The Time Value of Money

TUI University
Paul A. Krasulski
Module 2 Case Assignment: Time Value of Money
FIN 501: Corporate Finance
Dr. Robert Cohn
November 7, 2011

Abstract
Purpose: the purpose of this paper is to demonstrate a thorough understanding of the concepts associated with the time value of money (???TVM???); with emphasis in solving equations for present and future value.
Methodology/approach: for the case assignment, we will consider the time value of money through the following questions:
1. Why is the concept of present value so important to corporate finance (2 – 3 paragraphs)
2. Given a specific data set; how do we calculate present and future value
3. What do you perceive that you have learnt from the Module 2 case assignment
Findings: if ???adding value to the firm??? is the key role of corporate finance, and understanding how to predict and/or recognize ???value??? (in investments, capital budgeting, etc??¦) is only possible with a thorough understanding and ability to apply TVM principles; it follows then that TVM is the de facto foundation for corporate finance. This can and should apply to personal finance as well.
Conclusion: (including that which we have learnt in Module 2) By researching the time value of money during the Module 2 Case Assignment; my biggest takeaway here is that there is indeed a necessity to understand the time value of money as this concept is just as essential to personal finance ??“ and every day financial decisions ??“ as it is to corporate finance.
Paper type: Module 2 Case assignment

Introduction
What is the time value of money (???TVM???) and why is it so important to corporate finance What is the goal of corporate finance Moreover, what is the financial goal of a firm What are financial decisions and how are they made Does TVM give us a better understanding of how to make sound financial decisions Conversely, does TVM help us to recognize and/or avoid poor financial decisions
Let??™s analyze the time value of money as it relates to corporate finance and see if we can answer a few of these questions. Additionally, we??™ll look at some examples of present and future value computations. We??™ll conclude later on with some thoughts on how TVM relates just as much to personal finance as it does to corporate finance.

Section 1: TVM and Corporate Finance
The time value of money tells us that a dollar that you have in hand today is worth more than the promise or expectation that you will receive a dollar in the future (Cedar Springs Software, 2002). Putting that into perspective for corporations, this means that dollars available for use today will not be as valuable as those available at a future date. Logically, one can then make the connection that maximizing returns on ???today??™s??? dollars is a higher priority for corporations than those dollars received later; as today??™s dollars can be either be converted into tangible goods, or invested in order to earn interest (i.e.: more dollars). This is not to say that corporations don??™t think in terms of future value ??“ they do. Gitman (1994) simply concludes that financial managers making decisions at ???time zero??? of an investment opportunity tend to rely primarily on present value techniques (pg 159). Increasing today??™s dollars also add more value to the corporation which, in turn, increases shareholder??™s equity (read: wealth). Cherewyk (2011) states that shareholders typically value corporations by their ability to generate cash-flow back to the company; thereby maximizing the company??™s present value and attracting, potentially, more investors (and more dollars!). Thus, the maximization of ???present value??? of a corporation??™s available dollars (through its investments, or decisions not to invest!) becomes critical to the financial management of the corporation. Let??™s examine this a bit further.
Why is maximizing ???present value??? of significance to the firm Ramagopal (2008) states that while the goal of corporate finance may be the procurement and judicious use of funds (pg. 19); it is generally agreed that ???the financial goal of the firm should be the maximization of owners??™ economic welfare ??“ again, wealth (pg. 20). One way this is achieved is through sound financial decisions. Ultimately, financial executives think in terms of economic return, of growth and productivity. When comparing alternative decisions, they choose the one that provides the most return now (Gitman, 1994, pg. 157); this requires a thorough understanding of the time value of money. But does every opportunity merit investment
Even though we??™re looking to maximize present value, TVM doesn??™t always say ???buy-it-now???. There are instances where the opportunity cost of an investment may not be positive; therefore its purchase is foregone, whether for consumption now or possibly another investment in the future. This is key as financial and other resources are scarce, and thus costly; accordingly, seeking the best use of available funds requires accurate consideration of alternative returns over time (Peterson, 2010). ???Consideration??? here is the use of TVM to maximize present value; taking into account the associated risk with each of the investment alternatives that may be available and taking action on the one that returns the most value to the firm right now.

