Apv and Wacc

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APV vs. WACC Problem Given the following information, answer questions 1 and 2 below. Company and market data: Rf = 4% Rm = 10% βu = 0.9 D/V (target) = 40% RD = 4% Tc = 30% Project CFs: I0 = 1000, CF1 = 300, CF2 = 400, CF3 = 500 1) Calculate the project’s value using WACC 2) Calculate the project’s value using APV -Oops, we can’t until we know the financing (debt) pattern over time. (a) OK, assume the project is financed with 60% debt which is paid off in three equal, annual installments. (b) Now assume instead of (a) that the debt is rebalanced to be consistent with the firm’s target debt ratio (i.e. D/V = 40%). Solution – APV vs. WACC Basics: DV=40%,EV=60%→DE=0.40.6=0.667 βL= βU1+DE= 0.9 1+0.667= 1.5 rE= rf+ βLMRP= 4+1.510-4= 13% WACC=rD1-TcDV+ rEEV=0.041-0.30.4+0.130.6=0.0112+0.078=8.92% 1) Project value using WACC -1000+ 300(1+0.0892)+ 400(1+0.0892)2+ 500(1+0.0892)3= -0.46 2) Project value using APV a) 60% debt paid off in three equal annual installments APV=PVCFs at rU+ PVITS rU= rf+ βUMRP=4+0.910-4= 9.4% PVCFs at rU= -1000+ 3001.094+ 4001.0942+ 5001.0943= -9.69 ITS1=Debt x rD x Tc=0.610000.040.3= 7.2 ITS2=4000.040.3= 4.8 ITS3=2000.040.3= 2.4 PVITS= 7.21.04+ 4.81.042+ 2.41.043=13.49 APV= -9.69+13.49=3.8 b) Debt is rebalanced to be consistent with the target debt ratio (D/V = 40%) APV=PVCFs at rU+ PVITS PVCFs at rU= -9.69 (From 2a above) * PV0= 3001.0892+ 4001.08922+ 5001.08923=999.54 Debt0 =0.4999.54= 399.82 ITS1=Debt0 x rD x Tc=399.820.040.3= 4.80 * PV1= 4001.08921+ 5001.08922= 788.7 Debt1=0.4788.7= 315.48 ITS2=315.480.040.3= 3.79 * PV2= 5001.08921=459.05 Debt2=0.4459.05=183.62 ITS3=183.620.040.3=2.2 PVITS= 4.81.094+ 3.791.0942+ 2.21.0943=9.23 APV= -9.69+9.23= -0.46 Note: The APV under 2b equals the value using

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