transtutors time value of money
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Concepts covered: Concept of Time value of Money What is Time Line Concept of Future Value What is Simple interest and Compound Interest Using Financial Calculator or Excel functions What is Present value and Discounting Finding the discount rate Finding number of period Rule of 72TRANSCRIPT
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Concept of Time value of Money What is Time Line Concept of Future Value What is Simple interest and Compound Interest Using Financial Calculator or Excel functions What is Present value and Discounting Finding the discount rate Finding number of period Rule of 72
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Dollar in hand today is worth more than a dollar promised at sometime in the future.
One earns interest on the dollar value at a later stage.
Refer: http://www.transtutors.com/finance-homework-help/time-value-of-money/ for more details
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Present Value - An amount of money today, or the current value of a future cash flow
Future Value - An amount of money at some future time period
Period - A length of time (often a year, but can be a month, week, day, hour, etc.)
Interest Rate - The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)
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Time lines are used to help visualize what is happening in time value of money problems.
It is a graphical device used to clarify the timing of the cash flows for an investment
Cash flows are placed directly below the tick marks, and interest rates are shown directly above the time line; unknown cash flows are indicated by a symbol for the particular item that is missing.
Each tick mark represents single period.
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Which of the following is incorrect?
o Each tick mark in time line represents single period. o An amount of money at some future time period is
Future valueo The compensation paid to a lender (or saver) for the use
of funds expressed as a percentage for a period (normally expressed as an annual rate) is Interest.
o Cash flows are placed directly above the tick marks, and interest rates are shown directly below the time line
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The value of dollar in future
It refers to the amount of money an investment will grow to over some period of time at some given interest rate.
Refer: http://www.transtutors.com/homework-help/corporate-finance/money-time-value/future-value/ for more details
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Application of Simple Interest
Suppose that you have an extra $100 today that you wish to invest for one year. If you can earn 10% per year on your investment, how much will you have in one year?
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-100 ?
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This process of leaving your money and any accumulated interest in an investment for more than one period, thereby reinvesting the interest, is called compounding.
Compounding the interest means earning interest on interest, so we call the result compound interest.
With simple interest, the interest is not reinvested, so interest is earned each period only on the original principal.
Refer: http://www.transtutors.com/finance-homework-help/time-value-of-money/compounding-and-discounting-future-value-of-single-flow.aspx for more details
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If the investment is done for single period, which interest will have higher value:
o Simple Interesto Compound Interesto Both will give same value
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The expression (1 + r)t is sometimes called the future value interest factor (or just future value factor ) for $1 invested at r percent for t periods and can be abbreviated as FVIF(r, t).
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Assume that Mr. M has deposited $25000 in savings account which will earn an interest of 12% per annum for 10 years
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Future values depend critically on the assumed interest rate, particularly for long-lived investments.
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The expression (1 + r)t is called:
o Future value factoro Future value annuity factoro Present value factoro Future value interest factor
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PV - Present value FV - Future value Pmt - Per period payment amount NPER - Either the total number of cash flows or
the number of a specific period Rate - The interest rate per period Type = 1 is beginning of period and 0 is end of
period
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=FV (rate,nper,pmt,pv,fv,[type])
Example: Assume that Mr. M has deposited $25000 in savings account which will earn an interest of 12% per annum for 10 years.
Using excel formula:
=FV (12%,10,0,-25000,0,[0])
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Why in calculating Future value, through excel formula, we consider the value as negative
o Because it is a Present moneyo It is assumed to be a cash outflowo It is assumed to be a cash inflow
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Present value is thus just the reverse of future value. Instead of compounding the money forward into the future, we discount it back to the present.
It is referred as the present worth of money
Refer: http://www.transtutors.com/homework-help/corporate-finance/money-time-value/present-value/ for further reference
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The present value of $1 to be received t periods into the future at a discount rate of r is:
The quantity in brackets, 1/ (1 + r)t, is called as discount factor, discount rate, or present value interest factor or PVIF
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Suppose that your five-year old son who will be attending the college on his 18th birthday. It is assumed that for attending the college sum of 100000 will be required. If you can earn 8% per year on your investments, how much do you need to invest today to achieve your goal?
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=PV (rate,nper,pmt,fv,[type])
Example: Suppose that your five-year old son who will be attending the college on his 18th birthday. It is assumed that for attending the college sum of 100000 will be required. If you can earn 8% per year on your investments, how much do you need to invest today to achieve your goal?
Using excel formula:
=PV (8%,13,0,100000,[0]) =36769.79
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As the length of time until payment grows, present values decline.
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Calculating the present value of a future cash flow to determine its worth today is commonly called discounted cash flow (DCF) valuation.
Present value factor is just the reciprocal of (that is, 1 divided by) the future value factor
With increase in period and interest
o Present value increaseso Present value decreaseso Present value remains constant
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The rate at which the amount is discounted to the present value.
Apply PV formula
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=Rate (nper,pmt,pv,fv,[type])
Example: Assume that Mr. M has $2000 now which he wants to deposit for 15 years. He needs $25000 in 15 years
Using excel formula:
=Rate(15,0,-2000,25000) =18%
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The time at which the amount is will have a certain value
Apply PV formula
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=NPER (rate,pmt,pv,fv,[type])
Example: Assume that Mr. M has $2000 now and he needs $2500o. The interest rate is 18%.
Using excel formula:
=NPER (18%, 0,-2000,25000,0,[0]) =15 years
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Duration in which the amount is doubled
Example: What is the time taken to double the money, rate of interest is 12%
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Same as rule 72 is used to double money, rule of 114 and 144 are also used.
Rule of 114 is used to triple the money
Rule of 144 is used to quadruple the money
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