Quantitative questions-1.docx - Quantitative questions Chapter 2 question 13 If a firm with a \$5 billion fund charges a 2 percent management fee for

# Quantitative questions-1.docx - Quantitative questions...

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Quantitative questions Chapter 2, question 13: If a firm with a \$5 billion fund charges a 2 percent management fee for eight years, and 20 percent carried interest on all profits, and earns a 3 return on its investments, what is the true multiple of investment and IRR for the LP? Firm invests \$5 billion and sells for \$15 billion (3 times return on its investment) Management fee expense=2%*\$5 billion=\$0.1 billion Carried interest expense=20%*\$10 billion=\$2 billion Investment multiple=(final cost of investment-expenses)/initial investment=(\$15 billion-\$0.1 billion-\$2 billion)/\$5 billion=\$12.9/\$5=2.58 At the same time, Investment multiple=(1+IRR)^8 IRR=12.58% Chapter 4, question 6: Calculate the WACC using the following assumptions: D = \$200 million rd = 4% rf = 3% E = \$400 million τ = 30% β = 1.9 (rm - rf ) = 7.5% Cost of equity=rf+ β(rm-rf)=3%+1.9*7.5%=17.25% WACC=(D/D+E)*rd*(1- τ )+(E/D+E)*re=0.33*4%*0.7+0.67*17.25%=12.43% Chapter 4, question 7: Recalculate the NPV of Hi-Tech using the data in Table 4.6; but assume that the company is currently not at its target capital structure, which is 30 percent debt and 70 percent equity. Also assume the firm’s cost of debt is 8 percent.

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Step 1: Value Cash Flows Year 0 1 2 3 4 5 6 7 8 9 Revenues 100 140 210 250 290 380 500 650 900 Less: Costs 230 240 260 275 290 310 350 400 470 EBIT -130 -100 -50 -25 0 70 150 250 430 Less: Tax 0 0 0 0 0 0 0 26 172 EBIAT -130 -100 -50 -25 0 70 150 224 258 Less: Ch. NWC 10 4 7 4 4 9 12 15 25 Net Cash Flow -140 -104 -57 -29 -4 61 138 209 233 Discount Factor 0.87 2 0.76 1 0.66 4 0.57 9 0.50 5 0.44 1 0.38 4 0.33 5 0.29 2 Present Value (Cash Flow) -122 -79 -38 -17 -2 27 53 70 68 Present Value (Cash Flows) -40 Terminal Value 2,06 2 Present Value (Terminal Value) 602 Present Value (Cash Flows) -40 Present Value (Terminal Value) 602 Net Present Value \$562 β u = β t × (E/V) = β t × [E/(E + D)] β u = 1.2 β t = β u × (V/E) β t = 1.2 (100/70) = 1.714 r e = r f + β t (r m − r f ) r e = 18.86% = 6% + 1.714 (7.5%) WACC =D/V.r d (1− τ) + E/V.r e 14.64 = 30/100 × 8% × (1 − 40%) + 70/100 × 18.86% Chapter 4, question 10: Calculate the APV for Hi-Tech using the assumptions in Table 4.6 and assuming the firm takes on \$100 million debt at the time of the sale. At the end of each subsequent year to the sale, \$25 million of this debt is retired.
Step 1: Value Cash Flows Year 0 1 2 3 4 5 6 7 8 9 Revenues 100 140 210 250 290 380 500 650 900 Less: Costs 230 240 260 275 290 310 350 400 470 EBIT -130 -100 -50 -25 0 70 150 250 430 Less: Tax 0 0 0 0 0 28 60 100 172 EBIAT -130 -100 -50 -25 0 42 90 150 258 Less: Ch. NWC 10 4 7 4 4 9 12 15 25 Net Cash Flow -140 -104 -57 -29 -4 33 78 135 233 Discount Factor 0.870 0.756 0.658 0.572 0.497 0.432 0.376 0.327 0.28 4 Present Value (Cash Flow) -122 -79 -38 -17 -2 14 29 44 66 Present Value (Cash Flows) -105 Terminal Value 2,000 Present Value (Terminal

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