Assume the probability distributions for ( R ) and ( R_{T}^{*} ) are normal and you are given the following information. [ ar{R}_{mathrm{T}}^{*}=7 % quad sigmaleft(mathrm{R}_{mathrm{T}}^{*} ight)=4 % quad au=.40 ] Management is considering a capital structure with ( mathrm{L}=.50 ). With this capital structure, ( mathrm{k}_{mathrm{d}} ) will be ( 10 % ) and ( mathrm{k}_{mathrm{e}} ) will be ( 15 % ). What is the probability of achieving an ( R ) greater than ( mathrm{k}_{mathrm{e}} ) ? Suppose management wants the probability from part a to be ( 72 % ). With everything else equal, what would the necessary increase in ( ar{R}_{T}^{*} ) have to be to get a ( 72 % ) chance of having ( mathrm{R} ) greater than ( mathrm{k}_{mathrm{e}} ) ?
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Step 1: The geometric distribution function of X is defined as \(P(X < x) = 1 - Q^{x}\), where \(Q = 1 - P\). Show more…
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