consider a firm 1 that is unlevered and firm 2 which is levered with target debt
ID: 2805245 • Letter: C
Question
consider a firm 1 that is unlevered and firm 2 which is levered with target debt to equity ratio(b/s)=1.Both firm have exactly the same perpetualnet operating income,NOI OF 180 before tax.the before tax cost of debt,kb is the same as risk free rate.the corporate tax is 0.5 .given the following market parameters, E(rm)=0.12 d2(market variance)=0.0144 rf=0.06 beta of firm 1=1 beta of firm 2=1.5
required
a.)find the cost of capital for each of the firms (ignore personal taxes).
b. Evaluate the following four projects to determine their acceptance or rejection by firms 1 and 2 what do the results in this evaluation tell you about leverage in a world with corporate taxes but no personal taxes? (note r jm is the correlation between the unlevered free cash flows of each project and the market)
PROJECT
COST j
E(NOI)After-tax
j
r jm (correlation of j with market)
1
100
9
0.10
0.6
2
120
11
0.11
0.7
3
80
9
0.12
0.8
4
150
18
0.20
0.9
PROJECT
COST j
E(NOI)After-tax
j
r jm (correlation of j with market)
1
100
9
0.10
0.6
2
120
11
0.11
0.7
3
80
9
0.12
0.8
4
150
18
0.20
0.9
Explanation / Answer
Answer 1:
Kd = 0.06
Ke = 0.06+(0.12-0.06)*1 = 0.12
Unlevered WACC = 0.12 *1 = 12%.
Ke (levered) = 0.06+(0.12-0.06)*1.5 = 15%
Levered WACC = kd * (1-0.5)*0.5+Ke*0.5 = 0.06*0.5*0.5+0.15*0.5 =9%
Answer 2
Project 3 and 4 ranks higher with Project 3 leading in terms of NPV.
Project NPV Rf 6% E(Rm) 12% Project Sigma j Sigma m Cor (r,j) Beta Ke WACC 1 0.1 0.12 0.6 0.50 9.00% 6.00% 2 0.11 0.12 0.7 0.64 9.85% 6.43% Project 1 IRR (for 10 years NPV (Levered) Unlevered 3 0.12 0.12 0.8 0.80 10.80% 6.90% Cost -100 26% -16.34514466 -29.92465 4 0.2 0.12 0.9 1.50 15.00% 9.00% NOI 126 0.111111111 11.11 years Project 2 Cash Flow Cost -120 28% -20.3930006 -38.29962 Project Cost NOI after tax NOI 154 0.909090909 10.9 years 1 100 9 Project 3 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Cost -80 58% -0.816595271 -16.4939 1 0.943396 0.88999644 0.839619283 0.792093663 0.747258173 0.70496054 0.665057 0.627412 0.591898 0.558395 0.526788 0.496969 0.468839 0.442301 NOI 126 0.888888889 8.88 years -100 8.490566 8.00996796 7.556573547 7.128842969 6.725323556 6.344644864 5.985514 5.646711 5.327086 5.025553 4.741088 4.472724 4.219551 3.980709 Project 4 1 0.917431 0.841679993 0.77218348 0.708425211 0.649931386 0.596267327 0.547034 0.501866 0.460428 0.422411 0.387533 0.355535 0.326179 0.299246 Cost -150 68% -9.849293006 -46.95944 -100 8.256881 7.575119939 6.949651321 6.3758269 5.849382477 5.366405942 4.923308 4.516797 4.14385 3.801697 3.487796 3.199813 2.935608 2.693218 NOI 252 0.333333 8.33 years 144 2 120 11 1 0.910332 0.828704844 0.754396763 0.686751719 0.625172252 0.569114476 0.518083 0.471628 0.429338 0.39084 0.355795 0.323891 0.294849 0.26841 -120 10.01365 9.115753285 8.298364393 7.554268906 6.876894771 6.260259236 5.698916 5.187907 4.722719 4.299244 3.91374 3.562804 3.243336 2.952513 1 0.939629 0.882902369 0.829600535 0.779516594 0.732456278 0.688237048 0.646687 0.607646 0.570962 0.536492 0.504104 0.47367 0.445074 0.418205 -120 10.33592 9.711926063 9.125605885 8.574682532 8.057019058 7.570607524 7.113561 6.684107 6.28058 5.901414 5.545139 5.210373 4.895816 4.60025 3 80 9 1 0.902527 0.814555123 0.735158053 0.663500048 0.598826758 0.540457363 0.487777 0.440232 0.397322 0.358593 0.32364 0.292094 0.263623 0.237927 -80 8.122744 7.330996103 6.616422476 5.971500429 5.389440821 4.864116264 4.389997 3.962091 3.575894 3.227341 2.912763 2.628847 2.372606 2.141341 1 0.935454 0.875073616 0.818590847 0.765753833 0.716327252 0.670090975 0.626839 0.586379 0.54853 0.513125 0.480004 0.449022 0.420039 0.392927 -80 8.419083 7.87566254 7.367317624 6.891784494 6.44694527 6.030818775 5.641552 5.27741 4.936773 4.618123 4.32004 4.041197 3.780353 3.536345 4 150 18 1 0.869565 0.756143667 0.657516232 0.571753246 0.497176735 0.432327596 0.375937 0.326902 0.284262 0.247185 0.214943 0.186907 0.162528 0.141329 -150 15.65217 13.61058601 11.83529218 10.29155842 8.949181235 7.781896726 6.766867 5.884232 5.116723 4.449325 3.868978 3.364329 2.925503 2.543916 1 0.917431 0.841679993 0.77218348 0.708425211 0.649931386 0.596267327 0.547034 0.501866 0.460428 0.422411 0.387533 0.355535 0.326179 0.299246 -150 16.51376 15.15023988 13.89930264 12.7516538 11.69876495 10.73281188 9.846616 9.033593 8.2877 7.603395 6.975591 6.399625 5.871216 5.386436Related Questions
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