For corporate finance, TVM represents one of the most powerful tools available for making sound financial decisions. Because investment decisions commonly involve returns that are extended over a long period of time, and because companies can (and often do) greatly diversify their resources; it is critical for financial executives to be able to predict and compare the outcomes of various investment alternatives before they begin (Meigs and Meigs, 1981). Herein lays the core purpose in having people in your organization who have a thorough understanding of TVM: if ???adding value to the firm??? is the key role of corporate finance, and understanding how to predict that ???value??? (as well as recognizing lack of value) in an investment is done primarily through TVM; it follows then that TVM really is the foundation for finance.

Section 2: Determining Present and Future value:
This section will demonstrate the ability to solve for present and future value; utilizing the following equations: Present Value: PV = FV / (1+r)t and Future Value: FV = PV * (1+r)t. All computations are provided; with all ???present value interest factors??? (PVIF(r,n)) and ???future value interest factors??? (FVIF(r,n)) rounded to four decimal places (or the nearest ten thousandth).

Calculate the future value of the following:
a. Values:
FV = to be determined
PV = 49,298
R = .07
T = 5

$49,298 if invested for five years at a 7% interest rate
FV = PV * (1 + r)t
FV = 49298 * (1 + .07)5
FV = 49298 * 1.075
FV = 49298 * 1.4025
FV = $69,140.45
The Future value of $49,298.00, invested at 7% for 5 years would be approximately* $69,140.45
*Note: (FVIF(r,n)) of (1.07)5 was estimated to four decimal places, from 1.402551 to 1.4025.

b. Values:
FV = to be determined
PV = 79,119
R = .04
T = 3

$79,119 if invested for three years at a 4% interest rate
FV = PV * (1 + r)t
FV = 79119 * (1 + .04)3
FV = 79119 * (1.04) 3
FV = 79119 * 1.1249
FV = $89,000.96
The Future value of $79,119.00, invested at 4% for 3 years would be approximately* $89,000.96
Note: (FVIF(r,n)) of (1.04)3 was estimated to four decimal places, from 1.124864 to 1.1249.

c. Values:
FV = to be determined
PV = 69,124
R = .02
T = 7

$69,124 if invested for seven years at an 2% interest rate
FV = PV * (1 + r)t
FV = 69124 * (1 + .02)7
FV = 69124 * (1.02)7
FV = 69124 * 1.1487
FV = $79,402.74
The Future value of $69,124.00, invested at 2% for 7 years would be approximately* $79,402.74
Note: (FVIF(r,n)) of (1.02)7 was estimated to four decimal places, from 1.148685 to 1.1487.
d. Values:
FV = to be determined
PV = 39,929
R = .009
T = 10

$39,929 if invested for ten years with a 0.9% interest rate
FV = PV * (1 + r)t
FV = 39,929 * (1 + .009)10
FV = 39,929 * (1.009)10
FV = 39,929 * (1.0937)
FV = $43,670.35
The Future value of $39,929.00, invested at 0.9% for 10 years would be approximately* $43,670.35
Note: (FVIF(r,n)) of (1.009)10 was estimated to four decimal places, from 1.093733 to 1.0937.
Calculate the present value of the following:
a. $105,126 to be received three years from now with a 4% Interest rate
Values:
PV = to be determined
FV = 105,126
R = .04
T = 3

PV = FV / (1+r)t
PV = 105,126 / (1 + .04)3
PV = 105,126 / (1.04)3
PV = 105,126 / 1.1249
PV = $93,453.64

The Present value of $105,126.00, to be received in three years with a 4% interest rate would be approximately* $93,453.64
Note: (PVIF(r,n)) of (1.04)3 was estimated to four decimal places, from 1.124864 to 1.1249.

The other way that this equation could have been written would have been to convert the future value interest factor (FVIF(r,n)) to a multiplication equation (Finance Professor.com, 2011); resulting in the following:

Note: six decimal places, rounded to the nearest ten thousandth are utilized here for (FVIF(r,n,)).

