Chapter 17 Valuation and Capital Budgeting for the Levered Firm


Appendix 17A The Adjusted Present Value Approach to Valuing

Leveraged Buyouts1

A leveraged buyout (LBO) is the acquisition by a small group of equity investors of a public or private company financed primarily with debt. The equityholders service the heavy interest and principal payments with cash from operations and/or asset sales. The shareholders generally hope to reverse the LBO within three to seven years by way of a public offering or sale of the company to another firm. A buyout is therefore likely to be successful only if the firm generates enough cash to serve the debt in the early years, and if the company is attractive to other buyers as the buyout matures. In a leveraged buyout, the equity investors are expected to pay off outstanding principal according to a specific timetable. The owners know that the firm’s debt–equity ratio will fall and can forecast the dollar amount of debt needed to finance future operations. Under these circumstances, the adjusted present value (APV) approach is more practical than the weighted average cost of capital (WACC) approach because the capital structure is changing. In this appendix, we illustrate the use of this procedure in valuing the RJR Nabisco transaction, the largest LBO in history. The RJR Nabisco Buyout In the summer of 1988, the price of RJR stock was hovering around $55 a share. The firm had $5 billion of debt. The firm’s CEO, acting in concert with some other senior managers of the firm, announced a bid of $75 per share to take the firm private in a management buyout. Within days of management’s offer, Kohlberg, Kravis, and Roberts (KKR) entered the fray with a $90 bid of their own. By the end of November, KKR emerged from the ensuing bidding process with an offer of $109 a share, or $25 billion total. We now use the APV technique to analyze KKR’s winning strategy. The APV method as described in this chapter can be used to value companies as well as projects. Applied in this way, the maximum value of a levered firm (VL) is its value as an all-equity entity (VU) plus the discounted value of the interest tax shields from the debt its assets will support (PVTS).2 This relation can be stated as: VL VU PVTS UCFt ________ R0)t tC RB Bt 1 ∑ _________ (1 RB)t
t =1
∞ ∞

∑ (1
t =1

In the second part of this equation, UCFt is the unlevered cash flow from operations for year t. Discounting these cash flows by the required return on assets, R0, yields the allequity value of the company. Bt 1 represents the debt balance remaining at the end of year (t 1). Because interest in a given year is based on the debt balance remaining at the end of the previous year, the interest paid in year t is RBBt 1. The numerator of the second term,


This appendix has been adapted by Isik Inselbag and Howard Kaufold, The Wharton School, University of Pennsylvania, from their unpublished manuscript titled “Analyzing the RJR Nabisco Buyout: An Adjusted Present Value Approach.” 2 We should also deduct from this value any costs of financial distress. However, we would expect these costs to be small in the case of RJR for two reasons. As a firm in the tobacco and food industries, its cash flows are relatively stable and recession resistant. Furthermore, the firm’s assets are divisible and attractive to a number of potential buyers, allowing the firm to receive full value if disposition is required.


Part IV Capital Structure and Dividend Policy

Table 17A.1
RJR Operating Cash Flows (in $ millions)

1989 Operating income Tax on operating income Aftertax operating income Add back depreciation Less capital expenditures Less change in working capital Add proceeds from asset sales Unlevered cash flow (UCF) $2,620 891 1,729 449 522 (203) 3,545 $5,404

1990 $3,410 1,142 2,268 475 512 (275) 1,805 $4,311

1991 $3,645 1,222 2,423 475 525 200 $2,173

1992 $3,950 1,326 2,624 475 538 225 $2,336

1993 $4,310 1,448 2,862 475 551 250 $2,536

Table 17A.2
Projected Interest Expenses and Tax Shields (in $ millions)

