Sampa Video, Inc. A small video chain is deciding whether to engage in a new line of delivery business and is conducting an economic analysis of the valuation impacts of this decision. This is a case basically regarding how to measure the benefits of financial leverage via different valuation approaches.

Firm valuation (discount cash flow) and cost of capital When you use the after-tax cost of capital to be the discount rate, you basically take in the effect of the financing. If you discount the project cash flows (without financing) by the after-tax cost of capital, you will get the exact net present value as you use it to discount the total cash flows (project cash flows plus the financing cash flows). That is, when you use the after-tax cost of capital to discount financing related cash flows, the net present value would be zero.

（t=0） （t=1） （t=2） （t=3） （t=4） Initial invest. (total cost) (8,000,000) Inc. rev. 6,000,000 Inc. cost (2,000,000) Deprec. 2,000,000 OP CF 3,500,000 NOP CF 3,000,000 Project CF 6,500,000 Financing 8,000,000 Interest (AT) (360,000) Repay. Fin. Rel. CF (8,360,000) Total CF 3,140,000 (1,860,000)

Assuming that financing totally comes from debt, and the before-tax cost of capital is 6%, tax rate 25%, so the after-tax cost of capital 4.5%. （t=0） （t=1） （t=2） （t=3） （t=4） Project CF (8,000,000) 3,500,000 6,500,000 NPV (at 4.5%) 7,072,024 （t=0） （t=1） （t=2） （t=3） （t=4） Total CF 3,140,000 (1,860,000) NPV (at 4.5%) 7,072,024 （t=0） （t=1） （t=2） (t=3） （t=4） Fin. Rel. CF 8,000,000 (360,000) (8,360,000) NPV (at 4.5%)

Valuation Methods Adjusted Present Value (APV) Approach WACC approach VL = CFL / WACC where WACC = KSU[1-twd] Capital cash flows approach VL = (CFL+KDD) / KSU

Adjusted Present Value (APV) Approach APV = PV of asset flows + PV of side effects associated with the financing program.

Adjusted Present Value (APV) Approach 1. Calculate PV of project (or enterprise) assuming it is all equity financed (i.e. no interest expense) 2. Calculate value of tax shield. Compare tax payments with vs. without debt. The difference equals the tax savings available from the interest deduction (tax shield). Discount tax savings at pre-tax rate of return on debt 3. Total firm value = value of the all equity firm + side effects of financing.

All Equity Valuation of the Project Free Cash Flow to the Firm = EBIT (1 - tax rate) – (Capital Expenditures - Depreciation) – Change in Non-cash Working Capital If depreciation is straight line, the initial capital expenditure appears to be depreciated over 7.5 years ($200,000; or $1,500,000/7.5). The annual capital expenditures of $300,000 seems to be depreciated over 12 years. ($25,000; or 300,000/12)

All Equity Valuation – Cost of Capital (unlevered equity) Asset Beta [A] from Exhibit 2 1.50 Risk free rate [B] from Exhibit 2 5.0% Market risk premium [C] from Exhibit 2 7.2% Asset Return [D] = [B] + [A] * [C] 15.8%

All Equity Valuation of the Project 2002E 2003E 2004E 2005E 2006E TV Free CF -112.0 6.0 151.0 314.0 495.0 4812.5 Discount Rate 15.8% 15.8% 15.8% 15.8% 15.8% Discount Factor 0.864 0.746 0.644 0.556 0.480 0.480 Present Value -96.7 4.5 97.2 174.6 237.7 2311.1 TV=495(1+5%)/(15.8%-5%) = 4812.5 Total PV of FCF 2728.5 Less: Initial Investment 1500.0 Net Present Value 1228.5

The Value of the Levered Firm: The NPV of the Project with a Fixed Level of Debt To calculate the net present value of the firm assuming it borrows $750,000 in perpetuity to fund this project. Use APV approach.

Calculate the value of tax shield The present value of the expected interest tax shields equals the expected interest tax shields discounted at the appropriate cost of capital. The cost of debt is 6.8% in Exhibit 3, which is consistent with the debt beta of .25 from Exhibit 3. Because the debt will be in place forever, the value of the perpetual shield is equal to: V (Tax Shield) = $750,000 * .40 * 6.8% / 6.8% = $300,000.

