As financial advisors we are well aware that the value of money changes with time. It lies at the heart of any financial planning. There are many reasons or sources of change in the value of money. Understanding these sources of change as well as possessing the skill to calculate the time value of money is a must for every financial advisor. In this piece, we introduce our NJ Partners to these basic skills.
Primary Sources of Change:
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Cash flows: The primary source of change in an amount over time would obviously include the cash flow changes like additions or withdrawals from investments. These cash flows can be one time or recurring in nature like SIPs or SWPs.
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Returns:
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Simple Interest: Simple interest is a form of returns where a fixed amount of interest is earned only on the initial investment amount over time. The calculations for simple interest differs with compounding as we will know later.
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Compounding: Compounding returns is where your growth on investment is on the total amount at the beginning of the period. The total amount would consist both of your beginning period investment plus your growth on that investment. Thus it is like earning interest on interest. Over time, the power of compounding greatly affects any investment value.
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Real Value:
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Inflation: The factor of inflation has the power of reducing the underlying value of money over time. While it does not affect the absolute money calculations, adjusting for the inflation factor in our calculations will give us 'real' value of money. This is most important for planning for future goals.
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Deflation: Deflation on the other hand is literally the opposite of inflation or just negative inflation. It would mean that the value of any particular asset/object decreases with time. It has effect similar to discounting in calculations.
Calculations for TVM:
Excel (and other spreadsheet programs) is the greatest financial calculator which we can use. Excel can be effectively used for calculating results to any financial problems. They also have certain excel functions (built-in formulas) that help us in easily in our calculations. Every financial advisor should be familiar with few financial formulas and key excel functions as they are very commonly used while planning for investments. This piece, the first part of a series, will demonstrate these important formulas and financial functions to handle basic problems encountered in our profession. We will keep the examples simple and will assume that you are already familiar with a bit of excel.
The Basics:
Before making any calculations we must ensure that there are matching figure for rate and amount and they are as per corresponding period of measurement. For eg. if calculations are on a yearly basis, the rates and the amount should also be on a yearly basis. A common problem encountered here is the “effective rate” for a period since normally we have values which may not be suitable for the period under consideration. Getting this standard right is very important for getting accurate results.
Problem 1: Find actual periodic rate when only effective annual rate is given.
Formula: = (1+r) ^(1/n) – 1; where r = effective annual rate and n = number of periods in a year.
Example: If the annual returns are 15% then what is the effective monthly rate?
Result = (1+.15)^(1/12)-1 = 1.171%. Note that being compounded, it is less than 15% / 12 = 1.25% which would be result if there was no compounding involved.
Note: Most monthly SIP calculators available online give wrong answers ignoring is simple difference. They assume monthly returns as /12 which would obviously give higher effective returns annually.
Problem 2: Find Effective Annual Rate when only actual periodic rate is given.
Formula: = (1+r) ^(n) – 1; where r = periodic rate and n = number of periods in a year.
Example: If the effective monthly rate is 1.25% then what is the effective annual rate?
Result = (1+1.25%)^12-1 = 16.08%. Note that being compounded, it is more than 1.25% * 12 = 15%.
Problem 3: Find Effective Annual Rate when a nominal annual rate for periodic periods are mentioned.
Formula = (1+r) ^(n) – 1; where r = annual rate / n and n = number of periods in a year
Example: If the annual nominal interest rate is 10% and four interest calculation periods are defined, what is the actual interest rate (effective rate) annually?
Result = n is 4 and r is 10% /4 = 2.5%. (1+2.5%)^(4)-1 = 10.38% which is the effective annual rate. To find the monthly effective rate from 10.38, we can then use the solution given in Problem 1 which will give result as 2.5%.
Excel = EFFECTIVE (Nom,P) = where Nom is the nominal annual rate and P is the number of interest payment periods in a year.
The above case can be used when choosing between different investments which carry a different interest rates which are compounded at different frequencies.
Basic Excel Function Terms:
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FV = Future value remaining after the final installment has been made.
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PV = Present value that a series of future payments is worth right now.
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Rate = Defines the interest rate per period.
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NPer = Total number of periods (payment period).
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Pmt = Regular payment made per period.
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Type = Denotes due date for payments. Type = 1 means due at the beginning of a period and Type = 0 (default) means due at the end of the period. In calculations, we can consider beginning period or type=1 assuming that our plans will take effect immediately.
Note that the usual problem in all time value related problems are related to any one missing term/value from FV, PV, Rate, NPer or Pmt where other terms/values are known.
The FV calculations (lumpsum)
Problem 1: The present cost of a holiday package is Rs.5 Lacs. What will be it's cost after 3 years?
Problem 2: I have Rs.10 Lac that I wish to invest in an equity fund. What will be it's value after 5 years?
Formula: FV = PV * (1+r) ^ n where FV & PV is the future and present value; r is the rate of inflation or returns and n is the period. As financial advisors, we encounter these questions very often and we often have to assume the rate of inflation and returns while forecasting.
Result 1: n = 3 years and r = assumed inflation of 10%. = 5,00,000 * (1+10%)^3 = 6,65,500.
Excel Function: FV(rate,nper,pmt,pv,type). = FV(10%,3,0,-500000,1) = 6,65,500
Result 2: n = 5 years and r = assumed conservative returns of 12%. = 10,00,000 * (1+12%)^5 = 17,62,342.
Excel Function: FV(rate,nper,pmt,pv,type). = FV(12%,5,0,-1000000,1)
Note: In excel function, we use FV and PV values for lumpsum amounts and pmt for annuity calculations. Further, we use negative (-) sign in above examples to denote a cash outflow /outlay.
The above FV function can be used for many other calculations and is a very handy function for financial advisors. We also introduced you to the formula behind this function which we had learnt in our school. There are many more formulas and functions which we will introduce you to in later articles. Till then, keep practicing.
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