{"id":29630,"date":"2024-07-21T19:48:25","date_gmt":"2024-07-22T00:48:25","guid":{"rendered":"https:\/\/breakingintowallstreet.com\/?post_type=biws_kb&#038;p=29630"},"modified":"2024-11-19T22:45:30","modified_gmt":"2024-11-20T03:45:30","slug":"time-value-of-money","status":"publish","type":"biws_kb","link":"https:\/\/breakingintowallstreet.com\/kb\/finance\/time-value-of-money\/","title":{"rendered":"The Time Value of Money: Excel Calculations and Real-Life Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_81 counter-flat 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\">The Time Value of Money: Excel Calculations and Real-Life Examples<\/p>\n<span class=\"ez-toc-title-toggle\"><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/time-value-of-money\/#How_to_Apply_the_Time_Value_of_Money_in_Real_Life_Renting_an_Apartment\">How to Apply the Time Value of Money in Real Life: Renting an Apartment<\/a><\/li><li class='ez-toc-page-1'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/time-value-of-money\/#How_to_Apply_the_Time_Value_of_Money_in_Investment_Decisions\">How to Apply the Time Value of Money in Investment Decisions<\/a><\/li><li class='ez-toc-page-1'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/time-value-of-money\/#The_Time_Value_of_Money_Key_Takeaways\">The Time Value of Money: Key Takeaways<\/a><\/li><\/ul><\/nav><\/div>\n\n<blockquote><p><b>Time Value of Money Definition:<\/b> The time value of money means that money today is worth MORE than money tomorrow because you could invest it today and earn something on it the future.<\/p><\/blockquote>\n<p>For example, if you have $100 today, that $100 is worth more NOW than in a year from now because you could invest that $100 today and end up with $105 or $110 in a year.<\/p>\n<p><strong>The time value of money is critical in valuation because it is the foundation behind <a href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/present-value\/\" target=\"_blank\" rel=\"noopener\">Present Value<\/a> and <a href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/net-present-value\/\" target=\"_blank\" rel=\"noopener\">Net Present Value<\/a>, which determine what assets and companies are worth.<\/strong><\/p>\n<p><span>You have to discount future cash flow <\/span>to its Present Value based on your opportunity cost, i.e., what you would earn on it today if you invested it in other, similar opportunities.<\/p>\n<p>Many people misunderstand this concept and think that future cash flow is less valuable just because of inflation.<\/p>\n<p>It is true that inflation makes uninvested money less valuable over time.<\/p>\n<p>However, the <strong>REAL<\/strong> reason that future cash flow is less valuable than cash flow today is because of the <strong>time value of money<\/strong>.<\/p>\n<h3><strong>Files &amp; Resources:<\/strong><\/h3>\n<ul>\n<li><a href=\"https:\/\/youtube-breakingintowallstreet-com.s3.us-east-1.amazonaws.com\/Finance\/Time-Value-of-Money.xlsx\" target=\"_blank\" rel=\"noopener\">The Time Value of Money &#8211; Examples (XL)<\/a><\/li>\n<li><a href=\"https:\/\/youtube-breakingintowallstreet-com.s3.us-east-1.amazonaws.com\/Finance\/BIWS-Present-Value-Examples.xlsx\" target=\"_blank\" rel=\"noopener\">Present Value Calculations &#8211; Examples (XL)<\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Apply_the_Time_Value_of_Money_in_Real_Life_Renting_an_Apartment\"><\/span><strong>How to Apply the Time Value of Money in Real Life: Renting an Apartment<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>As an example of this concept, we&#8217;ll examine South Korea\u2019s \u201cunique\u201d real estate system (yes, I spent some time there a long time ago).<\/p>\n<p>When you rent an apartment there, there are two options: \uc804\uc138 (Jeon-se) and \uc6d4\uc138 (Wol-se). We\u2019ll label these choices Options #1 and #2.<\/p>\n<ul>\n<li><strong>Option #1:<\/strong> You pay an upfront deposit for 50 &#8211; 80% of the apartment\u2019s value, but you pay no monthly rent, and you get the deposit back at the end.<\/li>\n<li><strong>Option #2:<\/strong> You pay an upfront deposit for 5 &#8211; 10% of the apartment\u2019s value, but you pay monthly rent, and you get the deposit back at the end.<\/li>\n<\/ul>\n<p>Let\u2019s use some specific numbers and say that the apartment is worth <strong>$200,000<\/strong> ($200K).<\/p>\n<p>Here\u2019s what <strong>Option #1<\/strong> looks like:<\/p>\n<ul>\n<li>Deposit of $150K (75% of apartment\u2019s value).