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UMUC TMAN625 Class Notes

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Week 2: Annual Analysis
Week 2: Annual Analysis
Tasks for the week:
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Read this content,
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Read chapter 3 sections 3.3 through 3.4, skim sections 3.3.5 & 3.3.6
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Read the article: Bankrate.com 7 Psychological Money Traps and How to Avoid Them ,10/16/2008. Retrieved on 1/27/2012 fromhttp://www.bankrate.com/finance/personal-finance/7-psychological-money-traps-and-how-to-avoid-them-1.aspx#1
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Participate in the Week 2 Conference
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Submit Assignment 2 in the Assignment/Gradebook area.Last week, the content was limited to translating between present values and future valuesusing time value of money (TVOM) equations. This week we expand this to include periodic paymentsplus the use of spreadsheet software functions to perform the calculations. This week’s, content (andsections 3.3 and 3.4 in the textbook) are limited to annual payments only. Next week we will expandthis to periods other than years. The primary purpose of this week’s content is to bridge between theTVOM concepts, equations and spreadsheet functions.Investments and loans are like two sides of a coin. One side is the borrower and the side is theloaner. All that changes is the direction of the flow of funds that is indicated by the signs of themonetary values. A loan received by a borrower is positive (in their pocket), but to the lender, it isnegative (out of their pocket). Payments made by the borrower are negative (out of their pocket), andto the lender receiving these they are positive (into their pocket). An investment requires funds to moveout of one’s pocket (negative) into the bank account, stock or other fund. When the results of theinvestment are received by the individual, they are positive.The basic terminology for Time Value of Money analysis is shown in the following table.
1. Planning Period or Time Horizon
Planning periods obviously have length. They can be years, decades, quarters, months, days,or any units that is reasonably equal in length. Months do not all contain the same number of days, butare considered “reasonably” equal. Quarters are normally defined as 13 weeks to make them equal inlength but 365 days does not divide equally into 4 periods (365/4 = 91.25 days). Excel does containthe capability to analyze unequal time periods but we will not be using this. Although planning periods have length, financial analysis most commonly focuses on the end of periods. Loans payments and investment deposits are typically done at the end of a period; say end of
Terms, Symbols and Acronyms
Initial value, upfront value, present value
P or PV
Final or future value
F or FV
Payment (disbursement or receipt)A or pmt
Interest rate
r or i or rate
Number of planning periodsn or nper
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month or end of year. There are special cases where is appropriate to consider the beginningof a period. For instance, if one is withdrawing funds from a college fund or the like, the funds wouldoften be withdrawn at the beginning of a period to pay tuition, meaning they would not earn interest inthat period.The end of a period is identical to the start of the next period. December 31
st
of one year (12:60or 23:60 in a 24 hour clock) is identical to January 1
st
at 0:00 of the following year. Sometimes it iseasier to restate beginning of year payments or withdrawals as the end of the previous year, or viceversa.Because time periods can start at any time, they are normally just stated as period 0, period 1,up to period n, which is the last period in a planning horizon. Annual periods can be defined as endingon December 31
st
, April 15, or any other date. Months can be considered as starting or ending on the1
st
. 10
th
, 16
th
or last day. Financial analysis ignores this and simply uses period numbers of 0,1,2,3,etc. The following illustrates this for a six period monthly situation. Financial analysis seldomconsiders the particular date, only the period numbers.The length of a financial analysis is referred to alternatively as the planning horizon, time span,project length or others. It is simply the number of periods. The above is considered as having 6periods even though with period 0, there are seven columns. The end of period convention makesperiod 0 to have zero length.With the above in mind, the following terms can be defined:“
Present
” as used in present period and present value or such terms as initial value, initialdeposit, and initial withdrawal is the end of period 0. If an upfront investment is needed, or loanreceived, it would be on this “present” date, which again is the end of period 0.“
Future
” as in future value, or sometimes ending value, is the last period of the planninghorizon. There will be situations where one wants the value at the end of year 10 in a 30 year planninghorizon (as in a 30 year mortgage). Year 10 is in the future and equations for FV can be used to findthe value in year 10, but this should be labeled as the Year 10 value or the future value in year 10,rather than simply the future value.“
Periodic Payments
”, which can be deposits or withdrawals, are made in period 1 through andincluding the last period n. A payment is not made in period 0 as that is considered the present value,initial deposit, or loan value and therefore is considered as separate. But Payments are made in thelast period, and any other deposit or withdrawal in the last period is in addition to the period n payment.This is shown above in period 6 where $100 is deposited and $250 is withdrawn and the net amountreceived in period 6 is $150. Also note that since the values are deposits that come out of one’spocket , they are entered as negative numbers. The withdrawal in year 6 that goes into one’s pocket ispositive.If you take out a loan on a home or car, on the closing date, which is the present (end of period0), you receive the loan (so it is positive), and the first payment (negative) is normally one period later,or the end of period 1. I once had a banker infer that they were doing me a favor by my not having tomake a payment for 30 days, but in fact, that is standard operating procedure in finance.Further note that interest paid or earned is calculated at the end of a period based on thebalance at the end of the previous period (same as start of the present period). In the above example,
Date
7/15/2012
8/15/2012
9/15/201210/15/201211/15/201212/15/2012
1/15/2013
Period
0
1
2
3
4
5
6
Disbursements
($500)
($100)
($100)
($100)
($100)
($100)
($100)
Receipts
$250
Cash Flow
($500)
($100)
($100)($100)($100)($100)
$150
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interest on the $500 would be paid/earned at the end of period 1. In period 6, interest would bepaid/earned on the balance at the end of period 5, and the payment and withdrawal in period 6 wouldnot be included in the interest calculations since they were not involved during the period 6, only at thelast instant.
