Net Present Value: This is how you determine your in­vest­ment’s net present value

A good in­vest­ment is any in­vest­ment that yields returns. An in­vest­ment’s prof­itabil­i­ty is de­ter­mined by the expected profit’s re­la­tion­ship to the original invested amount. But how can future cash flows be assessed from the vantage point of the present?

In this context, the finance industry uses the term “time value of money” (TVM). What this means is that a deposit made today is more valuable than a future deposit of the same amount. The reason for this is that money that you have today can be invested in the capital market at a profit.

Let’s say you allocate 10,000 dollars for two years and then receive the full amount back. In this case you’d suffer a loss, and at that, one amounting to the interest earned on a two-year in­vest­ment. In this context, this is referred to as “op­por­tu­ni­ty costs”. You should also consider these when planning in­vest­ments. One way to do this would be to calculate the net present value.

The present value of future payments is de­ter­mined through dis­count­ing. This allows to you reduce the amount by the interest income that an al­ter­na­tive in­vest­ment in the same amount would generate over the re­spec­tive period.

We’ll demon­strate the cal­cu­la­tion step by step using a practical example.

The net present value (NPV) is an indicator for dynamic in­vest­ment cal­cu­la­tion. Investors use the NPV to determine the value of future deposits and payouts at the present time. In this way funds from different cal­cu­la­tion periods for com­pa­ra­ble and different in­vest­ment op­por­tu­ni­ties can be weighed against each other with respect to their prof­itabil­i­ty.

Net present values are de­ter­mined and assessed within the framework of the net present value method.

The meaning of the listed operands can be found in the following table.

Sometimes you’ll find an al­ter­na­tive notation in relevant lit­er­a­ture on the subject:

Both formulas produce the same result.

The method for cal­cu­lat­ing the net present value using the given formula looks very complex at first glance, however, it can be broken down into seven simple substeps.

In order to determine an in­vest­ment’s net present value, you need to proceed as follows:

1. Determine the in­vest­ment amount.
2. Determine the in­vest­ment period.
3. Calculate the cash flows for the re­spec­tive time intervals.
4. Establish the discount interest rate.
5. Determine the residual value of your in­vest­ment.
6. Determine the net present value of each in­vest­ment interval.
7. Determine the net present value of your in­vest­ment.

We’ll demon­strate the cal­cu­la­tion for you using an example.

Let’s say you’re operating a carpenter’s workshop and plan to invest in a new ex­trac­tion system that includes a bri­quet­ting press. The idea: The new machine will collect wood dust and chips, and press them into space-saving bri­quettes which can then be sold prof­itably. However, the cor­re­spond­ing equipment is expensive. To be able to estimate whether the in­vest­ment is worth­while, you’ll need to calculate its net present value.

For our cal­cu­la­tion example, we assume that a clean-air ex­trac­tion system with a bri­quet­ting press in the required size costs about 26,000 dollars. In addition, there are costs of 3,000 dollars for the in­stal­la­tion of the system and 1,000 dollars for in­struct­ing employees on how to use the new machine. The entire sum of the in­vest­ment thus amounts to 30,000 dollars, which are due at the beginning of the in­vest­ment period.

The net present value is de­ter­mined within the framework of a dynamic in­vest­ment cal­cu­la­tion method. Here you determine the in­vest­ment period (n) in time intervals (t) for which you determine and discount separate cash flows. The net present value thus takes into con­sid­er­a­tion both fluc­tu­a­tions in the deposits and payouts that result from the in­vest­ment, and those de­vel­op­ments in the capital market that effect the rate applied to the cash flow dis­count­ing.

To begin with, estimate the period for the planned in­vest­ment. This is the time span over which an in­vest­ment generates deposits and payouts. An in­vest­ment period is usually measured in years. In the case of dis­count­ing, it thus occurs at intervals of once per year.

In terms of our example, the man­u­fac­tur­er of the ex­trac­tion system states that the service life of the system is 20 years. However, we plan to replace the machine after 4 years with a more modern model and resell the old system at the highest possible price. Therefore, we assume an in­vest­ment period of four years (n = 4). This cor­re­sponds to four time intervals of one year, for which separate cash flows must each be de­ter­mined and dis­count­ed.

For our in­vest­ment example, we calculate the cash flows for four years while taking into account all expected deposits and payouts.

