What period should you use to present value the terminal year value in a mid- year convention model?
“Just when I thought I was out, they pull me back in.”3 It amazes us that this keeps popping up. We have been dealing with this for decades and the answer is always the same. The terminal year value is present valued back at the mid-year, not the end of the year.4 For example, assume that you have a five-year projection and you decide to use the mid-year convention because cash flows come in steadily during the year and not all at the end of the year. As stated in Financial Valuation Applications and Models: “It is important to note that the terminal year begins at 4.5, not 5.”5
3 Michael Corleone (as played by Al Pacino), Godfather III, 1990.
4 Note: Some valuation analysts assume end-of-year periods because, while cash flows may come in during the year, they are not distributed to shareholders until the end of the year.
5 James R. Hitchner, editor and coauthor, Financial Valuation Applications and Models, 3rd ed. (Hoboken, NJ: John Wiley & Sons, 2011), 147.
178 Financial Valuation
The mid-year convention formula is shown in Exhibit 5.38 (this includes the use of the Gordon Growth Model in the terminal year).
eXhIBIt 5.38 Mid-Year convention DcF Model
Present Value of NCFs during Explicit Period Terminal Value
PV NCF
1 k
NCF 1 k
NCF 1 k
1 n
2 n
n n 4 5
=( + ) =.5 + ( + )=1 5. + … + ( + ) =. + +..
NCF 1 g
k g 1 k
n
n=4 5
× +
− +
( )
( )
( ) .
Let’s calculate a value using the above formula, a 20 percent discount rate, and a 4 percent long-term growth rate.
Discount Rate 20%
Long-Term Growth 4%
Year 1 Year 2 Year 3 Year 4 Year 5
Terminal Year*
Cash Flow $1,000 $1,150 $1,228 $1,417 $1,516 $ 9,854
Period 0.5 1.5 2.5 3.5 4.5 4.5
PV Factor 0.9129 0.7607 0.6339 0.5283 0.4402 0.4402
PV of Cash Flow $ 913 $ 875 $ 778 $ 749 $ 667 $ 4,338
Sum $8,320
*The terminal year value is (1,516 × 1.04)/(.20 – .04) = 9,854.
Now, let’s calculate the value with the interim cash flows at mid-year and the terminal year at end of Year 5.
Discount Rate 20%
Long-Term Growth 4%
Year 1 Year 2 Year 3 Year 4 Year 5 Terminal Year
Cash Flow $1,000 $1,150 $1,228 $1,417 $1,516 $ 9,854
Period 0.5 1.5 2.5 3.5 4.5 5.0
PV Factor 0.9129 0.7607 0.6339 0.5283 0.4402 0.4019
PV of Cash Flow $ 913 $ 875 $ 778 $ 749 $ 667 $ 3,960
Sum $7,942
We have seen complex mathematical proofs confirming that the first formula is correct. However, we also like the simple proof, which is to take the cash flows out 75 years (it actually only takes 66 years here) at the mid-year convention and see what value we obtain (hint: it is $8,320, not $7,942).
Source: James R. Hitchner, editor and coauthor, Financial Valuation Applications and Models, 3rd ed.
(Hoboken, NJ: John Wiley & Sons, 2011), 147.
Income Approach 179 How do you normalize capital expenditures and depreciation in the terminal year?
Many analysts continue to equalize capital expenditures and depreciation. How- ever, while this is a simplifying assumption and convenient to use, in many cases it will result in a higher value. This is because capital expenditures are made in current dollars and depreciation is based on historical dollars. As such, in a situation of ris- ing costs, how could they ever be equal? Let’s take an example. Assume an initial purchase of $1,000 and a 3 percent capital expenditure increase each year. For sim- plicity, let’s also assume a 10-year life with straight-line depreciation, shown below.
As illustrated, when annual costs for capital expenditures increase, depreciation will always be less than capital expenditures. In the example below, in Year 10 depre- ciation is 88 percent of capital expenditures ($1,147/$1,305 × 100). Furthermore, the longer the life of the assets, the larger the gap between capital expenditures and de- preciation will be. The gap declines with an assumption of accelerated depreciation, but there is still a gap. For additional information see “The Ratio of Depreciation and Capital Expenditures in DCF Terminal Values,” M. Mark Lee, FVLE Issue 8, August/
September 2007, www.valuationproducts.com/pastFVLE.html.
Depreciation by Year
Year Cap Ex 1 2 3 4 5 6 7 8 9 10
1 $1,000 100 100 100 100 100 100 100 100 100 100
2 $1,030 103 103 103 103 103 103 103 103 103
3 $1,061 106 106 106 106 106 106 106 106
4 $1,093 109 109 109 109 109 109 109
5 $1,126 113 113 113 113 113 113
6 $1,159 116 116 116 116 116
7 $1,194 119 119 119 119
8 $1,230 123 123 123
9 $1,267 127 127
10 $1,305 131
Depreciation Year 10 $1,147
Do you match depreciation to capital expenditures or do you match capital ex- penditures to depreciation?
