Valuation: Apv vs Wacc

The tercet arisees observe the entire unassailable but they differ around the way they direct revenue shields. We testament first review the rational and the underlying assumptions tramp each shape up. We will hence use a numerical character to illust ordain the mechanics behind the three forward motiones and show under which assumptions they outlet the similar results. Enterprise rating According to Modigliani and Miller, the respect of a unions economic assets must equal the apprise of the claims against those assets.Enterprise valuation deterrent examples esteem the sum of the currency springs to all claim holders, including equity holders and debt holders and discount them to the impound woo of ceiling. The property scat available to all claim holders is called the bring out hard cash flow (FCF) from trading operations and is defined below FCF = EBIAT + Depreciation cracking Expenditure Increases in Working nifty EBIAT is the income the company earns after abide by without regard to how the company is financed. Non-cash expenses such as Depreciation are and so added.Because we are valuing a going concern we likewise take into depend the cash flow management will retain for new slap-up expenditures and possible increase in working hood. The be is in effectuate the cash available to owners and creditors. By definition free cash flow is main(a) from leverage (and is often referred as un-levered free cash flow). because the honour derived from the concern valuate shield (interest on debt is taxation deductible) has inactive to be incorporated in the enterprise valuation.This is where the three flakes WACC, APV and CCF differ The WACC move up set the tax shield by adjusting the make up of chief city The APV onset values the tax shield separately from the un-levered free cash flow The CCF approach values the tax shield by incorpo evaluation it in the cash flow The Weighted Average damage of Capital Appr oach To mould the value of the enterprise, the free cash flows from operations have to be discounted to register value. According to Modigliani and Millers proposition number one without taxes or monetary marketplace mperfections the cost of chief city does non depend on financing so the weighted average of the expected returns to debt and equity investors equals the probability cost of bully regardless of leverage Rd x D/V + Re x E/V = Ra = Constant independent of D/V Ra = Opportunity cost of crown = Un-levered cost of equity = glide by on assets = pre-tax WACC Rd = Cost of debt, Re = Cost of equity, D/V and E/V = Target trains of debt and equity utilize market values Fabrice Bienfait IFM final Paper Page 2 of 8None of the components of the cost of capital are directly observable and therefore need to be approximated exploitation various models and assumptions. The cost of equity is derived from the capital asset pricing model (CAPM) while the cost of debt burn down be estimated from the plastered credit rating and default try or from yields on publicly traded debt. save interest on debt is tax deductible so if we were to discount free cash flows from operations utilize Ra we would not take into account the value of the tax shield.Therefore the after-tax weighted average cost of capital (WACC) is employ instead. WACC includes an registration to the cost of debt by the marginal tax rate (Tm) WACC = Rd x (1-Tm) x D/V + Re x E/V (= Ra Rd x Tm x D/V) WACC is less than the opportunity cost of capital Ra because the cost of debt is calculated after tax as Rd (1-Tm). Thus the tax advantages of debt financing are reflected in a rase discount rate. The WACC equals the opportunity cost of capital when there is no debt and declines with financial leverage because of increasing interest tax shields.The WACC increases again when the debt level becomes portentous relative to the value of the dissipated reflecting the main be companiond with borr owing, the costs of bankruptcy. name 1 WACC as a Function of the Debt Ratio sites of go along Re R WACC Rd Debt to Equity push awaying all future cash flows using a continuous WACC assumes that the company manages its capital coordinate to a immovable debt to value ratio (D/V).Therefore the companys WACC is the right discount rate only if the companys debt ratio (D/V) is expected to remain somewhat close to constant. However if the company is expected to significantly