{"id":8550,"date":"2020-12-17T13:01:04","date_gmt":"2020-12-17T13:01:04","guid":{"rendered":"https:\/\/analystprep.com\/blog\/?p=8550"},"modified":"2025-09-26T07:35:21","modified_gmt":"2025-09-26T07:35:21","slug":"timelines-your-best-friends-calculations-for-cfa-and-frm-exams","status":"publish","type":"post","link":"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/","title":{"rendered":"Timelines \u2013 Your Best Friends (Calculations for CFA\u00ae and FRM\u00ae Exams)"},"content":{"rendered":"<div style=\"width: 640px;\" class=\"wp-video\"><video class=\"wp-video-shortcode\" id=\"video-8550-1\" width=\"640\" height=\"360\" preload=\"metadata\" controls=\"controls\"><source type=\"video\/youtube\" src=\"https:\/\/www.youtube.com\/watch?v=XYrtVvDJK7w&#038;&#038;_=1\" \/><a href=\"https:\/\/www.youtube.com\/watch?v=XYrtVvDJK7w&#038;\">https:\/\/www.youtube.com\/watch?v=XYrtVvDJK7w&#038;<\/a><\/video><\/div>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_83 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#What_is_a_timeline\" >What is a timeline?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Quantitative_Methods\" >Quantitative Methods<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Capital_Budgeting\" >Capital Budgeting<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Example_Calculating_NPV_and_IRR_of_a_project\" >Example: Calculating NPV and IRR of a project<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Solution\" >Solution<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Equity_Valuation\" >Equity Valuation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Example_Equity_Valuation\" >Example: Equity Valuation<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Solution-2\" >Solution<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Bond_Valuation\" >Bond Valuation<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Types_of_bond_valuation\" >Types of bond valuation<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Derivatives_Pricing_Valuation\" >Derivatives Pricing &amp; Valuation<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Example_Forward_Derivative_Pricing_and_Valuation\" >Example: Forward Derivative Pricing and Valuation<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/analystprep.com\/blog\/timelines-your-best-friends-calculations-for-cfa-and-frm-exams\/#Solution-3\" >Solution<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_timeline\"><\/span><span class=\"primary-color\">What is a timeline?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A timeline is an physical illustration of the amount and the timing of cash flows associated with an investment project.<\/p>\n<p>Some of the applications of a timeline include:<\/p>\n<ul>\n<li>Quantitative Methods: Time Value of Money<\/li>\n<li>Capital Budgeting<\/li>\n<li>Equity Valuation<\/li>\n<li>Fixed Income Valuation<\/li>\n<li>Derivatives Pricing &amp; Valuation<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Quantitative_Methods\"><\/span><span class=\"primary-color\">Quantitative Methods<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The time value of money (TVM) is used in calculation of Future Values and Present values of investments, annuities, perpetuities, retirement planning, and mortgage payments. The time value of money (TVM) is based on the concept that money you have now is worth more than the identical sum in the future due to its potential earning capacity.<\/p>\n<p>An illustration of a timeline of future values and present values is as follows:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8659 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods-300x158.png\" alt=\"\" width=\"589\" height=\"310\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods-300x158.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods-400x210.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods-484x254.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods-570x300.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Qualitative-methods.png 641w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Capital_Budgeting\"><\/span><span class=\"primary-color\">Capital Budgeting<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Capital budgeting in corporate finance involves analyzing the concepts of net present value (NPV) and internal rate of return (IRR). We use NPV and IRR in determining the right project (in case of a single project) or the correct sequence of projects (in case of multiple projects) using NPV and IRR.<br \/>\nNPV and IRR help us in selecting the best possible project. For instance, when we have multiple projects, we will sort the various NPVs in descending order, such that we select the project with the highest positive NPV.<\/p>\n<p><em>Note:<\/em> we reject a project with a negative NPV.<\/p>\n<p>We calculate the Net Present Value (NPV) using the formulae given below:<\/p>\n<p>$$\\begin{align*}NPV=&amp;\\sum_{t=1}^n\\frac{CF_t}{(1-r)^t}-Outlay\\end{align*}$$<\/p>\n<p>Where,<\/p>\n<p>\\(CF_t\\)= after-tax cash flow at time t<\/p>\n<p>\\(r\\)= required rate of return for the investment<\/p>\n<p>\\(Outlay\\)= Initial Investment Cashflow<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Example_Calculating_NPV_and_IRR_of_a_project\"><\/span><span class=\"primary-color\">Example: Calculating NPV and IRR of a project<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Assuming Company XYZ is considering investing in a four-year project characterized with an initial investment of $100, an annual after-tax operating cash flows of $20 and a terminal after-tax operating cash flow of $33 at a required rate of return on 8%. Determine whether the project is worth investing in.