The Adjusted Present Value calculation The value of the unlevered firm is $1,228,500, The value of the levered firm is equal to the value of the unlevered firm plus the present value of tax shields, $300,000, or $1,528,500

The Value of the Levered Firm: The NPV of the Project with a Fixed Proportion (25%) Debt To calculate the value of the project if the firm maintains a policy of maintaining debt-to-value at 25% in each period. To use the Weighted Average Cost of Capital (WACC) method. To use the WACC to discount the free cash flows, which is already calculated . VL = CFL / WACC

Calculation of cost of capital – levered firm Debt beta [E] from Exhibit 2 0.25 Debt percentage [F] from questions 25% Debt Return [G] = [B] + [F] * [C] 6.8% Debt beta contribution [H] = [E] * [F] 0.06 Equity beta [I] = ([A] - [H]) / [J] 1.92 Equity percentage [J] = 1 - [F] 75% Equity Return [K] = [B] + [I] * [C] 18.8% Equity beta contribution [L] = [I] * [J] 1.44 Asset beta [M] = [H] + [L] = [A] 1.50 Tax Rate [N] from Exhibit 2 40% WACC [O] = (1-[N]) * [F] * [G] + [J] * [K] 15.1%

Weighted Average Cost of Capital Valuation with a target debt-to-value ratio of 25% 2002E 2003E 2004E 2005E 2006E TV Free CF -112.0 6.0 151.0 314.0 495.0 5135.9 Discount Rate 15.1% 15.1% 15.1% 15.1% 15.1% Discount Factor 0.869 0.755 0.655 0.569 0.495 0.495 Present Value -96.7 4.5 97.2 174.6 237.7 2311.1 TV=495(1+5%)/(15.1%-5%) =5135.9 Total PV of FCF 2970.0 Less: Initial Investment 1500.0 Net Present Value 1470.0

Capital Cash Flow Valuation with a target debt-to-value ratio of 25%

Capital Cash Flow Valuation with a target debt-to-value ratio of 25%

Capital Cash Flow Valuation with a target debt-to-value ratio of 25% To calculate the end-of-year debt balances implied by the 25% target debt-to-value ratio. The capital cash flows are calculated by adding expected interest tax shield to the free cash flows. The terminal value is calculated using the capital cash flow for year 5. The value of the project using the Capital Cash Flow approach is $1,470,000, which is the same as the value using a tax adjusted discount rate

Weighted Average Cost of Capital Valuation with a target debt-to-value ratio of 25% 2002E 2003E 2004E 2005E 2006E TV PV of Future FCF 2970.0 3531.0 4058.9 4521.6 4891.3 Debt at 25% of Value 742.5 882.8 1014.7 1130.4 1222.8 Debt Rate 6.80% 6.80% 6.80% 6.80% 6.80% Tax Rate 40% 40% 40% 40% 40% Interest tax shield 20.2 24.0 27.6 30.7 33.3 Free CF -112.0 6.0 151.0 314.0 495.0 5135.9 Interest tax shield 20.2 24.0 27.6 30.7 33.3 Capital Cash Flow -91.8 30.0 178.6 344.7 528.3 5135.9 Discount Rate 15.8% 15.8% 15.8% 15.8% 15.8% Discount Factor 0.864 0.746 0.644 0.556 0.480 0.480 Present Value -79.3 22.4 115.0 191.7 253.7 2466.4 TV=495(1+5%)/(15.1%-5%) =5135.9 Total PV of FCF 2970.0 Less: Initial Investment 1500.0 Net Present Value 1470.0

Comparison between the WACC and CCF approaches Both the WACC and CCF approaches make the same assumption that debt is proportional to value, and because the approaches make the same assumption, they provide the same values. WACC and CCF are special valuation rules, when debt is assumed to be a fixed proportion of firm value, and therefore, it is appropriate to discount interest tax shields at the same rate as unlevered firm.

The Payoff: Reconciling the valuations Value of the project with no debt $1,228,500 Value of project with $750,000 debt forever $1,528,500 Value of project with 25% D/V forever $1,470,000

Why are the present values of the interest tax shield greater for the firm with $750,000 in debt that with the 25% debt-to-value ratio? The level of debt with the fixed debt policy is fixed and thus the interest tax shields have the same risk as the debt. The discount rate for interest tax shields with the fixed debt policy therefore is the debt rate of 6.8%. With the 25% debt-to-value policy, the amount of debt varies with the value of the firm so the expected interest tax shields also vary with the value of the firm. These tax shields therefore should be discounted at the expected asset return 15.8%, which is higher than the debt rate.