change its capital expression (i. e. Fabrice Bienfait IFM last Paper Page 3 of 8 constant level of debt, LBO, recapitalization), the WACC would have to be continuously adjusted which makes the approach to a greater extent difficult to apply.The Adjusted Present Value Approach The APV approach values the cash flows associated with capital structure independently by separating the value of operations into two components the value of the firm without debt and the benefits and the costs of borrowing Value of the firm = Value of the un-levered firm + Present value of interest tax shields cost of financial distress The value of the un-levered firm is obtained by discounting free cash flows at the return on assets (Ra).If the company manages its debt-to-value to a target level (D/V=constant) then the interest tax shield is as forged as the firm and should be discounted at Ra. In this exercise the APV approach yields the same results as the WACC approach but is computationally less in force(p). However if the debt is assumed to be a resolved amount (D=constant) the interest tax shield is less baseless than the firm but as risky as the debt itself and should be discounted at the cost of debt.In this case the APV approach is not only the only correct approach, it is as well computationally very efficient if the tax saving are considered as perpetuity since Present value of interest tax shields = (Tm x Rd x D) / Rd = Tm x D The main risk in using the APV approach is to ignore the costs of financial distress, especially at very high debt ratios, which leads to an overvaluation of the firm.The Capital Cash Flow Approach Capital cash flows are solely derived from free cash flows by adding interest tax shields CCF = FCF + Interest tax shield = FCF + Tm x Rd x D With this approach capital cash flows are then discounted at the return on assets. This implicitly assumes that interest tax shields are as risky as the firm and are discounted at the return on assets. This is true when debt is a fixed proportion of value. Under this assumption the capital cash flow approach will generate the same results as the WACC approach.Furthermore if the debt is forecasted in levels instead of a debt-to-value ratio the CCF approach is easier to use because the tax shield are plain to calculate and to include in the CCF. If the forecasted debt levels imply a change in the debt-to-value ratio, the CCF retains his simplicity since the discount rate, the return on assets, is independent of the capital structure and can be used for every forecast period. Therefore the approach is easier to apply in transactions involving change in capital structure such as a LBO or a restructuring.However in this case discounting the interest tax shields at Ra is a simplifying assumption since the risk of those cash flows is not anymore the same as the risk associate with the firm. Fabrice Bienfait IFM Final Paper Page 4 of 8 Numerical precedent Table 1 shows the financial assumptions underlying our numerical example. The firm is valued over a period of 5 years during which EBIT is growing at 5% per annum and depreciation, capital expenditure and increase in working capital are constant. However the firms capital structure changes significantly through the repayment of a major portion of its debt.Table 1 Assumptions (in ) attempt Free Rate Market Risk Premium measure Rate Asset Beta Debt Beta EBIT Depreciation Capex Increase in NWC Debt course of study 1 5% 7% 40% 1. 2 0. 4 100,000 5 0,000 60,000 10,000 100,000 social class 2 5% 7% 40% 1. 2 0. 35 105,000 50,000 60,000 10,000 50,000 yr 3 5% 7% 40% 1. 2 0. 3 110,250 50,000 60,000 10,000 25,000 category 4 5% 7% 40% 1. 2 0. 25 115,763 50,000 60,000 10,000 12,500 course of study 5 5% 7% 40% 1. 2 0. 2 121,551 50,000 60,000 10,000 6,250 We will start valuing the firm using the WACC approach (see table 2).This is the less appropriated and intimately complex methodology give the forecasted changes in capital structure. Indeed the WACC call for to be recalculated every year and an iterative calculation has to be used since the value of the firm for each year is required to derive the plowshare of debt and equity. The firm value in year N is the value of the remaining cash flows. For instance the value of the firm at the beginning of grade 3 is the value of the remaining cash flow in course of study 3, 4 and 5 discounted using the WACC in year 3, 4 and 5.Table 2 WACC Valuation (in ) EBIT Taxes on EBIT = EBIAT + Depreciation Capex Increase in NWC = FCF Percent Debt Cost of Debt After Tax Cost of Debt Percent Equity Return on Assets Cost of Equity WACC force out Factor PV level Value course of instruction 1 100,000 (40,000) 60,000 50,000 (60,000) (10,000) 40,000 61. 