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**Accounting and Finance in Travel, Hospitality and Tourism**

Unit 10 Time Value of Money Accounting and Finance THT Unit 10

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**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

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**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

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**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

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Time Value of Money FUTURE VALUE

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**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

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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

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**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

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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

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**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

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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

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Annuities An annuity is a stream of equal cash flows.

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**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

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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

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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:

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**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

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**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

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Time Value of Money PRESENT VALUE

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**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

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**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

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**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

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**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

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**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 :

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**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)

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**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

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**Practice and Exercises**

Time Value of Money Practice and Exercises

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