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Correctly Discounting the Terminal Value

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TERMINAL VALUE

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With our EIQF TIPS AND TRICKS, we would like to explain topics that we are frequently asked about by finance professionals and our students.

HOW IS THE TERMINAL VALUE CORRECTLY DISCOUNTED?

When valuing companies using discounted cash flows (DCF), accuracy is crucial—especially when discounting the Terminal Value (TV). However, even experienced analysts often make a conceptual error here.

DISCOUNTING THE CASH FLOWS OF THE DETAILED PLANNING PHASE

Calculating the present values for the first five planning years usually poses no problem. Each expected cash flow is discounted using a discount factor (1/(1+i)^t). The variable t represents the respective year: t = 1 for the first year, t = 2 for the second—and so on up to t = 5.

WHERE ERRORS ARISE: THE EXPONENT FOR THE TERMINAL VALUE

Significantly more uncertainty exists regarding the correct exponent t for the discount factor of the Terminal Value. A common assumption is that the Terminal Value is generated in year t = 6 and is therefore discounted with t = 6. However, this is an error. The correct exponent is t = 5.

WHY t = 5 IS CORRECT: THE PRINCIPLE OF THE VALUATION DATE

A simple example helps illustrate this: If a payment of 10 euros occurs for the first time in year t = 1 and then annually towards infinity, the present value is 10/0.1=100 and refers to the year t = 0. From this, we can draw the following conclusion: when we discount cash flows, the present value of these payments always refers to the point in time one period before the first cash flow occurs.

The same applies to the calculation of the Terminal Value: The TV is the present value of the payments in the continuing period, which arise in years t = 6, …, ∞. The Terminal Value aggregates all future payments from year t = 6 onwards—however, its calculation refers to the valuation date t = 5, i.e., one period before the first cash flow of the continuing period.

IMPLICATION FOR PRACTICE

If the Terminal Value is dated at t = 5, it must be discounted five times—just like the cash flow from the last planning year—to determine the present value (t = 0). The Terminal Value and the cash flow of year t = 5 are thus discounted with the same discount factor.

Those interested in other topics we address at the European Institute of Quantitative Finance are welcome to visit our redesigned homepage www.eiqf.de. Under BLOG, you will find articles, videos, and podcasts.

Warm regards until the next EIQF TIPS AND TRICKS

Dietmar Ernst and Joachim Häcker

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