3% 7. 8% 4. 7% 38. 7% 13. 4% 22. 3% 11. 5% 0. 90 35,878 163,178 course of study 2 105,000 (42,000) 63,000 50,000 (60,000) (10,000) 43,000 35. 2% 7. 5% 4. 5% 64. 8% 13. 4% 16. 6% 12. 4% 0. 80 34,329 141,923Year 3 110,250 (44,100) 66,150 50,000 (60,000) (10,000) 46,150 21. 5% 7. 1% 4. 3% 78. 5% 13. 4% 15. 1% 12. 8% 0. 71 32,666 116,451 Year 4 115,763 (46,305) 69,458 50,000 (60,000) (10,000) 49,458 14. 7% 6. 8% 4. 1% 85. 3% 13. 4% 14. 5% 13. 0% 0. 63 30,979 85,196 Year 5 121,551 (48,620) 72,930 50,000 (60,000) (10,000) 52,930 13. 3% 6. 4% 3. 8% 86. 7% 13. 4% 14. 5% 13. 1% 0. 55 29,325 46,817 Fabrice Bienfait IFM Final Paper Page 5 of 8 The cost of debt is calculated using CAPM The cost of equity is calculated using the M&M pro position IRd = Rf + ? d x MRP Re = (Ra D/V Rd) / (E/V) Using the WACC approach we find a value for the firm of 163,178. undermentioned we use the APV approach to value the firm calculating separately the value of the un-levered firm and the value of the interest tax shield (Tm x Rd x D). The approach is straightforward in this case since we are given a forecast of the level of debt. We find that the APV approach yields the same firm value (163,178) as the WACC approach when discounting interest tax shield at Ra.We also illustrate that using Rd would yield a higher valuation of the firm (this is not the correct discount rate in this case given that the debt is not constant). Table 3 APV Valuation (in ) FCF Return on Assets Discount Factor PV Value of Unlevered Firm Interest Tax screen out Return on Assets Ra Discount Factor PV Value of Interest Tax Shield Ra Interest Tax Shield Cost of Debt Rd Discount Factor PV Value of Interest Tax Shield Rd Value of Firm with ITS Ra Value of Firm with ITS Rd Year 1 40,000 13. 4% 0. 88 35,273 158,491 3,120 13. % 0. 88 2,751 4,686 3,120 7. 8% 0. 93 2,894 5,121 163,178 163,613 Year 2 43,000 13. 4% 0. 78 33,438 Year 3 46,150 13. 4% 0. 69 31,647 Year 4 49,458 13. 4% 0. 60 29,907 Year 5 52,930 13. 4% 0. 53 28,225 1,490 13. 4% 0. 78 1,159 710 13. 4% 0. 69 487 338 13. 4% 0. 60 204 160 13. 4% 0. 53 85 1,490 7. 5% 0. 86 1,286 710 7. 1% 0. 81 572 338 6. 8% 0. 76 255 160 6. 4% 0. 71 114 Finally we use the CCF approach. The calculation clear shows how the interest tax shields are incorporated in the cash flows and then discounted at Ra.The CCF approach is equivalent to the WACC approach. Furthermore the approach also produces the same value as the APV method with interest tax shields discounted at Ra. Fabrice Bienfait IFM Final Paper Page 6 of 8 Table 4 CCF Valuation (in ) EBIT Taxes on EBIT = EBIAT + Depreciation Capex Increase in NWC + Interest tax Shield = CCF Return on Assets Discount Factor PV Firm Value Year 1 100,000 (4 0,000) 60,000 50,000 (60,000) (10,000) 3,120 43,120 13. 4% 0. 88 38,025 163,178 Year 2 105,000 (42,000) 63,000 50,000 (60,000) (10,000) 1,490 44,490 13. 4% 0. 8 34,597 Year 3 110,250 (44,100) 66,150 50,000 (60,000) (10,000) 710 46,860 13. 4% 0. 69 32,134 Year 4 115,763 (46,305) 69,458 50,000 (60,000) (10,000) 338 49,795 13. 4% 0. 60 30,112 Year 5 121,551 (48,620) 72,930 50,000 (60,000) (10,000) 160 53,090 13. 4% 0. 53 28,311 Conclusions The three enterprise valuation techniques considered in this paper are different in the way they treat interest tax shields. However we have seen that the WACC approach and the CCF approach are identical and that under certain assumptions the APV approach also yields the same valuation.The WACC approach is easy to use and efficient when the assumption that capital structure will not change in the future can be made (D/V= constant). If debt level is forecasted to remain constant in absolute term (D=constant), the APV approach should be used discountin g the interest tax shield at the cost of debt. Finally the CCF approach is the appropriate and well-nigh efficient approach when forecasted debt levels imply a change in capital structure. In this case it is also equivalent to the APV approach discounting the interest tax shield at the return on assets. Fabrice Bienfait IFM Final Paper