### 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.

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Dear Naiyer Jawaid,

With regards to your NPV calculation spreadsheet , example 2,Row No 38, equity NPV calculaton , you have used , the WACC as the discount rate. As per my understanding of FCFE to which this example is similar, the equity cash flow is discounted by cost of equity which in this case is 14% and not 9.8%. Could you explain why you have used WACC for both row no 26 and Row no 38 in example 2 worksheet. Please reason out if I am wrong so that I can understand better.

Thanks

Srihari

You are correct Srihari. The equity cash flow should be discounted by the cost of equity rather than WACC. Thanks for pointing that.

Dear Naiyer Jawaid,

With regards to your NPV calculation spreadsheet , example 2,Row No 38, equity NPV calculaton , you have used , the WACC as the discount rate. As per my understanding of FCFE to which this example is similar, the equity cash flow is discounted by cost of equity which in this case is 14% and not 9.8%. Could you explain why you have used WACC for both row no 26 and Row no 38 in example 2 worksheet. Please reason out if I am wrong so that I can understand better.

Thanks

Srihari

You are correct Srihari. The equity cash flow should be discounted by the cost of equity rather than WACC. Thanks for pointing that.

Dear Naiyer,

Also, it seems rgar the cost of equity should also increase due to a high levered beta. Do let me know if this is the case.

Kind regards,

Arun

Dear Naiyer,

Also, it seems rgar the cost of equity should also increase due to a high levered beta. Do let me know if this is the case.

Kind regards,

Arun

Very helpful article! thanks ๐

Very helpful article! thanks ๐

Now that project NPV has excluded the interest, why using WACC as discount rate for calculating project NPV?

Sir what abt preferences share divided whether it is included in Equity Npv or Irr

Sir what abt preferences share divided whether it is included in Equity Npv or Irr

The NPV for equity and for project should be always identical. In the xls example you don’t comply with this requirement. The problem with your example is that you are assuming Ke = WACC and that is not correct. When properly done, they match. With my procedure I get the proper Ke’s and my NPV’s match. The Ke’s are: Ke 11.668% 11.390% 11.139% 10.911% 10.704% 10.516% 10.345% 10.189% 10.047% 9.918%. With these Ke’s I get NPV = 374,681.43 identical to the one calculated with WACC. The proper formula for Ke in this case (with no taxes) is Ke_t = Ku + (Ku-Kd)D_t-1/E_t-1- where Ku is the WACC you use in the example. This is a recursive equation that implies circularity that can be easily solved in Excel.

nachovelez@gmail.com

Ignacio, Could it be possible for you to elaborate more on the procedure you mention about applying the proper formula for Ke, perhaps make an xls available or detail were we may find more in depth info about it. I am currently reviewing a project and am having that exact same problem about a mismatch on the FCFF NPV and the FCFE NPV.

Thx

The NPV for equity and for project should be always identical. In the xls example you don’t comply with this requirement. The problem with your example is that you are assuming Ke = WACC and that is not correct. When properly done, they match. With my procedure I get the proper Ke’s and my NPV’s match. The Ke’s are: Ke 11.668% 11.390% 11.139% 10.911% 10.704% 10.516% 10.345% 10.189% 10.047% 9.918%. With these Ke’s I get NPV = 374,681.43 identical to the one calculated with WACC. The proper formula for Ke in this case (with no taxes) is Ke_t = Ku + (Ku-Kd)D_t-1/E_t-1- where Ku is the WACC you use in the example. This is a recursive equation that implies circularity that can be easily solved in Excel.

nachovelez@gmail.com

NPV of project and NPV of equity should by definition, be identical.

nachovelez@gmail.com

When calculating NPV with Excel the range in the formula goes from year 1 to year 10 and from that result, you subtract the investment at year t=0. Hence, the NPV = 374,681.43-

When calculating NPV with Excel the range in the formula goes from year 1 to year 10 and from that result, you subtract the investment at year t=0. Hence, the NPV = 374,681.43-

I posted two or three comments and they were rejected (eliminated). It seems that you don’t accept critical comments. Bad academic (or business) position.

nachovelez@gmail.com

Ignacio; thanks for visiting our blog.

We don’t reject or eliminate any comment apart from spams and promotional stuffs. All comments are moderated and it takes a day or two. Thanks again for your participation.

Thanks for the very helpful lectures. I have a question.

Why is the Cost of Debt always determiner of the relation between Project IRR and Equity IRR? I am still not sure about the logic of the conclusion you made above.

Appreciate your feedback.

thanks

thanks

Very Helpful thanks

Very Helpful thanks