**NPV**

## Net present value

Net present value (NPV) was introduced in more detail in Net present value. The calculation incorporates a discount rate to take into account the time value of money. The NPV in 2002 for the whole 20-year investment period ending in 2020 takes into account the lower value attached to future income than to present income. Applying a discount rate of 3 percent to the revised example from Simple Investment Stream results in a net present value in 2002 equal to **19 648 393** DKK, or 2 530 DKK per share. The investment will break even in its 8th year of operation, in 2011. The stream of investment returns is shown below.

This stream of investment returns reduces the initial investment as illustrated in the graph below:

The issue with this method of calculation is its sensitivity to the assumptions used. If the discount rate is 6 percent instead of 3 percent, the investment will break even in 2012, in its 9th year of operation, as is illustrated below.

Using a discount rate of 6% the total profit over the operating period amounts to app. 10.6 million DKK, or 1 362 DKK per share.

## Government Bonds

Alternatively, the original investment sum (24 459 750 DKK) could have been invested in government bonds. With government bonds, you invest the full sum at the start of the period, receive an interest payment annually, and at the end of the period the initial investment is returned to you. Like in the previous example, income tax is disregarded for simplicity.

Average returns on government bonds for a selection of EU countries vary between 3.8 and 4.4 percent. For the example below, an average yield of 4.2 percent is assumed. As the above example is in 2002-DKK, i.e. ignores inflation, an average rate of inflation (2 percent) is subtracted from the bond interest rate. This results in a normalised government bond rate of return of 2.2 percent.

The graph below illustrates the simple investment stream for 24 459 750 DKK invested in government bonds yielding a 2.2 percent annual return (in 2002 prices).

The investment generates annual returns of 538 115 DKK, or 69 DKK per share. The graph below illustrates the cumulative investment over time:

Unlike investing in the windmill park above, investing in government bonds only fully repays itself after the initial investment (*principal*) is returned at the end of the period.

The total profits for the period sum to 10 762 290 DKK, or 1 386 per share.

Using a discount rate of 3 percent over the period results in a NPV of the investment in 2002 equal to **negative** 2 911 195!!! In other words, this corresponds to a loss of 375 DKK per share for the full period. This is because using a discounting rate places lower value on income generated in the future relative to today. Since the principal is not returned until the end of the period 20 years later, it suffers a substantial discount. 24.5 million DKK in 20 years time with a discount rate of 3 percent is only worth 13.8 million in 2002.

If the discount rate is 6 percent instead, then receiving 24.5 million DKK in 20 years is only worth 7.8 million DKK in 2002. The total *loss* in terms of net present value would be 10.7 million DKK.