<\/li>\n<li><strong>No monthly rent<\/strong>.<\/li>\n<li>Get back $150K deposit after 2 years.<\/li>\n<\/ul>\n<p>And here\u2019s what <strong>Option #2<\/strong> looks like:<\/p>\n<ul>\n<li>Deposit of $10K (5% of apartment\u2019s value).<\/li>\n<li><strong>Monthly rent of $1K (Yearly at $12K, so $24K for two years).<\/strong><\/li>\n<li>Get back $10K deposit after 2 years.<\/li>\n<\/ul>\n<p>To many people, the options look like this:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-29740 size-full\" title=\"Time Value of Money - Large Upfront Deposit\" src=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193256\/TVM1.jpg\" alt=\"Time Value of Money - Large Upfront Deposit\" width=\"1060\" height=\"220\" srcset=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193256\/TVM1.jpg 1060w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193256\/TVM1-300x62.jpg 300w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193256\/TVM1-1024x213.jpg 1024w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193256\/TVM1-768x159.jpg 768w\" sizes=\"(max-width: 1060px) 100vw, 1060px\" \/><\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-29741 size-full\" title=\"Time Value of Money - Smaller Deposit and Annual Rent\" src=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193339\/TVM2.jpg\" alt=\"Time Value of Money - Smaller Deposit and Annual Rent\" width=\"1052\" height=\"232\" srcset=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193339\/TVM2.jpg 1052w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193339\/TVM2-300x66.jpg 300w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193339\/TVM2-1024x226.jpg 1024w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193339\/TVM2-768x169.jpg 768w\" sizes=\"(max-width: 1052px) 100vw, 1052px\" \/><\/p>\n<p>With Option 1, you first pay a deposit of $150K, and you get $150K back in Year 2 with no monthly rent.<\/p>\n<p>On the surface, it seems like you have not &#8220;lost&#8221; any money ($150K in Year 2 &#8211; $150K Deposit = 0).<\/p>\n<p>With Option 2, it looks like you &#8220;lose&#8221; $24K because you pay a $10K deposit upfront and annual rent of $12K for two years, and then you receive back the $10K deposit in Year 2.<\/p>\n<p>So, to many people, Option 1 sees like the better option because you do not lose the $24K of rent.<\/p>\n<p><strong>However, this is not an accurate comparison because of the following:<\/strong><\/p>\n<ol>\n<li>$150K received back in 2 years is worth <strong>LESS<\/strong> than $150K today. Even if we receive back \u201cthe same amount\u201d in the future, <strong>it\u2019s worth less than it is today<\/strong>.<\/li>\n<li>Paying <strong>$140K more<\/strong> for the deposit means that you <strong>CANNOT<\/strong> invest that $140K elsewhere and earn something with it. So, there\u2019s an <strong>opportunity cost<\/strong> associated with a higher deposit. You could have used that $140K to invest and earned more over these 2 years.<\/li>\n<\/ol>\n<p>Let\u2019s use Excel to illustrate these points:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-29742 size-full\" title=\"Time Value of Money - Opportunity Cost + &quot;Money Lost&quot;\" src=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193419\/TVM3.jpg\" alt=\"Time Value of Money - Opportunity Cost + &quot;Money Lost&quot;\" width=\"1222\" height=\"1038\" srcset=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193419\/TVM3.jpg 1222w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193419\/TVM3-300x255.jpg 300w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193419\/TVM3-1024x870.jpg 1024w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193419\/TVM3-768x652.jpg 768w\" sizes=\"(max-width: 1222px) 100vw, 1222px\" \/><\/p>\n<p>If we look at the Opportunity Cost + \u201cMoney Lost\u201d with Option #1, it&#8217;s $24K.<\/p>\n<p>With Option #1, we pay no rent, but we do pay an <em>extra<\/em> $140K upfront.<\/p>\n<p><strong>To determine if Option #1 or #2 is better, we need to know what we could EARN with this extra $140K.<\/strong><\/p>\n<p>In this example:<\/p>\n<ul>\n<li><strong>Year 1 Lost Earnings<\/strong> = $140K Deposit Difference * 8.2% Opportunity Cost = ~$12K<\/li>\n<li><strong>Year 2 Lost Earnings<\/strong> = (~12K Lost in Year 1 + $140K Deposit Difference) * 8.2% Opportunity Cost = ~$24K<\/li>\n<\/ul>\n<p><strong>So, in total, you could have earned $24K extra by paying a $140K lower upfront deposit.