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May 16th, 2014, 06:14 PM   #1
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Finding NPV - net present value of a complex investment

Net present value calculations require a lot more input than just the series of cash flows and the discount rate. An NPV is simply the sum of discounted cash flows but then there are many variables that come into play when finding net present value.

At first, one would have to define the length of the payment periods as payments may occur at varying time periods. For example, a business entity may have an accounts receivable for payments from different customers. For each of such transactions, the annuity amount may be required at different time. Payments from one customer may come in on monthly basis whereas payments from another customer may come in on weekly basis and similarly payments from various customers may be on the order of a daily, weekly, fortnightly, monthly, quarterly, half-yearly, yearly, bi-yearly, tri-yearly and so on. Similarly the accounts payable accounts of the business may be paid on similar payment frequencies.

Interest due or paid on business loans and savings may be compounded using various compounding frequencies of interest. Some accounts may require annual interest payments whereas others may require daily, weekly, fortnightly, monthly, quarterly, semi-annually, annually, bi-annually, tri-annually or even infinite or continuous compounding frequency of interest.

There may be a single interest rate paid or due on such transactions or there may be a schedule of interest rates such as those used for ARM - adjusted rate mortgages or interest rate shocks on bonds issued by government and businesses that adversely affect the market value of such debt. Thus a 30 year US Treasury bond issued at 4% at present may go through a series of term structures over its horizon of thirty years. Investors would demand higher yields on risky bonds such as those issued by economically stressed countries such as Greece, Spain, Ireland and Portugal. And just the hint of a default on sovereign debt of these countries would trigger a sudden rise in its interest rate driving down the market value of such bonds. Thus a bond analyst or a fixed income investor would want to find the net present value of their portfolio of bonds using a term structure of interest rates.

Yet expected payments due at future dates are likely to devalue due to inflation in prices of goods and commodities. Thus in finding net present value of such payments one would have to address the inflating money amounts that are expected at future dates.

A small grocery store on the corner of your street would only be earning and paying in local currency, however the fund managers at large investment banks and the online retailers and businesses accept payments from customers that are scattered throughout the globe thus the genie of globalization may have eradicated poverty in Bangalore, India's silicon valley, yet it left the aspiring American programmer out of work who is going through mid-life crisis and a mid-wife crisis. This would require the investor to apply the current exchange rate for the payment received or made in a foreign currency when finding the net present value in terms of the local currency.

But Uncle Sammy Davis Jr. wants a cut on every investment you make to pay for the expenses of those who are seen by some as burden on society be it in US or in Western Europe that has a large population of residents from their old colonies who insist on staying permanently even though the locals were told that they were there to stay temporarily. Thus finding net present value of your investment would have to ensure that money amounts used in calculations are adjusted for taxation.

As for the cash flow patterns one considers a series of periodic payments to be an annuity where ordinary annuity refers to end of period payments and annuity due refers to start of period payments. However it may be that one or more such payments are annuities in their own right. For example, a business may be obliged to make 12 monthly payments in uniform amounts followed by 52 weekly payments in constant amount and similarly other periodic payments for a given frequency of time period. This would require us to have the options where the net present value payments take single amounts and turn them into annuity payments for a given time period. This would the frequency of an annuity payment and all such payments would then become annuities of their own making it more manageable when finding the net present value.

In academia, the professors make use of simple net present value calculations by selecting a handful of cash flows and the discount rate applying the full year discounting convention. Whereas US government funded projects and those undertaken by investors make us of mid-year discounting convention. This would want us to have the ability to select from a arbitrary set of discounting conventions such as 1st Qtr, mid-year, 3rd Qtr, full-year, biennial, triennial and so on.

Now back to the recent past when the bond investors holding the Greek sovereign debt had to take a hair-cut on their investment when Greek economy came to its knees and had to be rescued by the ECB, IMF and the EuroGroup. The investors were left with only pennies out the Euro they purchased. Similarly in the United States where the municipality of City of Detroit filed for bankruptcy once it was unable to pay the charge of its interest rate swap on its debt. The filing of bankruptcy meant that those holding the stakes would have to endure losses on their investment only recovering a dime on a dollar. Such example would trigger a chill in the spinal chords of the investor who would want to adjust to expected hair-cuts on future earnings when finding the net present value of their investment.

Finally for those rouge traders who make a quick buck by rigging rates would want a way to forge the discount rate in finding net present value. Given that there would be a good number of such morally corrupt traders, you would have to built in options in your math to address the role of rigged rates when valuing investments.

Now that the introduction is complete, let me present the numbers for finding net present value that include all of the options explained thus far

What follows is a 13 x N matrix of data of an investment that included the schedule of discount rate, inflation, exchange rates, tax rates, cash flows, frequencies of annuity payments, compounding frequencies of interest, lengths of payment periods, the discounting convention of choice, a series of expected hair-curs and the rigged rates.

The task is to find the net present value, but how you ask.

At first the answer, the net present value of this investment is $6,883.43

It was calculated using a user defined Excel NPV function found using the latest version of tadXL v3.0 add-in

It may be downloaded for use by here at this link

http://finance.thinkanddone.com/32_b....0_en_demo.zip

v3.0 is under development so you will only find one financial function in it called tadNPV

To use all of the 100+ financial functions in older tadXL v2.5, follow this link. Note however that the functions in older version of tadXL only accept a single array of values unlike the matrix of data that is allowed in v3.0

http://finance.thinkanddone.com/32_b....5_en_demo.zip

Here is the schedule of data for our investment.

Code:
Rates			        8%	7%	6%	5%	4%	     3%	2%	   1%
Growth			1%	2%	3%	4%	5%	     6%	7%	   8%
Exchange_Rates		1	1	1	1	1	     1	        1	   1
Tax_Rates		        30%	31%	32%	33%	34%	     35%	36%	    37%
Cash_Flows		       ($100)	$200	$300	($50)	$400	     $500	$600	   $700
Adjust_for_inflation	0	0	0	0	0	     0	         0	   0
Frequencies		       10	365	24	365	INF	     260	INF	   5,200
Types			       1	1	1	1	1	     1	        1	   1
Compoundings		=1/4	=1/365 =1/12	=1/365    1	        =1/26	   1	=1/52
Periods			=1/4	=1/365 =1/12	=1/365    1	        =1/26	   1	=1/52
Concentrations		1	0.5	2	10	1	      0.5	1	  0.75
Hair_Cuts		        0%	20%	20%	20%	0%	      20%	20%	  20%
Rate_Rigged_By		0%	15%	15%	15%	0%	      15%	15%	  15%
A complete set of net present value calculations using tadNPV function in tadXL v3.0 will be demonstrated in later posts that will show a variety of example calculations for various scenarios.
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