1989 Interest expenses Interest tax shields (tC 34%) $3,384 1,151

1990 $3,004 1,021

1991 $3,111 1,058

1992 $3,294 1,120

1993 $3,483 1,184

tCRBBt 1, is therefore the tax shield for year t. We discount this series of annual tax shields using the rate at which the firm borrows, RB.3 KKR planned to sell several of RJR’s food divisions and operate the remaining parts of the firm more efficiently. Table 17A.1 presents KKR’s projected unlevered cash flows for RJR under the buyout, adjusting for planned asset sales and operational efficiencies. With respect to financial strategy, KKR planned a significant increase in leverage with accompanying tax benefits. Specifically, KKR issued almost $24 billion of new debt to complete the buyout, raising annual interest costs to more than $3 billion.4 Table 17A.2 presents the projected interest expense and tax shields for the transaction. We now use the data from Tables 17A.1 and 17A.2 to calculate the APV of the RJR buyout. This valuation process is presented in Table 17A.3. The valuation presented in Table 17A.3 involves four steps. Step 1: Calculating the present value of unlevered cash flows for 1989–1993 The unlevered cash flows for 1989–1993 are shown in the last line of Table 17A.1 and the first line of Table 17A.3. These flows are discounted by the required asset return, R0, which at the time of the buyout was approximately 14 percent. The value as of the end of 1988 of the unlevered cash flows expected from 1989 through 1993 is: 5.404 _____ 1.14 4.311 _____ 1.142 2.173 _____ 1.143 2.336 _____ 1.144 2.536 _____ 1.145 $12.224 billion

Step 2: Calculating the present value of the unlevered cash flows beyond 1993 (unlevered terminal value) We assume the unlevered cash flows grow at the modest annual rate of

The pretax borrowing rate, RB, represents the appropriate discount rate for the interest tax shields when there is a precommitment to a specific debt repayment schedule under the terms of the LBO. If debt covenants require that the entire free cash flow be dedicated to debt service, the amount of debt outstanding and, therefore, the interest tax shield at any point in time are a direct function of the operating cash flows of the firm. Because the debt balance is then as risky as the cash flows, the required return on assets should be used to discount the interest tax shields. 4 A significant portion of this debt was of the payment in kind (PIK) variety, which offers lenders additional bonds instead of cash interest. This PIK debt financing provided KKR with significant tax shields while allowing it to postpone the cash burden of debt service to future years. For simplicity of presentation, Table 17A.2 does not separately show cash versus noncash interest charges.

Chapter 17 Valuation and Capital Budgeting for the Levered Firm


Table 17A.3
RJR LBO Valuation (in $ millions except share data)

1989 Unlevered cash flow (UCF) Terminal value: (3% growth after 1993) Unlevered terminal value (UTV) Terminal value at target debt Tax shield in terminal value Interest tax shields PV of UCF 1989–1993 at 14% PV of UTV at 14% Total unlevered value PV of tax shields 1989–1993 at 13.5% PV of tax shield in TV at 13.5% Total value of tax shields Total value Less value of assumed debt Value of equity Number of shares Value per share $ 5,404

1990 $4,311

1991 $2,173



$2,336 $ 2,536 23,746 26,654 2,908 1,184

1,151 12,224 12,333 $24,557 3,834 1,544 5,378 29,935 5,000 $24,935 229 million $ 108.9




3 percent after 1993. The value, as of the end of 1993, of these cash flows is equal to the following discounted value of a growing perpetuity: 2.536(1.03) __________ 0.14 This translates to a 1988 value of: 23.746 ______ 1.145 $12.333 billion 0.03 $23.746 billion

As in Step 1, the discount rate is the required asset rate of 14 percent. The total unlevered value of the firm is therefore $12.224 $12.333 $24.557 billion. To calculate the total buyout value, we must add the interest tax shields expected to be realized by debt financing. Step 3: Calculating the present value of interest tax shields for 1989–1993 Under the prevailing U.S. tax laws in 1989, every dollar of interest reduced taxes by 34 cents. The present value of the interest tax shield for the period from 1989–1993 can be calculated by discounting the annual tax savings at the pretax average cost of debt, which was approximately 13.5 percent. Using the tax shields from Table 17A.2, the discounted value of these tax shields is calculated as: 1.151 _____ 1.135 1.021 ______ 1.1352 1.058 ______ 1.1353 1.120 ______ 1.1354 1.184 ______ 1.1355 $3.834 billion

Step 4: Calculating the present value of interest tax shields beyond 1993 Finally, we must calculate the value of tax shields associated with debt used to finance the operations of the company after 1993. We assume that debt will be reduced and maintained at 25 percent


