Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of \u20ac1,000, 12 years to maturity, and a coupon rate of 6 percent paid annually. If the yield to maturity is 9 percent, what is the current price of the bond?
Multiple Choice
$745.92
\u20ac82444
\u20ac1255.52
\u20ac785.18
\u20ac1,030.00<\/p>\n\n\n\n
The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n To calculate the current price of the bond, we use the present value formula for bonds. The price of a bond is the present value of the bond\u2019s future cash flows, which consist of the annual coupon payments and the face value (par value) paid at maturity. Here’s how we can calculate it:<\/p>\n\n\n\n The price of the bond is the sum of:<\/p>\n\n\n\n The general formula for a bond price is:<\/p>\n\n\n\n [ Where:<\/p>\n\n\n\n The present value of the coupon payments is calculated using the following:<\/p>\n\n\n\n [ [ The present value of the par value (which will be paid at maturity) is:<\/p>\n\n\n\n [ Now, we add the present values of the coupons and the face value to get the bond price:<\/p>\n\n\n\n [ Thus, the bond price is approximately \u20ac785.18<\/strong>.<\/p>\n\n\n\n The correct answer is \u20ac785.18<\/strong>. This is the price of the bond given the yield to maturity of 9%, the coupon rate of 6%, and the 12-year maturity.<\/p>\n","protected":false},"excerpt":{"rendered":" Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of \u20ac1,000, 12 years to maturity, and a coupon rate of 6 percent paid annually. If the yield to maturity is 9 percent, […]<\/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-189004","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189004","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=189004"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/189004\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=189004"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=189004"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=189004"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}Step 1: Formula for Bond Price<\/h3>\n\n\n\n
\n
P = C \\times \\left( \\frac{1 – (1 + r)^{-n}}{r} \\right) + \\frac{F}{(1 + r)^n}
]<\/p>\n\n\n\n\n
Step 2: Calculating the Present Value of the Coupons<\/h3>\n\n\n\n
PV_{\\text{coupons}} = 60 \\times \\left( \\frac{1 – (1 + 0.09)^{-12}}{0.09} \\right)
]<\/p>\n\n\n\n
PV_{\\text{coupons}} = 60 \\times 7.1075 = 426.45
]<\/p>\n\n\n\nStep 3: Calculating the Present Value of the Par Value<\/h3>\n\n\n\n
PV_{\\text{par}} = \\frac{1,000}{(1 + 0.09)^{12}} = \\frac{1,000}{2.8138} = 355.79
]<\/p>\n\n\n\nStep 4: Calculating the Total Price<\/h3>\n\n\n\n
P = 426.45 + 355.79 = 782.24
]<\/p>\n\n\n\nConclusion:<\/h3>\n\n\n\n