Lecture5 - ucf apv fte debt wacc

# Iiwithtaxes rsr0bs1tcr0rb222 wecanthencalculate

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Unformatted text preview: (1­t) + (S/(S+B)) rS = (1/(S+B)) [B rB (1­t) + S rS] (2) rS = ro + (B/S) (1­t) (ro­rB) = [1 + (B/S) (1­t)] ro ­ (B/S) (1­t) rB WACC = (1/(S+B)) { B rB (1­t) + [S + B (1­t)] ro ­ B (1­t) rB } WACC = [S/(S+B) + (B/(S+B) (1­t)] ro = [(1­wB) + wB (1­t)] ro WACC(wB=0) = rS = ro and ∂WACC / ∂wB = ­t < 0 Or try t =.3, and wB = {0 , .2 , .6 , 1} 13 Example 2: WACC Valuation Consider the valuation of the Singer Company, which is for sale for \$475,000, and has the following characteristics: – Cash sales: \$500,000 per year forever – Cash costs: 72% of sales – Corporate tax rate (TC): 34% – Cost of capital if unlevered (r0): 20% – Interest Rate (rB): 10% – Target B/S = 1/3 (thus B = 1, S = 3, and B + S = 4) 14 Example 2: Relevant discount rate First, calculate the weighted average cost of capital. One missing ingredient is the cost of levered equity, which is obtained using MM Prop. II with taxes: rS = r0 + (B/S)(1­TC)(r0­rB) = 22.2% We can then calculate WACC = (3/4) x 22.2% + (1/4) x 10% x (.66) = 18.3% 15 Example 2: Unlevered Cash Flows Annual UCFs (ignore interest payments) are: Cash inflows Cash costs Operating Income Corporate Tax (.34) Unlevered Cash Flow (UCF) \$500,000 ­360,000 140,000 ­47,600 92,400 PV of Singer = 92,400 / .183 = 504,918 PV NPV of acquisition = 504,918 – 475,000 = \$29,918 NPV With WACC, the value of the debt tax shield is reflected in the With denominator (discount rate), rather than the numerator (cash flows) 16 Adjusted Present Value (APV) The adjusted present value method begins by calculating the value of the unlevered firm, that is, its value with all equity financing (PVU). We then separately calculate the value of the debt financing (PVF), which includes debt tax shields & other financing effects, and add the two together. Mathematically: APV = PVU + PVF 17 Calculating PVU and PVF PVU is calculated by discounting the unlevered cash flows by r0: – PVU = Σ UCFt / (1+ r0)t – Or PVU = UCF/r0 for a perpetuity If debt tax shields are the only financing effect, PVF is calculated by discounting them by the cost of...
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