Valuation Dr Yifan Zhou Value a capital investment project • Explain and derive the after-tax WACC • Valuing Businesses Value a capital investment project How to value a capital investment project, “spend money” 1. Forecast after-tax cash flows, assuming all-equity financing. 2. Assess the project’s risk. 3. Estimate the opportunity cost of capital. 4. Calculate NPV by discount rate (opportunity cost of capital). The After-Tax Weighted-Average Cost of Capital Why implemented the after-tax WACC for project valuation? Under MM assumptions: • All financing decisions (raising money and spend money) are irrelevant. • Investment and financing decisions might interact. • One reason that financing and investment decisions interact is taxes. The After-Tax Weighted-Average Cost of Capital Why implemented the after-tax WACC for project valuation? The adjusted discount rate modifies the discount rate by: • To take into account capital structure, • After-tax WACC = rD (1 – TC) (D/V) + rE(E/V) • rD is the before-tax cost of debt. The (1 – Tc)rD is the after-tax cost of debt. • To captures the value of interest tax shields. The After-Tax Weighted-Average Cost of Capital When After-tax WACC = rD (1 – TC) (D/V) + rE(E/V) as adjustor: • All the variables in the WACC formula refer to the firm as a whole. • The formula works (set projects as the firm undertaking it). The After-Tax Weighted-Average Cost of Capital After-tax WACC = rD (1 – TC) (D/V) + rE(E/V), the formula works for: • The “average” project. • To discount future cash flows by current firms' characteristics. • It is incorrect for projects are: • Safer or riskier than the average of the firm’s existing assets. • Increase or decrease in the firm’s target debt ratio. The After-Tax Weighted-Average Cost of Capital Discounting cash flows by the WACC is: • Only approximately correct. • As the business risk and debt ratio are expected to change. Valuing Businesses Why valuing businesses? • To arranging financing decisions. • To help with operating the firm more effectively. Valuing Businesses Why valuing businesses? • The valuation of the business could be left to investors and financial markets. • But financial manager also has to take a stand on what business is worth. Valuing Businesses Why valuing businesses? • If firm A is about to make a takeover offer for firm B. ➢ It is particularly difficult if B is a private company (no observable share price). • To sell one of firm business line or divisions, ➢ Valuation is helpful for negotiations with potential buyers. Valuing Businesses Why valuing businesses? • When a firm goes public IPO ➢ The investment banker must evaluate firm so as to set the issue price. Valuing Businesses Why valuing businesses? • For owners to value the private firms. ➢ The fund’s directors are obliged to estimate a fair value for invested firms. Valuing Businesses Why valuing businesses? • To find out undervalued firms. ➢ The analysts in stockbrokers’ offices and investment firms Valuing Businesses How WACC can be used to value a company? If the firm is financed by a mixture of debt and equity? Just treat the company as if it were one big project. 1.To forecast the company’s free cash flows (the hardest part of the exercise) 2. To discount back to present value. Valuing Businesses Just treat the company as if it were one big project. To valuing a firm: 1.To forecast the company’s free cash flows (the hardest part of the exercise) 2. To discount back to present value. Valuing Businesses The cash flows and horizon value are then discounted back to the present: The value of a business = present value of free cash flows (FCF) + the present value of horizon value. PV= PV (free cash flow) + PV (horizon value) Valuing Businesses The cash flows and horizon value are then discounted back to the present: PV= PV (free cash flow) + PV (horizon value) PV = (FCF1)/(1+WACC) + (FCF2)/(1+WACC)2 +…+ (FCFH)/(1 +WACC)H + (PVH)/(1+WACC)H Where: PVH = (FCFH+1)/(WACC – g) Valuing Businesses Free cash flow or net income? Free cash flow and net income are not the same. ➢ Income is the return to shareholders, calculated after interest expense. ➢ Free cash flow is calculated before interest. Valuing Businesses Free cash flow or net income? Free cash flow and net income are not the same. ➢ Income is calculated after various non-cash expenses, including depreciation. ➢ Therefore, we will add back depreciation when we calculate free cash flow. Valuing Businesses Free cash flow or net income? Free cash flow and net income are not the same. ➢ Free cash flow can be negative for growing firms, even firms that are profitable. Valuing Businesses Valuing company A Valuing Businesses Valuing company A • Set the assumptions of growth ratios Valuing Businesses Valuing company A • Free cash flow = Profit after tax + depreciation − investment in fixed assets • − investment in working capital • of horizon value. Valuing Businesses Valuing company A • Free cash flow = Profit after tax + depreciation − investment in fixed assets− investment in working capital Valuing Businesses Valuing company A: Free cash flow of year 1 • Free cash flow = Profit after tax + depreciation − investment in fixed assets − investment in working capital = 8.7 + 9.9 − (109.6 − 95.0) − (11.6 − 11.1) = $3.5 million Valuing Businesses Valuing company A Valuing Businesses Valuing company A : Estimating present value of the cash flows • To find the present value of the cash flows in years 1 to 6 • The discount by WACC of 9%. Valuing Businesses Valuing company A : Estimating horizon value • Use the constant-growth DCF to estimating the horizon value • To find the value of the cash flows from year 7 Valuing Businesses Valuing company A : Estimating horizon value • To find the value of the cash flows from year 0 Valuing Businesses Valuing company A • PV(company) = PV(cash flow years 1 to 6) + PV(horizon value) = $20.3 + 67.6 = $87.9 million Valuing Businesses Valuing company A • To find the value of the equity, we simply subtract the value of the debt: Total value of equity = $87.9 − 36.0 = $51.9 million • To find the value per share, we divide by the total number of shares outstandin g: Value per share = 51.9/1.5 = $34.60 Valuing Businesses Valuing company A • To find the value per share, we divide by the total number of shares outstandin g: Value per share = 51.9/1.5 = $34.60 • Thus we could afford to pay up to $34.60 per share for buying company A. Valuing Businesses 1. If you discount at WACC Calculate taxes as if the company were all equity- financed. The value of interest tax shields is not ignored, because the after-tax cost of debt is used in the WACC formula. Valuing Businesses 2. Unlike most projects, companies are potentially immortal. No need to forecast every year’s cash flow from now to eternity. Can forecast to a medium-term horizon and add a terminal value to the cash flows in the ho rizon year. The terminal value is the present value at the horizon of all subsequent cash flows. Be careful, as terminal value often accounts for the majority of the company’s value. Valuing Businesses 3. To value the company’s equity, common stock: Don’t forget to subtract the value of the company’s outstanding debt. Some Tricks of the Trade ➢ Several questions immediately arise: • How does the formula change when there are more than two sources of financing? For example, if the capital structure includes both preferred and common shares: Some Tricks of the Trade ➢ Several questions immediately arise: • What about short-term debt? For small firms and firms outside US The short-term debt is an important, permanent source of financing The interest cost of short-term debt is then one element of the WACC Some Tricks of the Trade ➢ Several questions immediately arise: • How are the costs of financing calculated? The WACC is an expected, that is average, rate of return, not a promised one. Some Tricks of the Trade ➢ Several questions immediately arise: • Should I use a company or industry WACC? Industry WACCs are less exposed to random noise and estimation errors. Adjusting WACC When Debt Ratios and Business Risks Differ Valuing company Step 1 – Calculate the opportunity cost of capital. Step 2 – Estimate the cost of debt at the new debt ratio and calculate the new cost of equity. Step 3 – Recalculate the weighted-average cost of capital at the new financing weights. Value a capital investment project • Explain and derive the after-tax WACC • Valuing Businesses
