{"id":3088,"date":"2023-07-30T16:06:01","date_gmt":"2023-07-30T16:06:01","guid":{"rendered":"https:\/\/slyman.org\/blog\/?p=3088"},"modified":"2023-07-30T16:06:44","modified_gmt":"2023-07-30T16:06:44","slug":"modigliani-miller-theorem-from-wacc-algebraic-proof","status":"publish","type":"post","link":"https:\/\/slyman.org\/blog\/2023\/07\/modigliani-miller-theorem-from-wacc-algebraic-proof\/","title":{"rendered":"Modigliani-Miller Theorem from WACC (algebraic proof)"},"content":{"rendered":"\n<p>Starting with the formula for WACC (Weighted Average Cost of Capital) adjusted to express weights as quotients, we can prove the Modigliani-Miller Theorem as follows.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"945\" height=\"1024\" src=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-945x1024.jpg\" alt=\"\" class=\"wp-image-3089\" srcset=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-945x1024.jpg 945w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-277x300.jpg 277w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-768x832.jpg 768w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-1418x1536.jpg 1418w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_0914566872-1890x2048.jpg 1890w\" sizes=\"auto, (max-width: 945px) 100vw, 945px\" \/><\/a><\/figure>\n\n\n\n<p>Further, starting from the WACC formula, here is some algebra proving the <strong>Modigliani-Miller Theorem with Tax<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-scaled.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"978\" height=\"1024\" src=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-978x1024.jpg\" alt=\"\" class=\"wp-image-3090\" srcset=\"https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-978x1024.jpg 978w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-287x300.jpg 287w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-768x804.jpg 768w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-1468x1536.jpg 1468w, https:\/\/slyman.org\/blog\/wp-content\/uploads\/2023\/07\/IMG_20230725_113257724-1957x2048.jpg 1957w\" sizes=\"auto, (max-width: 978px) 100vw, 978px\" \/><\/a><\/figure>\n\n\n\n<p>I wrote this out because this proof isn&#8217;t included in the <a href=\"https:\/\/quantic.edu\/\" data-type=\"URL\" data-id=\"https:\/\/quantic.edu\/\">Quantic<\/a> EMBA course notes.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Starting with the formula for WACC (Weighted Average Cost of Capital) adjusted to express weights as quotients, we can prove the Modigliani-Miller Theorem as follows. Further, starting from the WACC formula, here is some algebra proving the Modigliani-Miller Theorem with &hellip; <a href=\"https:\/\/slyman.org\/blog\/2023\/07\/modigliani-miller-theorem-from-wacc-algebraic-proof\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[369],"tags":[372,370,371],"class_list":["post-3088","post","type-post","status-publish","format-standard","hentry","category-quantic-emba","tag-algebraic-proof","tag-modigliani-miller-theorem","tag-wacc"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/posts\/3088","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/comments?post=3088"}],"version-history":[{"count":2,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/posts\/3088\/revisions"}],"predecessor-version":[{"id":3092,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/posts\/3088\/revisions\/3092"}],"wp:attachment":[{"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/media?parent=3088"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/categories?post=3088"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/slyman.org\/blog\/wp-json\/wp\/v2\/tags?post=3088"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}