PV = FV * 1 / (1+r)t
PV = 105,126 * 1 / (1 + .04)3
PV = 105,126 * 1 / (1.04)3
PV = 105,126 * 1 / 1.1249
PV = 105,126 * .888968
PV = $93,453.64

b. Values:
PV = to be determined
FV = 228,231
R = .05
T = 5

$228,231 to be received five years from now with a 5% interest rate
PV = FV / (1+r)t
PV = 228,231 / (1 + .05)5
PV = 228,231 / (1.05)5
PV = 228,231 / 1.2763
PV = $178,822.38

The Present value of $228,231, to be received in five years with a 5% interest rate would be approximately* $178,822.38
Note: (PVIF(r,n)) of (1.05)5 was estimated to four decimal places, from 1.276281 to 1.2763.

c. $192,000 to be received two years from now with a 12% interest rate
Values:
PV = to be determined
FV = 228,231
R = .12
T = 2

PV = FV / (1+r)t
PV = 192,000 / (1 + .12)2
PV = 192,000 / (1.12)2
PV = 192,000 / 1.2544
PV = $153,061.22

The Present value of $192,000, to be received in two years with a 12% interest rate would be approximately* $153,061.22
Note: (PVIF(r,n)) of (1.12)2 = 1.2544; no estimation from six decimal places to four was required.

d. Values:
PV = to be determined
FV = 998,111
R = .01
T = 8

$998,111 to be received eight years from now with a 1% interest rate
PV = FV / (1+r)t
PV = 998,111 / (1 + .01)8
PV = 998,111 / (1.01)8
PV = 998,111 / 1.0828
PV = $921,787.03

The Present value of $998,111.00, to be received in eight years with a 1% interest rate would be approximately* $921,787.03
Note: (PVIF(r,n)) of (1.01)8 was estimated to four decimal places, from 1.082856 to 1.0828.

Calculate the following:
1) Suppose you are to receive a stream of annual payments (also called an “annuity”) of $72,394 every year for three years starting this year. The interest rate is 4%. What is the present value of these three payments
Although not specifically instructed, let??™s solve both for present value of this annuity and for present value of the three payments. This will be accomplished in two parts with the following:

Part 1) PV = CF * 1/(1 + r)t where we will determine the present value of each individual cash flow (and then add them to equal Part 2??™s computation).
Part 2) PV = PVAF(r,n) * CF to determine the annuity??™s value at maturity (which will show that our computations are sound).

Part 1) Let??™s solve for present value of each cash flow (highlighted in yellow below):
Values:
CF = 72,394
r = .04
n = 3

PV = [CF * 1/(1+r)t] + [CF * 1/(1+r)t] + [CF * 1/(1+r)t]
PV = [72394 * 1/(1.04)1] + [72394 * 1/(1.04)2] + [72394 * 1/(1.04)3]
PV = [72394 * 1/(1.04)] + [72394 * 1/(1.0816)] + [72394 * 1/(1.1249)]
PV = [72394 * .9615] + [72394 * .9246] + [72394 * .8889]
PV = $69,606.83 + $66,935.49 + $ 64,351.03
PV = $200,893.35

Part 2) Let??™s solve for present value interest factor PVAF(r,n) with:
PVAF(r,n) = 1/r ??“ 1/r(1+r)t
Plugging this value into our initial equation, we solve for present value of these three payments at the end of term and find that our computations are indeed sound.

PV = PVAF(r,n) * CF

PV = 2.775 * 72394

PV = $200,893.35

PVAF(r,n) = 1 – 1
.04 .04(1 + .04)3

PVAF(r,n) = 25 – 1
.04(1.04)3

PVAF(r,n) = 25 – 1
.04(1.1249)

PVAF(r,n) = 25 – 1
.044996

PVAF(r,n) = 25 – 22.2242

PVAF(r,n) = 2.7758

2) Suppose you are to receive a payment of $189,299 every year for three years. You are depositing these payments in a bank account that pays 2% interest. Given these three payments and this interest rate, how much will be in your bank account in three years
Values:
PV = 189,299
r = .02
n = 3

