Time Value of Money
A brief definition of time value of money
Time value of money simply means that the value of a unit of money is different when received in time periods that are different. In other words the value of a unit of money at hand today is different from the value of the same unit of money if it is to be received at a future date (Bianco, Nelson & Poole, 2010). Money held in hand now is of more value than the same amount of money if it is received some time in future. For example $100 at hand today has more value than if the $ 100 is received in a year’s time. This is because the $100 held today can be invested and earn a return by the end of the year. The concept of time value of money implies that a dollar in hand today is worthy more than a dollar to be received tomorrow (Benshoof, 2005). Time value of money can be paralleled to the wise saying that “a bird at hand is worth two in the bush”. This concept recognizes that the passage of time affects the value of money. This because a dollar in hand can be put to immediate productive use and also the dollar in hand is free from the uncertainties of future expectations (Bianco, Nelson & Poole, 2010).
- The importance of understanding the concept of time value of money by finance managers
The concept of time value of money is important to finance managers due to a number of reasons. The concept of time value of money is important in making investment decisions between mutually inclusive projects. Finance managers are charged with the responsibility of advising company shareholders on the attractiveness of investing in various investment opportunities (Benshoof, 2005). Finance managers are required to invest a company’s financial resources in ventures which generate the highest possible returns to maximize shareholder value. Finance managers in doing this rely on the concept of time value of money to make decisions. According to Freeman & Freeman (1993) finance managers rely on time value of money in determining the attractiveness of potential investment opportunities. Finance managers calculate the net present value of the various potential investment opportunities and choose the ones with the highest net present values to invest in. Without the concept of time value of money it would be practically impossible to choose between competing investment opportunities (Benshoof, 2005). Many companies grow their market share or revenues by investing through the stock exchange. The concept of time value of money assists managers to determine investment opportunities which are viable and the ones that are not (Benshoof, 2005).
Finance managers also rely on the concept of time value of money in determining the breakeven point of a project. Breakeven point is the point at which total cost of a business venture equal total revenues. Any additional revenue earned beyond the breakeven point revenue is considered as a profit to a company (Bianco, Nelson & Poole, 2010). Without considering time value of money, finance managers can invest in business ventures which lose value instead of adding it which jeopardizes the survival and growth prospects of a company. The concept of time value of money also assists finance managers to determine the opportunity cost of business ventures. Calculating opportunity cost of a project helps finance managers to choose which ventures are worthy investing in and which ones should be avoided (Bianco, Nelson & Poole, 2010).Time value of money computations assists finance managers in making financial structure decisions, lease versus purchase of capital assets choices, bond refinancing decisions, valuation of securities, cost of capital among others.
To illustrate the importance of time value of money we will use an example this is because if finance managers ignore the impact of time on their investments they will end up misleading their companies into making wrong investment decisions. For example assume a company is faced with two mutually exclusive investment opportunities. Assume the initial capital outlay (cost) is the same for the two opportunities. One of the investment opportunities, (Company A), will bring lump sum cash inflow at the end of 15 years of $ 4 million. If the company’s cost of capital is 10% then the present value of this investment is as follows. The general equation for present value is PVk,n=FVn/(1+k)n
Whereby PVk,n=Present value of a future amount to be received at n period at k opportunity cost
FVn=Amount of money to be received at future point n
K=opportunity cost
n=time period
Hence the present value of the $ 4 million will be =>
Present Value (PV) = $4million / (1+10%)15
- $4million / (1.10)15 => $4million / 4.177248169 = $ 957,568.20
From the foregoing the value of the $4 million will have fallen to $ 957,568.20 in the 15th year.
Assume the next business opportunity (Company B) will bring in $ 2.5 million in the 10th year with cost of capital at 10% then the Present value of the cash inflow will be as follows.
PV= $2.5million / (1+10%)10 => $2.5million / (1.10)10
- $2.5million / 2.59374246 = $ 963,858.22
In this case a finance manager who does not take into account the effects of time value of money will choose the option of investing in Company A because it will bring in $ 4 million in the 15th year. However, a prudent finance manager who takes into account the time value of money will choose Company B whose present value of $ 2.5 million is $963,858.22 and higher than the present value of the $ 4 million from company A whose present value on the 15th year will be $ 957,568.20 and less than the present value from company B. This not considering that the longer the period before the cash inflow is received the riskier a business venture is (Martinez, 2013).