Part IV Capital Structure and Dividend Policy

of the value of the firm from that date forward.5 Under this assumption it is appropriate to use the WACC method to calculate a terminal value for the firm at the target capital structure. This in turn can be decomposed into an all-equity value and a value from tax shields. If, after 1993, RJR uses 25 percent debt in its capital structure, its WACC at this target capital structure would be approximately 12.8 percent.6 Then the levered terminal value as of the end of 1993 can be estimated as: 2.536(1.03) ___________ 0.128 0.03 $26.654 billion

Because the levered value of the company is the sum of the unlevered value plus the value of interest tax shields, it is the case that: Value of tax shields (end 1993) VL (end 1993) VU (end 1993) $26.654 billion $23.746 billion $2.908 billion

To calculate the value, as of the end of 1988, of these future tax shields, we again discount by the borrowing rate of 13.5 percent to get:7 2.908 ______ 1.1355 $1.544 billion

The total value of interest tax shields therefore equals $3.834 $1.544 $5.378 billion. Adding all of these components together, the total value of RJR under the buyout proposal is $29.935 billion. Deducting the $5 billion market value of assumed debt yields a value for equity of $24.935 billion, or $108.9 per share. Concluding Comments about LBO Valuation Methods As mentioned in this chapter, the WACC method is by far the most widely applied approach to capital budgeting.

This 25 percent figure is consistent with the debt utilization in industries in which RJR Nabisco is involved. In fact, that was the debt-to-total-market-value ratio for RJR immediately before management’s initial buyout proposal. The firm can achieve this target by 1993 if a significant portion of the convertible debt used to finance the buyout is exchanged for equity by that time. Alternatively, KKR could issue new equity (as would occur, for example, if the firm were taken public) and use the proceeds to retire some of the outstanding debt. 6 To calculate this rate, use the weighted average cost of capital from this chapter: S B ______ R (1 RWACC ______ RS tC) S B S B B and substitute the appropriate values for the proportions of debt and equity used, as well as their respective costs. Specifically, at the target debt-to-value ratio, B (S B) 25 percent, and S (S B) (1 B (S B)) 75 percent. Given this blend: B RS R0 __ (1 tC) (R0 RB) S 0.14 0.141 Using these findings plus the borrowing rate of 13.5 percent in RWACC, we find: RWACC 0.75(0.141) 0.25(0.135)(1 0.34) 0.128 In fact, this value is an approximation to the true weighted average cost of capital when the market debt-to-value blend is constant or when the cash flows are growing. For a detailed discussion of this issue, see Isik Inselbag and Howard Kaufold, “A Comparison of Alternative Discounted Cash Flow Approaches to Firm Valuation,” The Wharton School, University of Pennsylvania (June 1990), unpublished paper. 7 A good argument can be made that because post-1993 debt levels are proportional to firm value, the tax shields are as risky as the firm and should be discounted at the rate R0. 0.25 ____ (1 0.75 0.34) (0.14 0.135)

Chapter 17 Valuation and Capital Budgeting for the Levered Firm


We could analyze an LBO and generate the results of the second section of this appendix using this technique, but it would be a much more difficult process. We have tried to show that the APV approach is the preferred way to analyze a transaction in which the capital structure is not stable over time. Consider the WACC approach to valuing the KKR bid for RJR. We could discount the operating cash flows of RJR by a set of weighted average costs of capital and arrive at the same $30 billion total value for the company. To do this, we would need to calculate the appropriate rate for each year because the WACC rises as the buyout proceeds. This occurs because the value of the tax subsidy declines as debt principal is repaid. In other words, no single return represents the cost of capital when the firm’s capital structure is changing. There is also a theoretical problem with the WACC approach to valuing a buyout. To calculate the changing WACC, we must know the market value of a firm’s debt and equity. But if the debt and equity values are already known, the total market value of the company is also known. That is, we must know the value of the company to calculate the WACC. We must therefore resort to using book value measures for debt and equity, or make assumptions about the evolution of their market values, to implement the WACC method.

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