2. Spreadsheet Functions: Present Value and Future Value
Last week the calculation of present and future values was performed using the TVOMequations FV= PV*(1+r)^n and PV=FV/(1+r)^n. Present and future vales can
also
be calculated usingthe spreadsheet functions named FV (Future Value) and PV (Present Value) and shown below in aspreadsheet format.
=FV(rate,nper,pmt,pv,type) where
rate is interest rate,
nper is number of periods (years, months, weeks, etc)
pmt is payment made per period (can be equal or unequal)
pv is the value at the end of period 0 (the present time)
type indicates end of period (0) or beginning of period (1) payments.
=PV(rate,nper,pmt,fv,type) where
rate is interest rate,
nper is number of periods (years, months, weeks, etc)
pmt is payment made per period (can be equal or unequal)
fv is the value at the end of period 6
type indicates end of period (0) or beginning of period (1) payments.
The following example shows how the examples from last week can be calculated using thespreadsheet functions and leads to three important points for functions.
If you have $500 and invest it at 4% for 6 years, the future value FV is:
FV = $500 x (1+4%)
6
= $632.66
FV= FV(4%,6,,500) = -$632.66
First note that since there are no payments in addition to the initial deposit (the PV) that thepayment argument is skipped by the two commas side-by-side. Essentially this says that the defaultvalue is zero.Second, only “end of period” payments will be considered this week, the type value in thespreadsheet function is zero. Since zero is the default value, this argument can be omitted as is donein the above and following examples. If payments were made at the beginning of periods, a Type = 1would be specified.Finally, note that the result of the function is negative. Functions include an indication of whichdirection that funds are flowing. A negative value indicates that funds are being paid out and is oftendescribed as “coming out of your pocket”. A positive value indicates that funds are received or “intoyour pocket”. So in this example, $500 goes into your pocket initially and at the end of year 6, the
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negative sign indicates that $632.66 “comes out of your pocket”.In contrast, if the function was entered as FV= FV(4%,6,,-500) = $632.66, the negative sign onthe 500 indicates that you paid $500 out of your pocket, and the positive value of $632.66 will go “intoyour pocket”.The PV function works similarly. Last week an example was:If you expect to have $10,000 in five years, and a rate of 4% is used, this would be valued at$8219.27 today.
PV = $10,000 / (1+4%)
5
= $8,219.27
Using the PV function, this would be:
PV = PV(4%,5,,10000) = -$8,219.27
The FV argument being a positive 10000 indicates that $10,000 will be received in 5 years, andthat to receive this, the negative amount of $8219.27 has to be paid out of your pocket today. This isan investment situation where you receive a future value in 5 years of $10,000 for an investment (paidout) today of $8,219.27.If this was alternatively entered with the signs reversed as PV = PV(4%,5,,-10000) = $8,219.27,the interpretation is a loan situation where you will pay out $10,000 out of your pocket in 5 years toreceive a loan of $8,219.27 today.This loans and investments use the same equations or function, but with functions the signs areused to indicate the direction in which funds flow. We will now look at the following categories of loans/investments in more detail.
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No periodic payments
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Equal periodic payments
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Unequal periodic payments
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Perpetuity: Interest only payments that can go on “forever”
3. No Periodic Payments
This first situation is for the same situation as above with no periodic payments, but will alsoinclude calculations for rates and number of periods.
3.1. Determining PV and FV
The first calculation below transforms a deposit (out of one’s pocket) in a fund of $100 to itsequivalent future value in five years or $127.63. As described above, the functions results in a signdifference that indicates whether the result is received or paid out.The second example starts with a future value five years hence of $100 and computes its valuetoday of $78.35.The last calculation, a check on the first FV calculation, starts with the future value of $127.63that was calculated in the first example and calculates the PV, which is $100.00 as it should be.
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