<\/strong><\/p>\n<p><strong>Therefore, in this case, the outcome is the same at an 8.2% opportunity cost, even though Option #2 &#8220;looks&#8221; worse due to the annual rent.<\/strong><\/p>\n<p>We use <em>the deposit difference<\/em> here because even with Option #2, we would still have to pay the $10K upfront deposit.<\/p>\n<p>So, it would not be correct to use the $150K total deposit under Option #1 as the comparison point here.<\/p>\n<p>If we use a higher percentage for the opportunity cost, the &#8220;Money Lost&#8221; is even greater with Option #1:<\/p>\n<p><img decoding=\"async\" class=\"aligncenter wp-image-29743 size-full\" title=\"Time Value of Money - Higher Opportunity Cost\" src=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193457\/TVM4.jpg\" alt=\"Time Value of Money - Higher Opportunity Cost\" width=\"1220\" height=\"964\" srcset=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193457\/TVM4.jpg 1220w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193457\/TVM4-300x237.jpg 300w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193457\/TVM4-1024x809.jpg 1024w, https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/07\/21193457\/TVM4-768x607.jpg 768w\" sizes=\"(max-width: 1220px) 100vw, 1220px\" \/><\/p>\n<p>By contrast, Option #2 still costs us only $24K.<\/p>\n<p>So, with this opportunity cost, Option #2 is superior even though it <em>seems<\/em> to result in more &#8220;money lost&#8221; on paper.<\/p>\n<div class='code-block code-block-2' style='margin: 8px 0; clear: both;'>\n<div class=\"kb-adinsert-modal\">\n    <div class=\"kb-adinsert-top\">\n      <div class=\"media\">\n          <img decoding=\"async\" class=\"alignnone size-full wp-image-28448\" src=\"https:\/\/biwsuploads-assest.s3.amazonaws.com\/biws\/wp-content\/uploads\/2024\/04\/24164120\/adv-fm-tile.png\" alt=\"PowerPoint Pro\" width=\"128\" height=\"128\" \/>\n      <\/div>\n      <div class=\"content\">\n          <h3>Master Financial Modeling for Investment Banking With <strong>BIWS Core Financial Modeling<\/strong><\/h3>\n      <\/div>\n    <\/div>\n    \n    <div class=\"full_text\">\n    \t<ul>\n        \t<li>\n            \t<h4>Become a financial modeling pro<\/h4>\n              <p>158 videos, detailed written guides, Excel files, quizzes, and more<\/p>\n\t\t\t    <\/li>\n          <li>\n          \t<h4>Complete 10+ detailed global case studies<\/h4>\n            <p>These include both the theory and the practical applications<\/p>\n\t\t\t    <\/li>\n          <li>\n          \t<h4>Prepare for your internship or full-time job<\/h4>\n            <p>Gain the skills you need to \u201chit the ground running\u201d on Day 1\n\n<\/p>\n\t\t\t  <\/li>\n      <\/ul>\n        \n      <a class=\"cta-link orange-button-medium\" href=\"https:\/\/breakingintowallstreet.com\/core-financial-modeling\/\" target=\"_blank\">Full Details<\/a>\n      \n      <a class=\"cta-link orange-button-medium bg-blue\" href=\"https:\/\/biws-support.s3.us-east-1.amazonaws.com\/Course-Outlines\/Core-Financial-Modeling-Course-Outline.pdf\" target=\"_blank\" rel=\"noopener\">Short Outline<\/a>\n    <\/div>\n<\/div><\/div>\n\n<h2><span class=\"ez-toc-section\" id=\"How_to_Apply_the_Time_Value_of_Money_in_Investment_Decisions\"><\/span><strong>How to Apply the Time Value of Money in Investment Decisions<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In investment analysis, the time value of money comes up most often when you are calculating the <strong>Present Value<\/strong> of an investment or the\u00a0<strong>annualized returns<\/strong> (<a href=\"https:\/\/breakingintowallstreet.com\/kb\/leveraged-buyouts-and-lbo-models\/cash-on-cash-return-vs-irr\/\" target=\"_blank\" rel=\"noopener\">the internal rate of return or IRR<\/a>).<\/p>\n<p>For example, if you&#8217;re valuing an asset that will generate $100 of cash flow each year for 10 years, the $100 of cash flow in Year 10 will be worth much less than the cash flow in Year 1 because of <strong>the time value of money<\/strong>.<\/p>\n<p>If you could earn an annualized return of 5% per year on other, similar assets, then the $100 of cash flow in Year 10 is worth:<\/p>\n<ul>\n<li>$100 \/ ((1 + 5%) ^ 10) = $61.4.<\/li>\n<\/ul>\n<p>If you could earn 10% per year on other, similar assets, it&#8217;s even worse:<\/p>\n<ul>\n<li>$100 \/ ((1 + 10%) ^ 10) = $38.6.<\/li>\n<\/ul>\n<p>This doesn&#8217;t mean that you\u00a0<em>shouldn&#8217;t<\/em> invest in this asset.