years at 12%per
annum. Find out present value?
FVn=100,000
R = 0.12
18. Present value of Uneven multiple flows:
PVn =FV (PVIF)m,n
Ex: In the first year cash flow is 2lakh and 2nd year 4lakh and 3rd year 6lakhs
and cost of capital is 12%. Evaluate the present value of cash inflow?
Year cash flow PV
1 2 = FV(PVIF)12,1 = 200,000(0.893) = 178000
2 4 =FV(PVIF)12,2 = 400,000(0.797) = 316000
3 6 =FV(PVIF)12,3 = 6000000(0.712) = 410000
12lakh 920000
There is a higher difference between the future value and current value of
the scheme. It is advisable to the borrower not to opt for this scheme.
19. Present value of Annuity:
PVAn= A [1-1 / (1+R)n /R]
Ex: Calculate the Present Value of 20lakh rupees for 25years at 6
percent?
Sol: PVAn =20,00,000[1 -1/(1+0.06)25/0.06]
=20,00,000(12.783)
=2,55,66,000
The present value of Annuity is 2,55,66,000rupees.