Why do the DCF and EP methods yield the same answer? Verifying the 'valuation twins' with numbers

When learning about M&A valuation, you will inevitably encounter this question.

Why do the DCF method and the EP method produce the same result?

In short, these two are mathematically completely equivalent. They are merely two sides of the same coin. However, because they present information differently, their uses also differ. This time, we will verify their structure using numbers and organize how to use them in practice.

■ First, let's grasp the difference in 'perspective' between the two methods

DCF Method: Counting the 'cash remaining on hand'

The DCF method is simple. It discounts the free cash flow (FCF) generated by the company each year by the cost of capital (WACC) and sums them up.

It is the image of accumulating the 'money that actually falls into your hands'.

EP Method: Counting the 'excess return beyond the cost of capital'

The EP (Economic Profit) method takes a slightly different perspective. It measures each year whether you are generating more profit than the capital invested.

It is the image of recognizing only the 'earnings that exceed the initial investment' as value.

■ Verifying with numbers

Seeing is believing. Let's verify this with concrete numbers.

Prerequisites

• Acquisition Price (Beginning Invested Capital): 10 million yen

• WACC: 10%

• Year 1: NOPAT 1.5 million, Additional Investment 1 million

• Year 2: NOPAT 2 million, Additional Investment 1 million

• Year 3: NOPAT 2.5 million, Recovery of all capital (12 million) through liquidation

Calculation from a DCF perspective

FCF = NOPAT − Additional Investment. In the third year, it is not 250 − 100 + 1,200 − 100 = 1,250, but rather 250 + 1,200 = 1,450, as all capital is recovered without additional investment at the time of liquidation.

Calculation from an EP perspective

Beginning invested capital accumulates with each year's additional investment.

Enterprise Value = Beginning Invested Capital 10 million + Present Value of EP 2.175 million = 12.175 million yen

They matched perfectly.

■ Why are they equivalent? — A mathematical intuition

An identity holds between NOPAT and invested capital. Both methods are simply calculating the 'present value of the value this company generates in excess of its cost of capital.' DCF directly accumulates cash, while EP accumulates excess profits and adds the beginning capital. The starting point and the path are different, but the answer is the same.

■ If the results are the same, why use them differently?

This is the practical point.

DCF's weakness: Most of the value is concentrated in the 'Terminal Value'

When creating a DCF model for a growth company, 60–80% of the enterprise value is often concentrated in the final year's Terminal Value. This Terminal Value is extremely sensitive to assumptions about growth rates and WACC, making it easy for executives to say, 'In the end, isn't it just based on assumptions?'

EP's strength: Value creation can be visualized 'every year'

The EP method can break down value creation on an annual basis. If the EP for a certain year is positive, it creates shareholder value; if negative, it destroys it—a simple judgment axis is created. This is why it is easy to use for KPI management by business division.

Why do Sony and Kao use EP?

The background to why major Japanese companies adopt EP (or EVA) as a management indicator lies in Japanese management culture. There is a strong awareness of 'judging by the results of the current term,' and EP, which visualizes annual excess profits, is easier to implement on the front lines than DCF, which depends on a distant future closing price. It is also suitable for cross-comparison between business divisions.

■ The pitfall of the EP method: The problem of defining invested capital

The most important point to be careful about when using the EP method is how to define beginning invested capital.

Whether to include goodwill, whether to capitalize R&D expenses, how to calculate working capital—if the definition changes, the EP figure changes significantly. Since DCF is less affected by this problem, DCF is the mainstream for external valuation (such as M&A price negotiations).

■ Summary

The two methods are like twins. Although they share the same origin, they excel in different fields. Gaining a deep understanding of this difference while learning valuation will certainly be useful in both practical work and interviews.

Next time, I plan to write about how to distinguish between the APV (Adjusted Present Value) method and the DCF method.