<\/p>\n<p>Instead, it means that you should <strong>focus on the asset&#8217;s near-term cash flows<\/strong> because they are worth more to you\u00a0<em>today<\/em> than the ones it will generate in Year 10, 20, or 30.<\/p>\n<p>This &#8220;discounting&#8221; approach is widely used in <a href=\"https:\/\/mergersandinquisitions.com\/dcf-model\/\" target=\"_blank\" rel=\"noopener\">Discounted Cash Flow (DCF) models<\/a> and other valuation methodologies such as the <a href=\"https:\/\/mergersandinquisitions.com\/dividend-discount-model\/\" target=\"_blank\" rel=\"noopener\">Dividend Discount Model (DDM)<\/a>.<\/p>\n<p>The time value of money also comes up in concepts such as bond valuation, <a href=\"https:\/\/breakingintowallstreet.com\/kb\/debt-equity\/bond-yield\/\" target=\"_blank\" rel=\"noopener\">bond yields<\/a>, <a href=\"https:\/\/breakingintowallstreet.com\/kb\/debt-equity\/yield-to-maturity\/\" target=\"_blank\" rel=\"noopener\">the yield to maturity<\/a>, and <a href=\"https:\/\/mergersandinquisitions.com\/lbo-modeling-test\/\" target=\"_blank\" rel=\"noopener\">leveraged buyout (LBO) models<\/a>.<\/p>\n<p>In these analyses, the assumption is that when an asset generates cash flows during the holding period, you <em>re-invest these proceeds at the same rate as the overall annualized return<\/em>.<\/p>\n<p>Therefore, the time value of money influences the results because this re-investment assumption means that cash flows earned during the holding period become more valuable by the end.<\/p>\n<p>There are ways to adjust for this, such as by using the MIRR function rather than IRR or XIRR; MIRR is the &#8220;Modified Internal Rate of Return&#8221; and lets you assume a different rate of return on the re-invested proceeds.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"The_Time_Value_of_Money_Key_Takeaways\"><\/span><strong>The Time Value of Money: Key Takeaways<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The main points of this article are:<\/p>\n<p><strong>1) Discounting <a href=\"https:\/\/breakingintowallstreet.com\/kb\/finance\/future-value\/\" target=\"_blank\" rel=\"noopener\">Future Values<\/a><\/strong> &#8211; Whenever an asset generates cash flow in the future, or you assume a sale of the asset in the future, you must\u00a0<strong>discount it<\/strong> to its Present Value because money today is worth more than money tomorrow.<\/p>\n<p><strong>2) Upfront Payment vs. Paying Over Time<\/strong> &#8211; Many people claim that buying a house or paying a large deposit in exchange for no rent is always a better deal because &#8220;you can get your money back,&#8221; but this is not true.<\/p>\n<p>It depends on <em>what you could earn<\/em> with the money you would have spent buying the house or putting down a larger deposit and how this compares to the ongoing rental cost of the property.<\/p>\n<p><strong>3) Comparing Assets and Investments<\/strong> &#8211; Finally, when you&#8217;re completing these types of exercises, you always want to compare\u00a0<em>similar types of assets<\/em> and what you could earn on each one.<\/p>\n<p>For example, it&#8217;s inappropriate to compare U.S. Treasuries (government bonds) with a real estate investment or the stock market because the risk and potential returns are completely different.<\/p>\n<p>It is more appropriate to compare the potential returns on a real estate investment to those of other, similar properties in the same geographic region.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The time value of money means that money today is worth MORE than money tomorrow because you could invest it today and earn something on it the future.<\/p>\n","protected":false},"featured_media":29745,"template":"","class_list":["post-29630","biws_kb","type-biws_kb","status-publish","has-post-thumbnail","hentry","kb_category-finance"],"acf":[],"_links":{"self":[{"href":"https:\/\/breakingintowallstreet.com\/wp-json\/wp\/v2\/biws_kb\/29630","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/breakingintowallstreet.com\/wp-json\/wp\/v2\/biws_kb"}],"about":[{"href":"https:\/\/breakingintowallstreet.com\/wp-json\/wp\/v2\/types\/biws_kb"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/breakingintowallstreet.com\/wp-json\/wp\/v2\/media\/29745"}],"wp:attachment":[{"href":"https:\/\/breakingintowallstreet.com\/wp-json\/wp\/v2\/media?parent=29630"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}