Is this the classic story about whether the chicken or the egg came first? No, it is not. You always match depreciation to capital expenditures and not the other way around. The assumption for capital expenditures comes first, followed by the assumption for depreciation. This is true whether you make capital expenditures the same as depreciation or, as the previous discussion shows, you make depreciation less than capital expenditures when costs are increasing.
How do you account for excess depreciation and amortization in the terminal year?
First off, you do not ignore it as many analysts do. Second, the question here is not whether you should calculate the excess depreciation and amortization. The answer to that question is an unequivocal “yes.” There is real additional value to the benefits of the tax shield attributable to higher, but temporary, levels of tax deprecia- tion and amortization.
180 Financial Valuation
The terminal year of a DCF model must reflect the normalized level of cash flows into perpetuity. The key word here is “normalized.” If the company has long-lived as- sets such as buildings and/or goodwill that are being depreciated or amortized over a long period of time for tax purposes, including such depreciation or amortization in the terminal year assumption will distort the cash flows. The long-term tax benefit of such level of depreciation and/or amortization should be reflected in the analysis but may be captured separately from the terminal year calculations. Some analysts improperly match capital expenditures to the depreciation/amortization, including the temporary increase in depreciation/amortization from the long-term assets. To reiterate, the assumption for capital expenditures should drive the depreciation/
amortization assumptions, not the other way around. An analyst matching capi- tal expenditures to depreciation/amortization, including this excess amount, would obtain an incorrect value. The normalized depreciation calculation should be driven by the normalized capital expenditures.
Now, what do you do with this depreciation/amortization overhang? You value it separately. You calculate the tax benefit of the annual excess amount and present value the benefit over the life of the excess amount at the terminal year. This amount is then present valued to period zero. (Or in one step, just use present value periods and factors representing the years in which such excess tax savings occur to calculate the value of the tax benefits at the valuation date.) The value of the tax benefit from the additional depre- ciation/amortization above the normalized level is then added to the value obtained from the DCF using normalized cash flows. For additional information, see “Amortization Should Be Excluded from Terminal Value Calculations,” Gilbert E. Matthews, FVLE Issue 47, February/March 2014, www.valuationproducts.com/pastFVLE.html.
How do you determine long-term working capital needs in the terminal year?
Let’s start with a mistake analysts sometimes make. Again, let’s assume a five- year projection. Some analysts will take the bottom-line cash flow in year five and grow it at the long-term growth rate to calculate the capitalized cash flows in the terminal year. This assumption only works if all the inputs to cash flow in the fifth year are consistent with that long-term growth rate (assume 4 percent). For example, if the company grew at 7 percent from year four to year five, embedded in year five’s cash flow is working capital needs based on a 7 percent growth rate and not the long-term growth rate, here 4 percent.
The way to fix this is to take year five, grow revenues and earnings at the long- term growth rate, and then determine cash flow using a working capital assumption that is consistent with the long-term growth rate.
How do you use RMA to determine debt-free working capital?
The Risk Management Association (RMA) data are one source for determining industry working capital needs. Beware of the sales-to-working-capital turnover ratio provided in RMA (the only sales-to-working capital ratio published by RMA). This calculation by RMA relies upon working capital including short-term debt, which means it is only applicable to direct-to-equity DCF models. It is inappropriate to use the ratio in a debt-free cash flow to invested capital model.
So, how do we determine an industry debt-free working capital for the termi- nal value calculation? With some simple mathematics, a debt-free working capital assumption can be calculated using data in the RMA exhibits. RMA presents detailed balance sheet data as a percentage of Total Assets. To obtain a debt-free working- capital-to-sales percentage you make the calculations shown below.
Income Approach 181 Assume that an analyst relied on the RMA published sales-to-working-capital ratio, including short-term debt of 20.6 The implied working capital as a percent of sales can be calculated by inverting the ratio, resulting in a 5 percent working- capital-to-sales ratio. This elimination of debt from the ratio can result in a huge difference in the working capital assumption in the cash flows and terminal year (in this example, 16 percent vs. 5 percent).
% of Total Assets for Example Category
Current Assets 50%
Less: Current Liabilities 40%
Working Capital 10%
Working Capital 10%
Plus: Notes Payable—Short-Term 10%
Plus: Current Mat.—L.T.D. 8%
Debt-free Working Capital (DFWC) 28%
Debt-free Working Capital 28%
Times: Total Assets—$000 $ 14,000,000
Debt-free Working Capital—$000 $ 3,920,000
Debt-free Working Capital—$000 $ 3,920,000
Divided by: Total Sales—$000 $ 24,000,000
DFWC as a % of Sales 16%
How do you normalize debt in and debt out in the terminal year of a cash-flow- to-equity model?
In a direct-to-equity DCF, the terminal year must be normalized for the amount of debt anticipated in the capital structure into perpetuity. This means an assumption as to debt principal in (new debt financing that increases cash flow) less debt principal out (the repayment of existing debt that decreases cash flow). To illustrate potential imbalances here, let’s look at three simplified examples from FVLE Issue 6, shown below.
