1. Accounting and Finance in Travel, Hospitality and Tourism
Unit 10
Time Value of Money
Accounting and Finance THT Unit 10

2. Unit 10 – Time Value of Money
Learning Outcome:
Describe the Concept of Time Value of Money
Determine the Future Value of a single sum of Money using: the Flat Rate Basis, Compounding Rate Basis & the Future Value Interest Factor Tables
Describe the Intra-year Compounding
Determine the Future Value of an Annuity mathematically & Using the Future Interest Value Factor Tables
Accounting and Finance THT Unit 10

3. Unit 10 – Time Value of Money
Learning Outcome:
Determine the Present Value of a Single sum mathematically & Using the Present Value Interest Factor Tables
Determine the Present Value of an Annuity mathematically & Using the Present Value Interest Factor Tables
Accounting and Finance THT Unit 10

4. Concept of Time Value of Money
It is important to understand the Time Value of Money as:
One dollar today may be worth more or less than a dollar tomorrow
Interest rates have effects on the value of money
Interest rates have widespread influence over decisions made by business

5. Time Value of Money
FUTURE VALUE

6. Determination of Future Value of Money using the Flat Rate Basis
Using the mathematical formula:
FVn = PV (1 + i )n
Where FVn = the future value of the investment at the end of year n
PV = initial principal or amount invested at the beginning of
year 1
i = annual rate of interest

7. Example:
Suppose James placed $100 in a savings account that pays 6% interest compounded annually. How will his savings grow after one year?
By Using the formula:
FV1 = PV (1 + i)
= $100 ( )
= $106

8. Future Value of Money using the Compounding Rate Basis
Assuming that the sum of money is carried forward for another another year at the rate of 6%, he is now earning interest on interest ie. Compound interest. Hence the formula with interest compounded annually at a rate of i for n years will be :-
FV = PV (1 + i) n n
Where FV = future value of the investment at n year
n = the number of years during which the
compounding occurs
i = the annual interest (or discount) rate
PV = the present value or original amount invested
at the beginning of the first year n

9. Example:
James has placed $800 in a savings account paying a 6% interest compounded annually. He wishes to determine how much money he will have at the end of five years.
By using the formula: FV = $800( )5
= $800(1.338)
= $1,070.40
Determination of Future Value of Money using Future Value Interest Tables
FV = P X FV1Fin
= $800 X 1.338
= $1,070.40

10. INTRA YEAR COMPOUNDING
Where interest is compounded more than once a year, the stated interest rate must be adjusted accordingly. The equation to be used would be:-
F = P( ) i m
m x n
Where m = the number of times per year interest is compounded
n = the number of years

11. Example:
If Steve deposits $100 at 8% interest compounded semi-annually, the amount he would have at the end of 2 years would be: 4
FV = $100 ( )
= $116.99

12. Annuities
An annuity is a stream of equal cash flows.

13. Determination of Future Value of an Annuity Mathematically
Mathematically, the future value of the annuity amount will be :-
FV = P(1 + i) + P(1 + i) + P(1 + i) + P(1 + i) + P(1 + i) 4 3 2 1
Using the Future Value Interest Factor for Annuity:
FA = A x FVIFAin
Where FA = future value of an annuity
A = amount of annuity deposited at one end of each period
i = the interest rate
n = number of periods

14. Example:
Mary wishes to determine how much money she will have at the end of five years if she deposits $1000 annually in a savings account paying 7 percent annual interest

15. Example: Part II
You will notice that in order the future value of the annuity, each & every annual amount must be multiplied by the appropriate future-value interest factors, and the results are added together to give the future amount at the end of the period
Mathematically, the future value of the annuity amount for the above example will be represented as:

16. Future-Value Using the Future Value Interest Factor Table for ANNUITY
The mathematical method of calculating future value of annuity is very tedious if deposits are made over too long a period.. The Future Value Interest Factor Table for Annuity will come in handy, again within the specific interest rates & periods
The calculation can be represented as:
FA = A X FVIFA in
Where FA = future value of an annuity
A = the amount of annuity deposited at the end of each period
i = the interest rate
n = the number of periods

17. Example: A = $600 FVIFA = 13.181 Therefore FA = $600 x 13.181
Rama wishes to determine the sum of money he will have in his savings account, which pays 6% annual interest, at the end of ten years if he deposits $600 at the end of each year for the next ten years. Using the Future Value Interest Factor for Annuity Table,
A = $600
FVIFA =
Therefore FA = $600 x
= $7,908.60

18. Time Value of Money
PRESENT VALUE

19. Determining the Present Value of a Single Sum (1)
The process of finding the present value is sometimes called discounting
This is the inverse of compounding
The Mathematical expression for present value is :-
PV = F
( 1 + i) n
Where PV = the present value of the future sum of money
F = the future value of the investment at the end of n years
n = the number of years until the payment will be received
i = the annual discount (or interest) rate

20. Determining the Present Value of a Single Sum (2)
Example:
Jimmy wishes to find the present value of $1,700 that will be received eight years from now. The interest rate is 8%.
Using the formula. PV = $1,700
( )
= $918.46 8

21. Present Value of a Single Sum using the Present Value Interest Tables
We can calculate the present value using the Present Value Interest Tables
P = F x PVIF
= $1,700 x
= $918.51 in

22. Determining the Present Value of an Annuity using the Present Value Table
Example: Summer Co. is attempting to determine the most it should pay to purchase a particular annuity. The Co. requires a minimum return of 8% on all investments, the annuity consists of cash flows of $700 per year for five years.
Accounting and Finance THT Unit 10

23. Present Value of an Annuity using Mathematical formula -Part II
Mathematically, the present value of the annuity for the above example will be represented as :

24. Present Value of an Annuity using the Present Value Interest Factor
It is extremely tedious to calculate the present value of each individual cash flows & adding the sum together to obtain the present value of the annuity
The shorter method would be to use the present value interest factor table for annuity
PA = A x PVIFA
Where PA = present value of the annuity
A = annuity (equal stream of cash flows)

25. Example: Here A = $160,000 Therefore PA = $160,000 x 8.514
Matterhorn Company expects to receive $160,000 per year at the end of each of the next 20years from a new mine. If the firm’s opportunity cost of funds is 10%, how much is the present value of this annuity?
Here A = $160,000
Therefore PA = $160,000 x
= $1,362,240

26. Practice and Exercises
Time Value of Money
Practice and Exercises