{"id":2056,"date":"2020-10-17T02:38:20","date_gmt":"2020-10-17T10:38:20","guid":{"rendered":"http:\/\/wonghoi.humgar.com\/blog\/?p=2056"},"modified":"2021-04-12T21:32:08","modified_gmt":"2021-04-13T05:32:08","slug":"mathematics-of-calculating-overheads-to-charge","status":"publish","type":"post","link":"https:\/\/wonghoi.humgar.com\/blog\/2020\/10\/17\/mathematics-of-calculating-overheads-to-charge\/","title":{"rendered":"Mathematics of calculating overheads to charge"},"content":{"rendered":"<p>It&#8217;s very common to have a percentage fee (called <em>tax<\/em> <em><strong>rate<\/strong><\/em> below) slapped on our earnings:<\/p>\n<ul>\n<li>Commissions (e.g. eBay final value fees)<\/li>\n<li>Sales Tax<\/li>\n<li><span style=\"text-decoration: underline;\">Incremental<\/span> income taxable within the same bracket.<\/li>\n<\/ul>\n<p>Many adults cannot directly figure out how much EXTRA do they need to earn to get the <em><strong>target<\/strong><\/em> amount of that are rightfully theirs (after fees).<\/p>\n<p>They are missing out these handy intuitions:<\/p>\n<ul>\n<li>If your EXTRA earnings are taxed at 40%, not wasting an extra &#36;100 is almost as good as earning &#36;166.67!<\/li>\n<li>You always undercharge the fee overhead if you just multiply your <em><strong>target<\/strong><\/em> amount with it (intuitive but WRONG). The amount you get <em>shortchanged<\/em> goes up like a rocket for rates past 10%!<\/li>\n<\/ul>\n<p><span style=\"color: #008000;\">All you need is <strong>grade school math<\/strong> to figure it out<\/span>, but the results are highly non-linear and are not easy to remember. This means the tutorial below makes an excellent discussion material to motivate mathematics education in grade school!<\/p>\n<p>If you want to copy or use the materials, just remember to reference &#8220;Rambling Nerd with a Plan&#8221; blog page or &#8220;Humgar LLC&#8221;. You don&#8217;t have to ask and you are welcome. I certainly appreciate comments about this tutorial.<\/p>\n<hr \/>\n<p><span style=\"color: #993300;\">Before I start, hints for working with percentages:<\/span><\/p>\n<ul>\n<li><span style=\"color: #993300;\">divide percentages by 100.\u00a0Think multipliers\/factors in your head.<\/span><\/li>\n<li><span style=\"color: #993300;\">a factor of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-69a7c7fb1023d315f416440bca10d849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\"\/> represents the full amount<\/span><\/li>\n<li><span style=\"color: #993300;\">division by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/> is multiplication by reciprocal <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-39fb32cb8eebca504639a739b362516e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#47;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"\/><\/span><\/li>\n<li><span style=\"color: #993300;\">preferably work in terms of shrink\/expand factors (multiplications only) over the FULL amount, rather than working out the excesses (additions\/subtractions)<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #993300;\">Assigning intuitive names are very important for interpreting algebraic expressions with familiar life concepts!<\/span><\/p>\n<p>Let&#8217;s define these variables first:<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> is the <strong>target price<\/strong> you want to get AFTER the fees<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> is the <strong>damage<\/strong> you should charge<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is the <strong>rate<\/strong> (fee\/tax percentages)<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> is the <strong>excess<\/strong> that goes to the fee\/tax collector<\/li>\n<\/ul>\n<p>These derived variables will be discussed in the body of the tutorial<\/p>\n<ul>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is the <strong>shrinkage<\/strong> (multiplier), where\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-626fa735548d73e43ef53b7cf8d29b12_l3.png\" height=\"19\" width=\"84\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#115;&#92;&#101;&#113;&#117;&#105;&#118;&#40;&#49;&#45;&#114;&#41;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> is the <strong>magnifier<\/strong> (multiplier),\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-0d5ee12af4fa8cd57c8fe066d0e177b4_l3.png\" height=\"36\" width=\"50\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#109;&#92;&#101;&#113;&#117;&#105;&#118;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is the <strong>compensation<\/strong> (multiplier) for billing,\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 12px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b4e88e894801bcd11e8e93d5d3190bee_l3.png\" height=\"12\" width=\"77\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#61;&#109;&#45;&#49;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/li>\n<\/ul>\n<hr \/>\n<p>If somebody pays you the total damage <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> before tax\/fees (at <em><strong>rate<\/strong><\/em>\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>), you are home free with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> after subtracting the fees <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a96387d0bbb4a653bb354b92eda9d92c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;&#32;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"45\" style=\"vertical-align: 0px;\"\/> from <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-82ab00b057c162d03207bee9780275dd_l3.png\" height=\"19\" width=\"236\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#68;&#32;&#45;&#32;&#114;&#68;&#32;&#61;&#32;&#40;&#49;&#45;&#114;&#41;&#68;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#115;&#68;&#32;&#61;&#32;&#84;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>In other words, you the FULL damages gets <strong><em>shrunk<\/em> <\/strong>by a factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-178e1bc6123baece9354017b04269d54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#40;&#49;&#45;&#114;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"\/> which becomes the target amount <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> you get to keep for yourself.