Prof. Enrico C Perotti, Univ of Amsterdam
Leveraged Recapitalizations and LBOs
How to value a leverage recapitalization
A firm may choose to increase significantly its leverage ratio. This may happen as a result of: • A large dividend. • A leveraged recapitalization, when newly issued debt is exchanged for equity. • A LBO (Leveraged Buy-Out)
Typically, the market value of listed equity jumps at the announcement of a leveraged recapitalization.
How would you value the equity after the capital structure change?
The weighted average cost of capital (WACC) method
Firm Value = Equity Value + Debt Value
Enterprise risk = Average risk of its assets
The risk of assets will be absorbed by equity and (if risky) debt in proportion to their value.
Prof. Enrico C Perotti, Univ of Amsterdam
Average risk of assets = Average Risk of Equity and Debt Financing
From a CAPM point of view therefore: βASSETS = (E/V) β EQUITY + (D/V) β DEBT
since portfolio betas are weighted averages of component betas (NB: the covariance is a linear operator).
Suppose the firm is initially entirely equity financed; then βE = βAssets
and the firm's opportunity cost of capital is equal to its cost of equity capital.
Suppose now that the company retires equity by issuing debt. Alternatively, suppose that the firm is taken over using a LBO.
What is the required rate of return on equity after a leveraged recapitalization ? From CAPM: Pre-tax cost of equity: rE = rF + βE [rM – rF ] Pre-tax cost of debt: rD = rF + βD [rM – rF ] After computing the tax shield, the cost of debt is only rD(1-Tc).
Prof. Enrico C Perotti, Univ of Amsterdam
Of course, if the debt is riskless then its beta is zero and its cost should be the riskless rate.
Suppose that the new debt is riskless. Does it mean that the required rate of return on equity is unchanged ?
What is the beta of the equity afterwards ?
βE = βAssets + (D/E) (βAssets – βD ) If βD = 0 then: βE = βAssets + (D/E) βAssets
which implies that the new beta has risen: βE = βAssets + (D/E) βAssets
Prof. Enrico C Perotti, Univ of Amsterdam
In general, the WACC (Weighted average cost of capital) is
rWACC = D/(D+E) rD (1- Tc) + E/(D+E) rE
rWACC is the weighted average of the cost of the individual sources of capital.
This is the most commonly used approach in practice. Note that it neglects any analysis of potential costs of financial distress. The common reason is that it is assumed that the level of debt is sustainable.
Important: In the WACC approach the weights depends on capital structure target levels (in terms of market value).
You can use the WACC approach if the firm’s target debt-to-value ratio is constant.
If the firm keeps growing, the firm then needs to keep increasing its debt level to keep the ratio constant.
But the firm may wish to maintain constant or reduce the level of debt after the recapitalization. For instance, many LBOs repay the debt taken on at the time of the acquisition.
How would you value the equity then ?
Prof. Enrico C Perotti, Univ of Amsterdam
Second approach
The adjusted-present-value (APV) method
APV = Value of all equity firm + NPVF
where NPVF stands for financing side effects:
♦ The tax subsidy to debt ♦ The cost of issuing new securities ♦ Any cost of financial distress ♦ Any eventual subsidies for debt financing
You should use the APV approach if the project’s level of debt is known over the life of the project.
This is usually the case for LBOs (and leases). In general it is also good for situations where the capital structure is unstable over time and we must base the valuation on an expectation of the level of leverage.
Prof. Enrico C Perotti, Univ of Amsterdam
Example: The RJR Nabisco Buyout
VL = VU + PVTS =
∑
∞
t =1
UCFt ∞ T r D + ∑t =1 C B t −t1 t (1 + r0 ) (1 + rD )
After 1993 the debt will be reduced and maintained at 25% of the value of the unlevered firm from that day forward. The new cost of debt (because of lower leverage) will be 10%.
RJR Operating Cash Flows (in $ millions)
1989 1990 $3,410 1,142 2,268 475 512 (275) 1991 $3,645 1,222 2,423 475 525 200 1992 $3,950 1,326 2,624 475 538 225 1993 $4,310 1,448 2,862 475 551 250
Operating Income (OI) - Tax on OI After tax OI + depreciation - capital expenditures - change in working capital + proceeds from asset sales Unlevered cash flow (CF before interest)
$2,620 891 1,729 449 522 (203)
3,545
1,805
$5,404
$4,311
$2,173
$2,336
$2,536
Projected Interest Expenses and Tax Shields (in $ millions)
1989 1990 $3,004 1,021 1991 $3,111 1,058 1992 $3,294 1,120 1993 $3,483 1,184
Interest expenses I. tax shields @34%
$3,384 1,151
Prof. Enrico C Perotti, Univ of Amsterdam
The idea is that you can use the APV approach for the first few years, when you know the exact amount of debt payments; and use the WACC approach after 1993 when the capital structure is set as a fraction of value. So you should calculate the NPV for the total cash flows for 1989-1993; add the tax shields in this period; then compute the terminal value by estimating the value of later cash flows, discounted at WACC. The terminal value has to be discounted back to today using today's cost of capital. Finally, you have to subtract the current stock of debt to obtain the current market value of the equity.
1. PVUCF calculations for 1989-1993, given that the required rate of return on assets is 14%:
2. PV of interest rate tax shields for 1989-1993, where the average pretax cost of debt is 13.5%
3. PV calculations for after 1993, assuming a growth rate for the unlevered cash flows of 6 %, using the new WACC
4. Calculate the estimated value of the debt in 1988, using the average interest charge for the period 1989-1993 and using the information on the cost of debt (13.5 %)
5. Calculate the value of one share at the end of 1988, given there are 229 million shares outstanding (take into account the stock of debt !) Note 1: You can calculate the future expected rate of return on equity from the pre-tax rWACC (which has not changed !) and the information on the new rD. Note 2: You should discount tax shields at the pre-tax cost of debt.