{"id":220421,"date":"2025-05-28T10:05:19","date_gmt":"2025-05-28T10:05:19","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=220421"},"modified":"2025-05-28T10:05:22","modified_gmt":"2025-05-28T10:05:22","slug":"yan-yan-corp","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/05\/28\/yan-yan-corp\/","title":{"rendered":"Yan Yan Corp"},"content":{"rendered":"\n

Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the price of the bond?<\/p>\n\n\n\n

Looking for the formula and breakdown.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the price of a bond<\/strong>, we use the present value (PV) formula<\/strong> that includes:<\/p>\n\n\n\n

    \n
  1. Present value of the coupon payments<\/strong> (annuity).<\/li>\n\n\n\n
  2. Present value of the par value<\/strong> (lump sum at maturity).<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Bond Price Formula<\/strong>:<\/h3>\n\n\n\n

    Price=\u2211t=1nC(1+r)t+F(1+r)n\\text{Price} = \\sum_{t=1}^{n} \\frac{C}{(1 + r)^t} + \\frac{F}{(1 + r)^n}<\/p>\n\n\n\n

    Where:<\/p>\n\n\n\n

      \n
    • CC = Coupon payment per period<\/li>\n\n\n\n
    • FF = Face (par) value of the bond<\/li>\n\n\n\n
    • rr = Periodic yield (YTM \/ number of periods per year)<\/li>\n\n\n\n
    • nn = Total number of periods (years \u00d7 number of periods per year)<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      Given:<\/strong><\/h3>\n\n\n\n
        \n
      • Par Value F=2,000F = 2{,}000<\/li>\n\n\n\n
      • Coupon Rate = 4.9% annually \u2192 C=0.049\u00d72,0002=49C = \\frac{0.049 \\times 2{,}000}{2} = 49 every 6 months<\/li>\n\n\n\n
      • YTM = 3.8% annually \u2192 periodic rate r=0.0382=0.019r = \\frac{0.038}{2} = 0.019<\/li>\n\n\n\n
      • Years to maturity = 13 \u2192 periods n=13\u00d72=26n = 13 \\times 2 = 26<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n

        Breakdown of Price Calculation:<\/strong><\/h3>\n\n\n\n

        1. Present value of coupon payments:<\/strong> PVcoupons=C\u00d7(1\u22121(1+r)n)\u00f7r\\text{PV}_{\\text{coupons}} = C \\times \\left(1 – \\frac{1}{(1 + r)^n}\\right) \\div r =49\u00d7(1\u22121(1.019)26)\u00f70.019=49\u00d7(1\u221211.558)\u00f70.019=49\u00d7(1\u22120.6417)\u00f70.019=49\u00d70.3583\u00f70.019\u224849\u00d718.8579\u2248924.04= 49 \\times \\left(1 – \\frac{1}{(1.019)^{26}}\\right) \\div 0.019 = 49 \\times \\left(1 – \\frac{1}{1.558}\\right) \\div 0.019 = 49 \\times (1 – 0.6417) \\div 0.019 = 49 \\times 0.3583 \\div 0.019 \\approx 49 \\times 18.8579 \\approx 924.04<\/p>\n\n\n\n

        2. Present value of par value:<\/strong> PVpar=2,000(1.019)26=2,0001.558\u22481,283.50\\text{PV}_{\\text{par}} = \\frac{2{,}000}{(1.019)^{26}} = \\frac{2{,}000}{1.558} \\approx 1{,}283.50<\/p>\n\n\n\n

        \n\n\n\n

        Total Price:<\/strong><\/h3>\n\n\n\n

        Price=PVcoupons+PVpar=924.04+1,283.50=2,207.54\\text{Price} = \\text{PV}_{\\text{coupons}} + \\text{PV}_{\\text{par}} = 924.04 + 1{,}283.50 = \\boxed{2{,}207.54}<\/p>\n\n\n\n

        \n\n\n\n

        Explanation (300 words):<\/strong><\/h3>\n\n\n\n

        The price of a bond represents the present value of all future cash flows expected from the bond. These include periodic interest payments (coupons) and the final repayment of the par value at maturity. Since money has a time value (i.e., a dollar today is worth more than a dollar tomorrow), future payments are discounted to their present value using the bond\u2019s yield to maturity (YTM), which reflects current market interest rates.<\/p>\n\n\n\n

        For Yan Yan Corp., the bond has a par value of $2,000 and pays a 4.9% annual coupon, which is $49 every six months due to semiannual payments. The bond\u2019s YTM is 3.8% annually or 1.9% per six-month period. Over the 13-year remaining term, there will be 26 such semiannual periods.<\/p>\n\n\n\n

        First, we calculate the present value of the 26 coupon payments using the present value of an annuity formula. This gives us the total value today of all the interest payments. Then, we compute the present value of the lump-sum $2,000 repayment at the end of 13 years, discounted back over 26 periods at the 1.9% periodic rate.<\/p>\n\n\n\n

        Adding both components together gives us the total bond price, which comes to $2,207.54<\/strong>. This price is above par because the bond\u2019s coupon rate (4.9%) is higher than the market YTM (3.8%), making it more attractive to investors. When coupon rates exceed market rates, investors are willing to pay a premium. Conversely, if coupon rates are lower than market rates, the bond sells at a discount.<\/p>\n\n\n\n

        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        Yan Yan Corp. has a $2,000 par value bond outstanding with a coupon rate of 4.9 percent paid semiannually and 13 years to maturity. The yield to maturity of the bond is 3.8 percent. What is the price of the bond? Looking for the formula and breakdown. The Correct Answer and Explanation is: To find […]<\/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-220421","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220421","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=220421"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/220421\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=220421"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=220421"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=220421"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}