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### Net present value (NPV) is defined as the sum of the present values of the individual cash flows (both incoming and outgoing) of a series of cash flows. In other words, it is the current worth of a future sum of money or stream of cash flows at a certain discount rate.

In one of the previous posts, we have discussed in detail the definition, calculation and Excel formula for net present value. Refer this net present value post for more details.

In this post we will be calculating the net present value (NPV) for the project and for the equity holders; and will be exploring the relation between these two.

Consider a project with construction cost of \$ 1,000,000 and annual rental income of \$ 120,000. Assume the property will be sold in the 10th year for \$ 1,607,023. You can construct the project cash flows and calculate the project NPV by using the Excel NPV formula. Assume discount rate same as the cost of equity. You can see the net present value is very sensitive to the discount rate.

Now introduce debt component in it, assume 30% of the project cost is funded by the equity and remaining 70% by debt. Assume the cost of equity to be 14% and the cost of debt 8%. The weighted average cost of capital (WACC) will be 9.8%. Assume the term of debt is 10 years.

You can project the cash flows for the equity holders and calculate the net present value for the equity holders using the same Excel formula as above. This is demonstrated below: Did you notice that the net present value for the equity holder is greater than the project NPV? Will the equity NPV always greater that the project NPV? No, not really.

Once the cost of debt exceeds the project IRR, the equity NPV will be lower than the project NPV. Also both project NPV and equity NPV will be negative.

Look at the chart below, I have plotted project NPV and equity NPV for different debt costs. Did you notice something? We can conclude the followings:

• If cost of debt < Project IRR; Equity NPV is greater that project NPV and both are positive

Equity holders make more money than debt holder.

• If cost of debt > Project IRR; Equity NPV is lower that project NPV and both are negative

Equity holders lose more money than debt holder.

So, what is the lesson?

Debt is a double-edged sword! So be thoughtful while using debt as a source of fund.

Wondering about the relation between project IRR and equity IRR? Refer this post Project IRR and Equity IRR: A Curious Connection for the same.

What do you think about this post on net present value (NPV), use the comment section below. You can also download the unprotected Excel workbook containing the examples. Check out more useful articles on Our Blog Page

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