How Can Net Present Value Analysis Help Contractors Make Sound Investment Decisions

A dollar today is worth more than a dollar tomorrow; it is a statement that is often brought up by financial professionals engrossed in conversations on the concept of time value of money. The generality of the statement has thrown many unaccustomed to finance for a loop. In fact, it is as simple as it sounds. It is based on the idea that money received today is more valuable than the same amount of money in the future as it has the potential to be invested and generate interest over time.

Suppose that you have borrowed a friend $2000, and you have just received a call from him asking if you would prefer getting the $2000 back today or next week. Of course, the most rational choice will be today as you can invest the $2000 immediately, and it will have grown in value by next week. To spice the scenario up, what if he is offering to pay you back either the full amount today or the full amount in 3 years plus an additional $200 per year? – here is a little food for thought for you, but we will come back to this later.

Essentially, as a contractor, you will want to make sure that you get the most out of every dollar you have spent. In the past, you may have encountered a situation where you had multiple projects on the table, and you, having limited resources, leaped at the opportunity to choose one that just seemed better than the rest. However, how could you have justified that the one you had decided to proceed with was definitely the best investment option? Without having conducted proper analysis on the project, which would provide a numerical justification of some sort, you may have chosen a less-profitable one.

What is The Concept of the Time Value of Money?

One of the fundamental tenets of investing is that getting a dollar today is better than getting the same sum tomorrow. To explain this, let us go back to the scenario where you have been given two payback options by your friend to whom you borrowed $2000: getting the $2000 back today or allowing him to pay you back in 3 years plus an additional $200 per year.

Let us say that the bank offers you 15% interest annually on a compound interest basis, and if you choose the first payback option and put the $2000 in the bank today, the sum of money that you will get in 3 years is calculated as follows:

$2000(1+0.15)^3=$3041.75

On the other hand, choosing the second option will give you $200 in the first year, $200 in the second year, and $2200 in the third year. At first glance, the second option seems better as you can get a fraction of your money back and reinvest it every year by putting it in the bank until the third year. However, let us find out if this is really the case by mathematically analyzing this further on the assumption that the annually-compounded interest rate on your savings account will stay the same in the second and third years.

$2200+$200(1+0.15)^2+$200(1+0.15)^1=$2694.50

The first option will get you a sum of $3041.75 in the third year, whereas the second option will generate a return of $2694.50 in the same year. if we hadn’t done all the calculations, you would probably choose the second option – indeed, things aren’t always what they seem.

Perhaps, let us not lose touch with reality and accept the fact that things sometimes don’t go as planned. What if your friend has retracted his offer to pay you back the $2000 today, leaving you with only the second option? And, with the second option, can you get the same amount of return as you would if your friend hadn’t changed his mind?

Let us set up a system of equations containing x and y below, assuming that the sum of x and y cannot be more than 1:

$2200+$200(1+x)^2+$200(1+y)^1=$3041.75…………………..(1)

x+y=1…………………….(2)

By using algebra, we can arrange the second equation for y and substitute the arranged equation into the first equation:

y=1-x…………………….(3)

$2200+$200(1+x)^2+$200(1+(1-x))^1=$3041.75…………………….(4)

Again, algebraically, we can simplify the fourth equation and solve for x:

x^2+x+14=15.2075………………(5)

x=0.70726………………(6)

There are actually two solutions to the fifth equation, but the other solution has purposely been ignored as it is a negative value. Lastly, to find the value for y, we plug the value that we have found for x into the third equation:

y=1-0.70726=0.29274………………(7)

The above calculations tell us that one of the ways for the second option to generate a return of around $3041.75 is to re-invest the $200 collected in the first year in something that yields an annual interest rate of 71% on a compound interest basis for two years. On top of that, the $200 collected in the second year must also be re-invested in an investment with an annual interest rate of 30% for one year. In reality, investments with such high-interest rates tend to be very risky.

Now that you’ve got a basic grasp on the concept of the time value of money, we shall delve into how you can analyze different projects using the principle of the time value of money and cherry-pick one that will yield the most favorable return.

Net Present Value Analysis

Net present value (NPV) analysis is a method of investment appraisal. It discounts all the future cash flows expected to be generated by a project to their present values at a predetermined rate while also considering the sum of the initial capital investment to be injected into the project. It is typically used in capital budgeting and investment planning to establish which projects have the greatest probability of generating the largest profits.