3) Calculate the future value of the following:
- a) $120,537.19 if invested for three years at a 3% interest rate
Future value techniques measure cash flow at some future point in time. It is the value at some time in future of a present sum of money or a series of payments or receipts. In other words the future value refers the amount of money an investment will grow to over some period of time at some given interest rate.
The general equation for future value at end of n periods can be formulated as;
FVn=po(1+k)n
Where FVn=future value at end of end of period n
Po=Initial principal or present value
K=annual rate of interest
n=number of period the money is left on deposit
Hence Future Value (FV)=$120,537.19 *(1+3%)3=>$120,537.19 *(1+0.03)3
=>$120,537.19 *(1.092727) = $131,714.24
- b) $337,891.22 if invested for seven years at a 6% interest rate
Future Value (FV) = $337,891.22 *(1+6%)7=> $337,891.22*(1+0.06)7
=>$337,891.22*(1.503630259) = $508,063.46
- c) $420,891.12 if invested for 11 years at an 12% interest rate
Future Value (FV) =$420,891.12 * (1+12%)11=>$420,891.12 *(1.12)11
=>$420,891.12 *(3.478549993) = $1,464,090.80
- d) $525,520.22 if invested for 14 years with a 15% interest rate
Future Value (FV) =$525,520.22 *(1+15%)14=>$525,520.22 *(1.15)14=>
=>$525,520.22*(7.075705764) = $3,718,426.45
4) Calculate the present value of the following:
- a) $262,126.17 to be received six years from now with a 4% interest rate
The general equation for present value is PVk,n=FVn/(1+k)n
Whereby PVk,n=Present value of a future amount to be received at n period at k opportunity cost
FVn=Amount of money to be received at future point n
K=opportunity cost
n=time period
Hence=> PresentValue (PV) = $262,126.17/(1+4%)6 => $262,126.17/(1.04)6
=> $262,126.17 / 1.265319018 = $207,162.12
- b) $325,003.21 to be received eight years from now with a 7% interest rate
Present Value (PV) = $325,003.21/(1+7%)8=>$325,003.21/(1.07)8
=> $325,003.21 / 1.71818618 = $189,154.83
- c) $421,567.35 to received 10 years from now with an 10% interest rate
Present Value (PV) = $421,567.35/(1+10%)10=> $421,567.35/(1.10)10
=> $421,567.35 / 2.59374246 = $162,532.46
- d) $631,500.05 to be received 12 years from now with a 13% interest rate
Present Value (PV) = $631,500.05/(1+13%)12 => $631,500.05/(1.13)12
=>$631,500.05 / 4.3345231 = $145,690.78
5) Suppose you are to receive a stream of annual payments (also called an “annuity”) of $525,891.12 every year for seven years starting at the end of this year. The interest rate is 15%. What is the present value of these seven payments?
This is calculated using present value interest factor of an annuity (PVIFA) tables. PVIFA cannot be greater than 1 or less than 0.
PVA=PMT*PVIFA
Where PVA=Present value of an annuity
PMT=future cash flows
PVIFA= present value interest factor of an annuity
Hence= PVA=$525,891.12*0.376=197,735.06
6) Suppose you are to receive a payment of $637,891.24 at the end of each year for six years. You are depositing these payments in a bank account that pays 12% interest. Given these six payments and this interest rate, how much will be in your bank account in six years?
To determine the amount of money that will be in my bank I will use the tables to calculate the future value of the annuity of receiving a payment of $637,891.24 at the end of each year for six years and depositing the money in a bank account at a rate of 12% interest
FVn=P0*FVIF
Where FVn=Future value of the annuity
Po=Present value of instalments
FVIF=Future value interest factor
Hence=$637,891.24*1.974=$1,259,197.31
The amount of money that will be in your bank is =$1,259,197.31 at the end of 6 years.
References
Benshoof, M. (2005).THE TIME VALUE OF MONEY.Professional Builder, 70(3), 74. Retrieved from http://search.proquest.com/docview/194232521?accountid=45049
Bianco, C. A., Nelson, D. T., & Poole, B. S. (2010).Teaching time value of money. The Business Review, Cambridge, 16(1), 25-31. Retrieved from http://search.proquest.com/docview/818356218?accountid=45049
Freeman, M., & Freeman, K. (1993).Considering the time value of money in breakeven analysis.Management Accounting, 71(1), 50. Retrieved from http://search.proquest.com/docview/195672414?accountid=45049
Martinez, V. (2013). Time value of money made simple: A graphic teaching method. Journal
of Financial Education, 39(1), 96-117. Retrieved from http://search.proquest.com/docview/1435377604?accountid=45049
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