TIME VALUE OF MONEY
DEFINITION
Time value of money means that the value of a unit of
money is different in different time periods.
The time value of money can also be referred to as time
preference for money.
Reasons for individual’s Time Preference for Money:
1. Uncertainty
2. Preference for Consumption
3. Investment Opportunities
DIMENSIONS OF TIME VALUE OF MONEY
Single Sum
Future Value
Annuity &
Annuity Due
Dimension
Single Sum
Present Value
Annuity &
Annuity Due
FUTURE VALUE
Compounding: Related to determine the future value of a
present amount.
Types:
1. Annual Compounding
2. Semi-annual Compounding
3. Quarterly Compounding
CONTINUOUSLY/ EXPONENTIALLY
FV= PV * E TO THE POWE I INTO N
FUTURE VALUE
What will a deposit of $4,500 at 10% compounded
semiannually be worth if left in the bank for six years?
What will a deposit of $4,500 at 7% annual interest be
worth if left in the bank for nine years?
What will a deposit of $4,500 at 12% compounded
monthly be worth at the end of 10 years?
How much will $1,000 deposited in a savings account
earning an annual interest rate of 6 percent be worth at
the end of 5 years?
If you deposit Rs. 1000 today in a bank which pays 10%
interest compounded annually, how much will the
deposit grow to after 8 years and 12 years?
PRESENT VALUE
Discounting: Related to determine the present value of a
future amount.
𝐹𝑉 𝑛
𝑃𝑉 𝑛= 𝑛
(1+𝑖 )
Suppose someone gives you Rs1000 six year hence.
What is the present value of this amount if the interest
rate is 10%?
Find the present value of Rs1000 receivable 20 years
hence if the discount rate is 8%.
FUTURE VALUE OF ANNUITY
An annuity is a series of periodic cash flows (payments
or receipt\pts) of equal amounts. The premium payment
of a life insurance policy, for example, is an annuity.
Suppose you deposit Rs 1000 annually in a bank for 5
year and your deposits earn a compound interest rate of
10%. What will be the value of series of deposits at the
end of 5 years?
PRESENT VALUE OF AN ANNUITY
Present value of a 4 year annuity of Rs10000 discounted
at 10%.
1 1
𝑃𝑛 = 𝐴
𝑖 [
−
𝑖 (1+𝑖 )𝑛 ]
SOME QUESTIONS
How long does it take for $856 to grow into $1,122 at an
annual interest rate of 7%?
What is the present value of $800 to be received at the
end of 8 years, assuming an interest rate of 20 percent,
quarterly compounding?
What is the present value of $800 to be received at the
end of 8 years, assuming an annual interest rate of 8
percent?
Find the present value of $1,000 to be received at the end
of 2 years at a 12% nominal annual interest rate
compounded quarterly.
FUTURE VALUE OF ANNUITY DUE
There are two types of annuity. The one in which
payments occur at the end of each period is called
ordinary annuity and the other in which payments occur at
the beginning of each period is called annuity due.
(1 + i)n − 1
FV of Annuity Due = A × × (1 + i)
i
Calculate the future value of 12 monthly deposits of
$1,000 if each payment is made on the first day of the
month and the interest rate per month is 1.1%. Also
calculate the total interest earned on the deposits if the
whole amount is withdrawn on the last day of 12th month.
PRESENT VALUE OF AN ANNUITY DUE
An annuity is a series of evenly spaced equal payments made for a
certain amount of time. Annuity due is the one in which periodic
payments are made at the beginning of each period.
(1+i)
A certain amount was invested on Jan 1, 2010 such that it generated
a periodic payment of $1,000 at the beginning of each month of the
calendar year 2010. The interest rate on the investment was 13.2%.
Calculate the original investment and the interest earned.
PRESENT VALUE OF PERPETUITY
Perpetuity is an infinite series of periodic payments of equal face
value. In other words, perpetuity is a situation where a constant
payment is to be made periodically for an infinite amount of time. It
as an annuity having no end and that is why the perpetuity is
sometimes called as perpetual annuity.
𝐴
𝑃𝑉 𝑜𝑓 𝑃𝑒𝑟𝑡𝑢𝑖𝑡𝑦 =
𝑖
Calculate the present value on Feb 1, 2018 of a perpetuity paying
$1,000 at the end of each month starting from February 2018. The
monthly discount rate is 0.8%.
LOAN AMORTIZATION SCHEDULE
Amortization schedule is a table that shows total
payments to be made on an amortizing loan, the loan
balance at the start of each period, total payment during
each period bifurcated into (a) interest payment and (b)
principal repayment and the closing balance of the loan
at the end of each period.
Opening loan Principle (
LOAN AMORTIZATION SCHEDULE
Suppose, you work at EZ publishing, Inc., a printing
business. On 1 January 2017, your company signed a
lease for printing equipment for 6 years at 8% per
annum. Lease payments are to be made semiannually.
The present value of the minimum lease payments is $10
million. Your CEO has asked you to calculate the interest
expense related to the lease in financial year ended
December 2022, the amount by which lease liability is
reduced during the year, the lease liability balance as at
the year end and relevant cash outflows for the year.
LOAN AMORTIZATION SCHEDULE
At first we have to find the total payment for each period
that is A, after-that prepared the amortization table.
Now,
So, A = 1,065,522
1st Period Interest (10,000,000 × 0.04) = 4,00,000
1st Period Principle Payment (1,065,522 – 4,00,000 =
6,65,522)
1st Period Closing Balance (10,000,000 – 6,65,522 =
9334478)
LOAN AMORTIZATION SCHEDULE
Payment Payment Opening Total Interest Principal Closing
No. Date Balance Payment Expense Repayment Balance
A B C = A×8%/2 D=B-C E =A-D
0 1-Jan-17 10,000,000 0 0 10,000,000
1 30-Jun-17 10,000,000 1,065,522 400,000 665,522 9,334,478
2 31-Dec-17 9,334,478 1,065,522 373,379 692,143 8,642,336
3 30-Jun-18 8,642,336 1,065,522 345,693 719,828 7,922,507
4 31-Dec-18 7,922,507 1,065,522 316,900 748,621 7,173,886
5 30-Jun-19 7,173,886 1,065,522 286,955 778,566 6,395,320
6 31-Dec-19 6,395,320 1,065,522 255,813 809,709 5,585,611
7 30-Jun-20 5,585,611 1,065,522 223,424 842,097 4,743,513
8 31-Dec-20 4,743,513 1,065,522 189,741 875,781 3,867,732
9 30-Jun-21 3,867,732 1,065,522 154,709 910,812 2,956,920
10 31-Dec-21 2,956,920 1,065,522 118,277 947,245 2,009,675
11 30-Jun-22 2,009,675 1,065,522 80,387 985,135 1,024,540
12 31-Dec-22 1,024,540 1,065,522 40,982 1,024,540 0
LOAN AMORTIZATION SCHEDULE
Suppose a homeowner borrows $ 100,000 on a mortgage
loan, and the loan is to be repaid in five equal payments
at the end of each of the next 5 years with 6% rate of
interest. Calculate the amount of each year interest and
principle payment.
