{"id":202583,"date":"2025-03-17T17:23:30","date_gmt":"2025-03-17T17:23:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=202583"},"modified":"2025-03-17T17:23:32","modified_gmt":"2025-03-17T17:23:32","slug":"a-new-business-will-generate-a-one-time-cash-flow-of-22000-after-one-year","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/17\/a-new-business-will-generate-a-one-time-cash-flow-of-22000-after-one-year\/","title":{"rendered":"A new business will generate a one-time cash flow of $22,000 after one year"},"content":{"rendered":"\n

A new business will generate a one-time cash flow of $22,000 after one year. The business will be financed with 80% equity and 40% debt. If the firm’s unlevered equity cost of capital is 11%, what is the levered value of the firm with perfect capital markets? <\/p>\n\n\n\n

A. $18,182 <\/p>\n\n\n\n

B. $19,580 <\/p>\n\n\n\n

C. $19,820 <\/p>\n\n\n\n

D. $24,200 <\/p>\n\n\n\n

E. $20,000<\/p>\n\n\n\n

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

The correct answer is B. $19,580<\/strong>.<\/p>\n\n\n\n

To determine the levered value of the firm<\/strong>, we need to calculate the value of the firm using perfect capital markets<\/strong> and the Modigliani-Miller Proposition I<\/strong> (M&M Proposition I), which states that in perfect capital markets, the value of the firm is independent of its capital structure. However, we need to calculate the levered value<\/strong> considering debt financing.<\/p>\n\n\n\n

Steps to solve:<\/h3>\n\n\n\n
    \n
  1. Unlevered Value of the Firm:<\/strong>
    First, we calculate the unlevered value<\/strong> of the firm (V_u), which is the present value of the future cash flow generated by the firm assuming no debt. The formula for the unlevered value (V_u) is:
    [
    V_u = \\frac{CF}{(1 + r_u)}
    ]
    Where:<\/li>\n<\/ol>\n\n\n\n
      \n
    • ( CF ) = cash flow generated by the business = $22,000<\/li>\n\n\n\n
    • ( r_u ) = unlevered cost of equity = 11% or 0.11 Plugging the numbers:
      [
      V_u = \\frac{22,000}{1.11} = 19,820
      ] So, the unlevered value<\/strong> of the firm is $19,820<\/strong>.<\/li>\n<\/ul>\n\n\n\n
        \n
      1. Levered Value of the Firm:<\/strong>
        Under perfect capital markets, the levered value<\/strong> is the same as the unlevered value because the debt does not affect the total value of the firm. There are no taxes or bankruptcy costs to consider. Therefore, the levered value<\/strong> of the firm will also be $19,820<\/strong>.<\/li>\n<\/ol>\n\n\n\n

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

        In perfect capital markets, the value of the firm is determined by its cash flows and risk-adjusted cost of equity<\/strong> (or the discount rate). The capital structure (i.e., whether the firm is financed with debt or equity) does not affect the overall firm value.<\/p>\n\n\n\n

        Thus, the firm’s total value, whether levered or unlevered, remains $19,820<\/strong>, which matches the calculation. Option C<\/strong> ($19,820) is the correct answer.<\/p>\n\n\n\n

        Why are other options incorrect?<\/h3>\n\n\n\n
          \n
        • A. $18,182<\/strong>: This is incorrect because it\u2019s too low. This might be the result of using an incorrect discount rate.<\/li>\n\n\n\n
        • D. $24,200<\/strong>: This is too high. It doesn’t fit with the unlevered value calculation.<\/li>\n\n\n\n
        • E. $20,000<\/strong>: This is close but still off from the calculated value of $19,820.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"

          A new business will generate a one-time cash flow of $22,000 after one year. The business will be financed with 80% equity and 40% debt. If the firm’s unlevered equity cost of capital is 11%, what is the levered value of the firm with perfect capital markets? A. $18,182 B. $19,580 C. $19,820 D. $24,200 […]<\/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-202583","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202583","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=202583"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202583\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=202583"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=202583"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=202583"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}