1) Only New Debt In
Cash flows before debt $1,000,000
Plus: New debt in $200,000
Less: Debt paid back $0
Net cash flows to equity $1,200,000
Assumed cap rate 15%
Terminal value $8,000,000
Making an assumption of $200,000 of new debt financing and no debt repay- ment implies that the company can borrow $200,000 per year, every year into per- petuity, without ever paying the principal of the debt back.
6 Note: These are fictitious numbers for illustration purposes only.
182 Financial Valuation
2) Only Existing Debt Repaid
Cash flows before debt $1,000,000
Plus: New debt in $0
Less: Debt paid back $200,000
Net cash flows to equity $800,000
Assumed cap rate 15%
Terminal value $5,333,333
The analysis is making an assumption that the company must repay $200,000 per year on principal, every year into perpetuity. Well, let’s assume the company’s current debt level is $1,000,000, meaning that the debt will be repaid in five years.
The model is implying that the company will continue paying $200,000 long after the debt has been repaid.
3) Normalized Debt In and Out
Cash flows before debt $1,000,000
Plus: New debt in $0
Less: Debt paid back $0
Net cash flows to equity $1,000,000
Assumed cap rate 15%
Terminal value $6,666,667
NOTE: The assumption of zero debt in and zero paid back does not assume zero debt.
It assumes the debt/equity structure in the normalized terminal year.
As you can see, the choices for debt into perpetuity can have a large impact on the terminal value. There is one last concept to consider. Some analysts believe that debt in from new financing can be larger than debt repaid and should be built into a perpetuity assumption when the company is growing and uses debt to fund that growth. For additional information, see “The Ratio of Depreciation and Capital Expenditures and the Related Capital Expenditures Debt Service: The Mark Lee Model Continued,” Steven W. Campana, FVLE Issue 12, April/May 2008, www .valuationproducts.com/pastFVLE.html.
What methodology is better in the terminal year, the Gordon Growth Model or exit multiples?
In theory, the application of each of the methods should result in the same or similar value. However, that is often not the case. We believe that the use of the Gor- don Growth Model (GGM) maintains the independence of the income approach, particularly in the terminal year of a DCF model. Since the present value of the terminal year value is usually over 50 percent of the total value, infusing market multiples means that over 50 percent of the income approach is actually a market approach, not an income approach. This is one of the primary reasons to use a GGM.
However, we recommend that the analyst initially apply the GGM and then calculate the implied multiple based on the GGM value, typically a multiple of invested capital to EBITDA as a test of reasonableness or to explain the reasons for the differences.7
7 Invested capital = the market value of equity, interest-bearing debt, and capital leases. EBIT- DA is earnings before interest, taxes, depreciation, and amortization.
Income Approach 183 However, as previously said, both applications should give the same or similar value. As such, for those champions of exit multiples, we suggest that you also cal- culate the implied long-term growth rate embedded in the exit multiple. We often find that there is a disconnect, typically with an unsupportable long-term growth rate. The following formula can be used to determine the long-term (LT) growth rate embedded in an exit multiple:
LT Growth=[DR Exit Value( )−NCF]/(NCF Exit Value+ )
Where:
DR = discount rate NCF = net cash flow
Exit Value = value in the terminal year obtained through the application of an exit multiple
Let’s take an example from FVLE Issue 44:
Assumptions
■ Five-year interim period
■ Discount rate (DR) is 20%
■ EBITDA in year five of $1,000,000
■ Exit value is EBITDA multiple × $1,000,000
■ Net cash flow (NCF) in the 5th year here of $500,000
■ Terminal year cash flow = $500,000 × (1 + LT Growth) Example using an exit multiple of 5 × EBITDA ($000s)
■ Implied LT Growth = [DR(Exit Value) – NCF]/(NCF + Exit Value)
■ Implied LT Growth = [.20($5,000) – $500]/($500 + $5,000)
■ Implied LT Growth = $500/$5,500
■ Implied LT Growth = .091 = 9.1%
As you can see, in this example a 9.1 percent long-term growth rate would be highly suspect and unsupportable. For further information, see the front-page article, “Business Valuation Mistakes: How to Avoid Them—DCF Terminal-Year Exit Multiples,” FVLE Issue 44, August/September 2013, and Harold Martin Jr. and Peter Thacker Jr., “Calculating the Terminal Period Value When Using the Discounted Cash Flow Method: Gordon Growth Model or Exit Model,” FVLE Issue 24, April/May 2010, www.valuationproducts.com/pastFVLE.html.
CONCLUSION
As you can see, the terminal year valuation has many moving parts that require many assumptions. We hope this article has guided you as to best practices with those assumptions or at least has made you think about them.
Financial Valuation: Applications and Models, Fourth Edition By James R. Hitchner
Copyright © 2017 by John Wiley & Sons, Inc.
185