# Net present value in capital expenditure

## What is net present value?

Net present value (NPV) is the ‘today’ net value that deprives from ‘future’ cash flow of an investment or a capital purchase.

## Why does Net Present Value (NPV) matter?

Imagine you are buying car for personal use. Would you buy a fresh new car or an used car? Of course, fresh new car is often more expensive than the used one, but its life-time tends to be longer. For example, price for a new car is US$15,000 and the expected life-time is 10 years, while the used car is expected to last 7 years but it costs only US$6,500. Which option will be the most economic?

If you deploy a simple whole-life costing model, the decision seems clear: buying new car makes less negative cash flow over a life-time. However, there are some problems to this calculation:

- The calculation above only considers annual costs including tax, operation and maintenance. Mortgage and interest are not taken into account. Generally, people tend to finance expensive assets with mortgages from the bank. In the example above, since the new care is more expensive, the mortgage for it will be greater. So will the interest paid.
- The new and used car will be disposed at different moment. As you already know, the same amount of money (i.e. $100) has different purchasing power at different moment because of inflation/deflation. The calculation above does not take this factor into account.

Because of the above problems, one should calculate the future cash flow at ‘present’ value to compare different options.

## The formula of Net Present Value

The following formula is used to calculate NPV

Where:

Rt is the net cash flow (cash inflow – cash outflow) during the period t

i is the discount rate

t is the number of time periods

# The discount rate

As you can see from above formula, discount rate is an important part of calculating Net Present Value. The calculation of discount rate is not straight forward.

Discount rate in NPV is the rate of diminishing value of an investment/purchase. In other words, the discount rate is the speed in which an amount of money is losing its value.

There are different methods for calculating discount rate:

- Risk-free rate of return: The risk-free rate of return is the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. The real risk-free rate can be calculated by subtracting the current inflation rate from the interest rate that you receive from the investment. For example, you buy bonds from security market with 11% yield, the inflation in the year is 4.8%, so the risk-free rate of return is 11% – 4.8%=5.2%. Risk-free rate of return is commonly used when assessing an investment in bonds.
- Weighted average cost of capital (WACC): WACC is the calculation of an organisation’s cost of capitals in which all sources of capital (equity, shares, bonds, mortgages,…) are considered. Each capital category is assigned by an appropriate ‘weight’. This method is often used when assessing the profitability of a capital purchase. The formula for WACC is:

Where:

- E is the total equity
- Re is the cost of equity. Sometimes this factor is hard to be estimated. Cost of equity can be the opportunity cost that an individual/business may have missed because they invest in the assets. The opportunity can be the interest paid by deposit account in banks, or profits paid by a more lucrative investment. Cost of equity can also be the cost of acquiring the equity, i.e. the interest paid to shareholders to keep them make investment into the business.
- D is the total debt
- Rd is the cost of debt. This figure is more straightforward. It is, indeed, the interest charged by the banks when they issue loans; or the interest paid to bond investors when they buy bonds from a business
- V is the total asset (sum of equity and debt)
- Tc is the corporate tax charge

As you can see from this formula, WACC takes equity, loans and interest into account. This is the most comprehensive formula for the calculation of discount rate.

Now we go back to the car buying example above and apply the NPV & discount rate (WACC) formulae. Presume that I have $10,000 in my bank balance, which can be used to acquire an old car. If I wanted to buy a new one, I would need to finance my purchase by bank loans. I would not use all $10.000 to buy new car because I need to invest or spend somewhere else (i.e. buying foods, house rentals), so I would finance the new car with $6.000 from my account and $9.000 from bank loan.

Next, we need to identify the cost of debt and cost of equity. My favourite bank tells me that they will pay 6% per year for deposit account, while they charge 9% per year for car buying. I don’t need to pay any corporate tax. So the discount rate for each option will be as the following:

Now I insert these discount rate to my Excel worksheet, and compare between the two buying options

The cash flow in the two options is a bit different from the above table. Still, buying a new car is better option, but we have compare these two options on the same method.

In practice, you can use the function NPV in Excel to calculate the net cash flow in total life time of an asset. This tool will give you a scientific way to decision (or convince others on deciding) on buying fixed assets.

In the above scenario, I only use one static discount rate to simplify the calculation. Real world scenarios may be more complicated, which require several different discount rates.

## Disadvantages of Net Present Value

Net Present Value is a very helpful tool for decision on investment or capital purchase because it considers the value of money overtime, takes interest and inflations into account. It also requires simple tool (i.e. Microsoft Excel) to calculate

However, NPV has some inherent disadvantages that procurement professionals or investors should know

- First, NPV requires the knowledge on the assets so that the estimated cash flow in the future can be more ‘realistic’.
- Second, NPV was made based on an assumption that the predicted cash flow will be most likely to happen, there would be no variations to the scenario. This assumption reduces the accuracy of the prediction. At the same time, risks are excluded. Back to the car buying example, we cannot assure that during the life time, the new (or used) car has absolute zero accident after which the maintenance fees would be much higher or the car would written off. To compensate for this weakness, we strongly recommand the professionals to combine NPV with Monte Carlo simulation model as in this research. By doing this, you will know the ‘most likely’ net cash flow in total life time while being more aware of possible risks.

## Conclusion

When investing in securities or fixed assets, most people are attracted by advertisement or sellers’ pitches without considering future cash flow or inherent risks. Net Present Value is a helpful tool for assessing the total lifetime value of an investment. Procurement professionals or investors can base on this value to make decision to achieve value for money. But NPV also has weaknesses which require more sophisticated investigation and studies.