{"id":198836,"date":"2025-03-10T12:28:51","date_gmt":"2025-03-10T12:28:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198836"},"modified":"2025-03-10T12:28:53","modified_gmt":"2025-03-10T12:28:53","slug":"two-companies-are-identical-in-all-respects-except-that-x-ltd","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/10\/two-companies-are-identical-in-all-respects-except-that-x-ltd\/","title":{"rendered":"Two companies are identical in all respects except that X Ltd"},"content":{"rendered":"\n

Two companies are identical in all respects except that X Ltd., has debt of Rs 5,00,000 borrowed at the rate of 12% whereas Y Ltd., has no debt in its capital structure. The total assets of both the companies amount to Rs 15,00,000 on which the companies have earnings of 20%. You are required to do the following: <\/p>\n\n\n\n

(i) Calculate value of companies and k0 using NI approach taking ke as 18%. <\/p>\n\n\n\n

(ii) Calculate value of companies and ke using NOI approach taking k0 as 18%. (iii) Compare the results and comment on the difference of the two approaches.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

Explanation<\/h3>\n\n\n\n

In this problem, we analyze two companies, X Ltd. (leveraged) and Y Ltd. (unleveraged), under the Net Income (NI) Approach<\/strong> and Net Operating Income (NOI) Approach<\/strong> to determine their value and cost of capital.<\/p>\n\n\n\n

\n\n\n\n

(i) NI Approach<\/strong><\/h3>\n\n\n\n

The NI approach<\/strong> assumes that the cost of equity (ke) remains constant and that the firm can increase its value by using cheaper debt financing.<\/p>\n\n\n\n

    \n
  • X Ltd. (Leveraged)<\/strong><\/li>\n\n\n\n
  • Interest on debt = ( 500,000 \\times 12\\% = 60,000 )<\/li>\n\n\n\n
  • Net income = ( (15,00,000 \\times 20\\%) – 60,000 = 240,000 )<\/li>\n\n\n\n
  • Value of equity = ( 240,000 \/ 18\\% = 1,333,333 )<\/li>\n\n\n\n
  • Value of firm = Equity + Debt = ( 1,333,333 + 500,000 = 1,833,333 )<\/li>\n\n\n\n
  • Overall cost of capital ( k_0 ) = ( 300,000 \/ 1,833,333 = 16.36\\% )<\/li>\n\n\n\n
  • Y Ltd. (Unleveraged)<\/strong><\/li>\n\n\n\n
  • Net income = ( 15,00,000 \\times 20\\% = 300,000 )<\/li>\n\n\n\n
  • Value of firm = ( 300,000 \/ 18\\% = 1,666,667 )<\/li>\n\n\n\n
  • Overall cost of capital ( k_0 = 18\\% )<\/li>\n<\/ul>\n\n\n\n

    \ud83d\udd39 Conclusion (NI Approach):<\/strong><\/p>\n\n\n\n

      \n
    • X Ltd. (with debt) has a higher firm value than Y Ltd. due to lower financing costs.<\/li>\n\n\n\n
    • The cost of capital ( k_0 ) decreases due to cheaper debt financing.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      (ii) NOI Approach<\/strong><\/h3>\n\n\n\n

      The NOI approach<\/strong> assumes that the firm’s overall cost of capital (k0) remains constant, irrespective of capital structure.<\/p>\n\n\n\n

        \n
      • Firm value for both X Ltd. and Y Ltd.:<\/strong><\/li>\n\n\n\n
      • ( Value = EBIT \/ k_0 = 300,000 \/ 18\\% = 1,666,667 )<\/li>\n\n\n\n
      • Cost of Equity (ke) for X Ltd.:<\/strong><\/li>\n\n\n\n
      • ( ke = k_0 + (k_0 – Interest Rate) \\times (Debt \/ Equity) )<\/li>\n\n\n\n
      • ( ke = 18\\% + (18\\% – 12\\%) \\times (500,000 \/ 1,166,667) = 20.57\\% )<\/li>\n<\/ul>\n\n\n\n

        \ud83d\udd39 Conclusion (NOI Approach):<\/strong><\/p>\n\n\n\n

          \n
        • The firm\u2019s value remains the same, regardless of capital structure.<\/li>\n\n\n\n
        • Higher debt increases the cost of equity due to increased financial risk.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          (iii) Comparison and Comments<\/strong><\/h3>\n\n\n\n
            \n
          • Under the NI approach<\/strong>, X Ltd. (leveraged) has a higher firm value because it benefits from cheaper debt.<\/li>\n\n\n\n
          • Under the NOI approach<\/strong>, the firm\u2019s value remains unchanged, as it assumes an increase in the cost of equity offsets the benefit of debt financing.<\/li>\n\n\n\n
          • Key Difference:<\/strong> The NI approach supports leverage to increase firm value, while the NOI approach states that leverage does not impact the overall value.<\/li>\n<\/ul>\n\n\n\n

            Thus, Modigliani & Miller’s irrelevance theorem<\/strong> aligns more with the NOI approach<\/strong>, stating that in a perfect market, capital structure does not impact firm value.<\/p>\n","protected":false},"excerpt":{"rendered":"

            Two companies are identical in all respects except that X Ltd., has debt of Rs 5,00,000 borrowed at the rate of 12% whereas Y Ltd., has no debt in its capital structure. The total assets of both the companies amount to Rs 15,00,000 on which the companies have earnings of 20%. You are required to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-198836","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198836","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=198836"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198836\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198836"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198836"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198836"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}