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Solution\"><\/span><span class=\"primary-color\">Solution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>We know that,<\/p>\n<p>$$\\begin{align*}NPV=&amp;\\sum_{t=1}^n\\frac{CF_t}{(1-r)^t}-Outlay\\end{align*}$$<\/p>\n<p>Thus,<\/p>\n<p>$$\\begin{align*}{NPV}=&amp;\\frac{20}{1.08^1}+\\frac{20}{1.08^2}+\\frac{20}{1.08^3}+\\frac{33}{1.08^4}-100\\\\=&amp;18.519+17.147+15.1877+24.256-100\\\\=&amp;-$24.201 million\\end{align*}$$<\/p>\n<p>We realize that the NPV of this project is negative; therefore, we reject it.<br \/>\nA timeline can be used to illustrate this calculation, as shown below:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8661 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-300x92.png\" alt=\"\" width=\"581\" height=\"178\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-300x92.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-768x236.png 768w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-1024x315.png 1024w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-400x123.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-484x149.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1-570x175.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Capital-budgeting1.png 1086w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>The timeline implies that at year zero, we have a cash outflow of $100 (the initial investment), while at year one, two, three, and four, we have a cash inflow of $20, $20, $20, $33, respectively.<\/p>\n<p>Also, we can calculate the IRR using excel, where;<\/p>\n<p>$$-100+\\frac{20}{(1+IRR)^1}+\\frac{20}{(1+IRR)^2}+\\frac{20}{(1+IRR)^3}+\\frac{33}{(1+IRR)^4}=0:IRR=-2.62\\%$$<\/p>\n<blockquote class=\"wp-embedded-content\" data-secret=\"dP1cRUZSJc\"><p><a href=\"https:\/\/analystprep.com\/shop\/unlimited-package-for-frm-part-i-part-ii\/\">Unlimited Package (for FRM Part I &#038; Part II)<\/a><\/p><\/blockquote>\n<p><iframe loading=\"lazy\" class=\"wp-embedded-content\" sandbox=\"allow-scripts\" security=\"restricted\" style=\"position: absolute; clip: rect(1px, 1px, 1px, 1px);\" title=\"&#8220;Unlimited Package (for FRM Part I &#038; Part II)&#8221; &#8212; AnalystPrep\" src=\"https:\/\/analystprep.com\/shop\/unlimited-package-for-frm-part-i-part-ii\/embed\/#?secret=dP1cRUZSJc\" data-secret=\"dP1cRUZSJc\" width=\"600\" height=\"338\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\"><\/iframe><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Equity_Valuation\"><\/span><span class=\"primary-color\">Equity Valuation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>An equity valuation involves using the dividend discount model, the free cash flow model, and the residual income model to value a stock. These models rely on discounting the cash flows. The method of computing the equity valuation remains the same despite determining the different cash flows that change in the different models. After determining what these cash flows are, you will put them on a timeline and then discounted them back to time zero. The application of the timeline is the same across all three models.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Example_Equity_Valuation\"><\/span><span class=\"primary-color\">Example: Equity Valuation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">For the next three years, the annual dividends of a stock are expected to be \u20ac1.00, \u20ac1.50, and \u20ac2.0.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">The stock price is expected to be \u20ac20.00 at the end of three years.\u00a0<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">If the required rate of return on the shares is 10 percent, what is the estimated value of a share?<\/span><\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Solution-2\"><\/span><span class=\"primary-color\">Solution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>By applying the timeline we see that;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-8584 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-300x63.png\" alt=\"\" width=\"576\" height=\"121\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-300x63.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-768x162.png 768w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-400x84.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-484x102.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222-570x120.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Equity-Valuation-222.png 1012w\" sizes=\"auto, (max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Where;<\/p>\n<p><span style=\"font-weight: 400;\">$$\\begin{align*}V_0&amp;=\\frac{1.0}{1.1}+\\frac{1.5}{1.1^2}+\\frac{(2.0+20)}{1.1^3}\\\\&amp;= 18.67\\end{align*}$$<\/span><\/p>\n<p>According to this calculation, the stock should be valued at\u00a0\u20ac18.67; thus, if in the market, the value is higher than\u00a0\u20ac18.67, then we should not buy that stock because it is <em>overvalued.\u00a0<\/em>However, if the stock market value is less than\u00a0\u20ac18.67, it means that it is\u00a0<em>undervalued, <\/em>and we should go ahead and buy that stock.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Bond_Valuation\"><\/span><span class=\"primary-color\">Bond Valuation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Bond valuation is a method used to determine the theoretical fair value of a particular bond.\u00a0\u00a0It involves calculating the present value of a\u00a0<b>bond&#8217;s<\/b>\u00a0expected future coupon payments, or cash flow, and the\u00a0<b>bond&#8217;s<\/b>\u00a0value upon maturity, or face value.