We??™ll solve for present value of this annuity with the following:
PV = PVAF(r,n) * CF

We??™ll start by solving for the present value interest factor for
PVAF(r,n). This can be solved with the following equation:

Plugging this value into our initial equation, we solve for present value in the account after three years:

PV = PVAF(r,n) * CF

PV = 2.875 * 189,299

PV = $544,234.63

PVAF(r,n) = 1/r ??“ 1/r(1+r)t

PVAF(r,n) = 1 – 1
.02 .02(1 + .02)3

PVAF(r,n) = 50 – 1
.02(1.02)3

PVAF(r,n) = 50 – 1
.02(1.061)

PVAF(r,n) = 50 – 1
.02122

PVAF(r,n) = 50 – 47.125

PVAF(r,n) = 2.875

/.02 – 1/.02(1+.02)3

Conclusion
In the Module 2 Case Assignment, we were to demonstrate the ability to: ???Make basic calculations concerning present and future value??? as well as ???Understand and discuss the concepts of present and future value. This was to be accomplished, specifically, through the case assignment by discussing the relevance of the time value of money to corporate finance, and by providing financial computations of both present and future value.

So what have we learned during this case assignment Sure, we??™ve established that TVM is essential to corporate finance, and demonstrated an ability to solve for present and future value; but what does TVM really mean for me What??™s the big deal Is there truly a necessity to understand this concept Isn??™t it enough to know that you can simply rely upon the experience of others, like those in corporate finance (i.e.: bankers, financial advisors, tax attorneys, estate planners, etc??¦) who have to know this sort of thing in order to make a living We just spent a couple of paragraphs establishing why it??™s important for them to know it; so why not just rely upon their expertise Haven??™t we always gone to these folks before Besides, in a busy world, who has the ???time??? to learn about the ???value of money??? anyway Isn??™t my paycheck spent before I ever get it Why would I bother learning about the value of investments when, again, I either don??™t have the money for them, or, if I did, could just hire someone to do it for me

These are fairly typical questions that people may ask; particularly those who may not understand the TVM principle. For example, for some people, especially in the tech age, buying a home is sometimes reduced to inputting numbers on a mortgage calculator ??“ typically found through Google or similar ??“ and figuring out if they can afford the monthly payments. There isn??™t an understanding (or appreciation) of the historical or long term value of the investment; let alone how the calculator arrived at the result (Le, 2003). In the stock market, purchasing securities is considered too ???risky???; after all, one has to ???have money to make money???, right Or as even I stated in my Module 2 SLP, one should only ???invest the money that he can afford to lose???. Risk is not understood, so it is avoided altogether (Reybern, 2010).
Unwittingly, these are a few, of many behaviors, that expose the core problem that a good number of people face when making financial decisions: chiefly, that they don??™t see any ???value??? for them in understanding the time value of money. ???So what if it??™s important to corporate finance??¦what does that have to do with me??? Regardless of learning simple computations, they don??™t see the logic behind TVM either; therefore, they might be apathetic towards it.

The reality is that having the ability to determine risk and maximize return ahead of time, on an investment, saves the time that would have been otherwise wasted later on trying to rescue that investment. It??™s actually a simple concept to understand: it would be counterintuitive to invest in a financial instrument and then spend all of one??™s time monitoring that instrument; as, naturally, that would detract from one??™s ability to investigate an alternative investment that might add further value to his/her overall financial position. And that??™s ???the point???, as it were: bringing us full circle to where this paper started with the notion that a proper understanding of TVM provides one more of an ability to add value to his/her organization (even if that ???organization??? is their own personal finances). Having a thorough understanding of TVM, and also the opportunity to use it allows individuals to add value to their ???bottom lines???, much the same as those in corporate finance do. Module 2 does a very good job of demonstrating that there is a basic necessity (if not responsibility!) to understand how to make one??™s money increase in value over time. It??™s not enough to simply rely upon the knowledge of others; the reality is that we??™re just as able to maximize our own value through the TVM principle.

References
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