A whole­saler of green fuels offers to purchase the bri­quettes. Each year generates deposits of 10,000 dollars. However, use of the ex­trac­tion system also entails elec­tric­i­ty and main­te­nance costs. According to the man­u­fac­tur­er, these amount to 4,000 dollars per year. In addition, costs of 2,000 dollars are incurred every two years due to the re­place­ment of worn-down parts.

This results in the following cash flows for the in­vest­ment period’s four time intervals.

The residual value is only to be de­ter­mined when necessary. This is because not every in­vest­ment is connected with a liq­ui­da­tion process. Training, for example, con­sti­tutes an in­vest­ment in employee qual­i­fi­ca­tions that yields no residual value.

In our cal­cu­la­tion example, on the other hand, we assume that the clean-air ex­trac­tion system with the bri­quet­ting press can be sold for half of the new price after four years. The residual value thus amounts to 13,000 dollars.

Cash flows are dis­count­ed during the in­vest­ment period using a rate specif­i­cal­ly es­tab­lished for this purpose. This is the main operand for cal­cu­lat­ing net present value.

De­ter­min­ing how high of a discount interest rate should be applied involves taking into account the op­por­tu­ni­ty cost principle and deriving the best al­ter­na­tive in­vest­ment op­por­tu­ni­ty from the interest rate. You also take inflation into con­sid­er­a­tion.

In contrast to static methods for cal­cu­lat­ing in­vest­ments, the net present value method also takes into account the term structure of interest rates and compound interest. As needed, a different discount interest rate can be applied in each time interval.

In our example, we assume that you have the option to invest the in­vest­ment sum (30,000 dollars) risk-free on the capital market at an interest rate of 0.2 percent. This is why we use this interest rate as a discount rate.

In our example, we obtain a net present value of 1086.33 dollars. But how should this result be assessed?

If the sum of all present values (also called “earning value“(EV₀) is higher than the in­vest­ment sum, the result is a positive net present value (as in the example given above).

A positive net present value (NPV₀ > 0) –1086.33 dollars, for example – shows that the planned in­vest­ment generates more profit than a bank deposit at the chosen discount interest rate. Such an in­vest­ment is eco­nom­i­cal­ly sensible.

If, on the other hand, you receive a negative present current value (NPV₀ < 0), the in­vest­ment is likely to be a loss and you should not make it.

If the net present value amounts to exactly zero, your in­vest­ment will only generate the discount interest but beyond that no further profit, and thus offers no advantage - from a purely financial per­spec­tive - when compared with putting the money in a risk-free savings account.

The net present value makes it possible to assess a single in­vest­ment or to compare several in­vest­ment op­por­tu­ni­ties. If you compare the prof­itabil­i­ty of different in­vest­ments, the most eco­nom­i­cal­ly ad­van­ta­geous is the one for which you have de­ter­mined the highest net present value.

When cal­cu­lat­ing the NPV according to the method given above, all time intervals for the in­vest­ment period are con­sid­ered in­de­pen­dent­ly. The NPV method thus counts among the dynamic methods for ac­count­ing. Compared to static methods, this offers the advantage of modeling more complex cir­cum­stances, for example, different cash flows in the time intervals or a change in the discount interest rate.

The present net value enjoys great pop­u­lar­i­ty, above all due to the rel­a­tive­ly simple cal­cu­la­tion method. The indicator is un­am­bigu­ous and leaves no room for in­ter­pre­ta­tion. However, critics question the net present value’s validity.

The net present value method is prob­lem­at­ic mainly because of the following issues:

• The cal­cu­la­tion of the net present value assumes a perfect capital market.
• In several respects, the cal­cu­la­tion is based on sub­jec­tive pre­sup­po­si­tions which have a sig­nif­i­cant effect on the amount of the net present value.

The net capital value method assumes a highly sim­pli­fied capital market – among other things, the equal­iza­tion of debit and credit interest. Tax reg­u­la­tions are not con­sid­ered either. In practice, these pre­con­di­tions do not exist. As a con­se­quence, it is an indicator that cannot be readily trans­ferred to real cir­cum­stances.

In addition, there’s the risk that en­tre­pre­neurs will try to make those un­prof­itable in­vest­ments based on false pre­sup­po­si­tions look better. Both the discount interest and the cash flow amount are based on pro­jec­tions and are more or less de­ter­mined ar­bi­trar­i­ly if there is in­suf­fi­cient data. All pre­sup­po­si­tions of the net present value cal­cu­la­tion should therefore be commented on and suf­fi­cient­ly sub­stan­ti­at­ed by (as examples) specific bank offers, industry data or business figures from previous years.

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