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Types_of_bond_valuation\"><\/span>Types of bond valuation<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>Plain vanilla bond<\/li>\n<li>Zero coupon bonds<\/li>\n<li>Deferred coupon bonds<\/li>\n<li>Step-up bonds<\/li>\n<\/ul>\n<p>Regardless of the type of bond we are dealing with, the valuation occurs in the timeline only. The bond valuation is similar to equity valuation, only that we take the coupons as the cashflow.<\/p>\n<p>The timeline below illustrate bond valuation:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-8662 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-300x78.png\" alt=\"\" width=\"654\" height=\"170\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-300x78.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-768x200.png 768w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-1024x267.png 1024w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-400x104.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-484x126.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1-570x149.png 570w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Bond-Valuation1.png 1047w\" sizes=\"auto, (max-width: 654px) 100vw, 654px\" \/><\/p>\n<p>Where:<\/p>\n<p>\\(C\\)= Coupon on the bond, i.e., what the issuer is giving<\/p>\n<p>\\(Y\\)= Yield to Maturity (YTM), i.e., minimum rate that we require, given the risk<\/p>\n<p>The value of the bond depends on the relationship between the Coupon of the bond (C) and Yield to Maturity (Y), where:<\/p>\n<ul>\n<li>If \\(C&gt;Y\\), then the bond trades at a premium<\/li>\n<li>If \\(C&lt;Y\\), then the bond trades at a discount<\/li>\n<li>If \\(C=Y\\), then the bond trades at the par value<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Derivatives_Pricing_Valuation\"><\/span><span class=\"primary-color\">Derivatives Pricing &amp; Valuation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The different types of derivative pricing and valuation include:<\/p>\n<ul>\n<li>Forwards<\/li>\n<li>Futures<\/li>\n<li>Forward Rate Agreements (FRAs)<\/li>\n<li>Options<\/li>\n<li>Swaps<\/li>\n<\/ul>\n<p>All of these types are valued using the timeline. However, the complexity could increase when dealing with options and swaps, but the fundamental mathematical concept is the timeline of discounted cashflows.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Example_Forward_Derivative_Pricing_and_Valuation\"><\/span><span class=\"primary-color\">Example: Forward Derivative Pricing and Valuation<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Assuming that:<\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Spot Price of a stock is $90<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">The risk-free rate is 4% p.a.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Forward contract expires in one year<\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">What is the correct forward price?<\/span><\/p>\n<h4><span class=\"ez-toc-section\" id=\"Solution-3\"><\/span><span class=\"primary-color\">Solution<\/span><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>Applying the timeline we have:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone  wp-image-8663 aligncenter\" src=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Pricing-and-valuation-300x183.png\" alt=\"\" width=\"491\" height=\"299\" srcset=\"https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Pricing-and-valuation-300x183.png 300w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Pricing-and-valuation-400x245.png 400w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Pricing-and-valuation-484x296.png 484w, https:\/\/analystprep.com\/blog\/wp-content\/uploads\/2020\/12\/Pricing-and-valuation.png 533w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Therefore, Forward Pricing Equation is given as:<\/p>\n<p>$$\\begin{align*}{F_0(T)}=&amp;{S_0(1+r)^t}\\end{align*}$$<\/p>\n<p>Where:<\/p>\n<p>\\(F_0(T)\\)= Forward pricing<\/p>\n<p>\\(s_0\\)= spot price<\/p>\n<p>\\(t\\)= time<\/p>\n<p>\\(r\\)= risk-free rate<\/p>\n<p>Thus,<\/p>\n<p>$$\\begin{align*}=&amp;90(1+0.04)^1\\\\=&amp;93.6 \\text{dollars}\\end{align*}$$<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What is a timeline? A timeline is an physical illustration of the amount and the timing of cash flows associated with an investment project. Some of the applications of a timeline include: Quantitative Methods: Time Value of Money Capital Budgeting&#8230;<\/p>\n","protected":false},"author":4,"featured_media":8602,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[70,71],"tags":[78,83,99],"class_list":["post-8550","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cfa","category-frm","tag-cfa","tag-frm","tag-timeline","blog-post","animate"],"acf":[],"post_mailing_queue_ids":[],"_links":{"self":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8550","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/comments?post=8550"}],"version-history":[{"count":31,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8550\/revisions"}],"predecessor-version":[{"id":9710,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/posts\/8550\/revisions\/9710"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media\/8602"}],"wp:attachment":[{"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/media?parent=8550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/categories?post=8550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/analystprep.com\/blog\/wp-json\/wp\/v2\/tags?post=8550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}