The formula for NPV may seem intimidating – don’t let it scare you off; I will provide a simple explanation later, and it is as follows:

NPV=Σ(Rt/(1+i)^t)

Where:  Rt=net cash flow during a single period t

i=discount rate or expected rate of return

t=number of time periods

If you are unfamiliar with the weird-looking symbol, Σ, in the formula, a simpler way of understanding the concept of NPV is that the NPV for a project equals to today’s value of all the expected cash flows minus the amount of initially-invested cash. For instance, imagine another scenario where you have a project that requires an initial investment of $100000 and will generate four cash inflows of $20000, $30000, $40000, and $80000 over the next four years. Let us also assume that your expected rate of return is 10%. The NPV for the project is computed as follows:

NPV=-$100000/(1+0.10)^0+$20000/(1+0.10)^1+$30000/(1+0.10)^2+$40000/(1+0.10)^3+$80000/(1+0.10)^4=$127668.875

You have probably noticed that the calculations are very similar to the one we did before this. Instead of bringing a certain value to its future value, which is what we did when we analyzed the first scenario, it does the reverse by bringing an expected, future value to its present value. Now, you may be asking yourself, “what is the purpose of all this?”.

Looking at the calculations, we see that the NPV is a positive value. This means that instead of investing $127668.875 initially to get that particular kind of return, you will only need to make an initial capital investment of $100000. Because of this, the project actually yields a rate of return of more than 10%, but how can we find out what the actual rate of return is? You will need to dust off your maths skills for what is about to come.

To start off, we shall set the previous NPV equation to zero and let the discount rate be the unknown variable that we are trying to find:

0=-$100000+$20000/(1+x)^1+$30000/(1+x)^2+$40000/(1+x)^3+$80000/(1+x)^4………….(1)

Algebraically, we can simplify the equation:

0=x^4+(19x^3)/5+(51x^2)/10+12x/5-7/10………….(2)

Again, we should simplify the equation further to get rid of the fractions:

0=10x^4+38x^3+51x^2+24x-7………….(3)

Now, to actually solve for x, it is easier to just use a calculus-based technique known as the Newton-Raphson method. To begin, we differentiate the equation:

y(x)=10x^4+38x^3+51x^2+24x-7………….(4)

y'(x)=40x^3+114x^2+102x+24………….(5)

By looking at the graph of the fourth equation, we know that the positive value of x that makes the equation equal to zero is somewhere between 0.19 and 0.20, and to find out the value, we use the Newton-Raphson formula:

X=x-(10x^4+38x^3+51x^2+24x-7)/(40x^3+114x^2+102x+24)………….(6)

We now try to plug in 0.20 and the resulting value into the sixth equation:

=0.20-(10(0.20)^4+38(0.20)^3+51(0.20)^2+24(0.20)-7)/(40(0.20)^3+114(0.20)^2+102(0.20)+24)=0.19675………….(7)

=0.19675-(10(0.19675)^4+38(0.19675)^3+51(0.19675)^2+24(0.19675)-7)/(40(0.19675)^3+ 114(0.19675)^2+102(0.19675)+24)=0.19673………….(8)

Looking at the calculations, we can conclude that the solution for x is around 0.19673. Let us plug the value into the first equation to verify this:

-$100000+$20000/(1+0.19673)^1+$30000/(1+0.19673)^2+$40000/(1+0.19673)^3+$80000/(1+0.19673)^4=1.62064……………(9)

With 0.19673, the equation yields an answer that is very close to zero. Therefore, the actual rate of return is somewhere around 19.673%, which is more than your expected rate of return of 10%. In reality, if you come across a project that is similar to this hypothetical one in terms of its NPV and rate of return, you should consider adding it to your project portfolio.

Contact Leopard Project Controls for your next CPM Scheduling Project.

With the knowledge of how the value of money changes over time and the skills to make relevant computations, you will be in a better position to make sound investment decisions. Net present value analysis is just one of the many investment appraisal techniques that utilize the concept of the time value of money to evaluate a project’s long-term financial performance. If you are still struggling to decipher the concept, the Internet is a pool of resources, which can help increase your knowledge on this topic.