<\/p>\n<p><span style=\"color: #000000;\">Don&#8217;t be scared by the algebra!\u00a0<\/span>It&#8217;s just the other way of saying, i<span style=\"color: #0000ff;\">f your tax rate is 30%, it means you get to keep 70% of your income, because 100%-30% = 70%<\/span><span style=\"color: #000000;\">, so the <strong><em>shrinkage<\/em> <\/strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a0f37a31374a0be2a03be4e521fa8582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: 0px;\"\/>.\u00a0<\/span><\/p>\n<p>Since you have the target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> in mind and want to undo the <em>shrinkage<\/em> (<strong>multiplication<\/strong>) to calculate the full amount you should charge <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/>, you <strong>divide<\/strong> the target price by the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> by the same factor to <strong><em>magnify<\/em> <\/strong>it back:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 37px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f6c303e4a7da3b6ce5f9a0d01e6e8f46_l3.png\" height=\"37\" width=\"121\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#68;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#84;&#125;&#123;&#115;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#84;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p><span style=\"color: #ff6600;\">It is NEVER helpful to directly multiply the fee\/tax percentage with the target price<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> like what most people would intuitively do. We can think of the division above as multiplying by the reciprocal of the loss factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> or <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-92e4e13afeeb29457d9919571949e79f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#49;&#45;&#114;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"\/>, which we will call <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> the <em><strong>magnifier<\/strong><\/em>:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a1148e8b6b8932a9732ed014b10f2b76_l3.png\" height=\"36\" width=\"117\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#109;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#115;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<hr \/>\n<p>An alternative view is to break the <em><strong>damage<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> into <em><strong>target<\/strong> <\/em>price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> along with <em><strong>excess<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> to bill the customers for the fees\/taxes (which goes to the collector):<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 14px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-d50d8d002a07d16702e211c8c5f9f46e_l3.png\" height=\"14\" width=\"87\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#68;&#32;&#61;&#32;&#84;&#32;&#43;&#32;&#69;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>My preferred way to calculate the excess is simply compute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> first by finding calculating the magnifier <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/>, or simply dividing the target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> by the shrinkage <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/><\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 37px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-aa5c39d90cb43e79b6c1ca128b6e56d4_l3.png\" height=\"37\" width=\"173\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#68;&#32;&#61;&#32;&#109;&#84;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#84;&#125;&#123;&#115;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#84;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>then subtract the target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> from the damage <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> to get the excess:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 12px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b6a6ef4bcc2237d5ac5842ff298383cf_l3.png\" height=\"12\" width=\"88\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#69;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#68;&#45;&#84;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>which you can write it in terms of target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> which you know so you don&#8217;t have to work out the total damages <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-c10ec9debc8ec5dce4c3c5887557202d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#68;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"\/> first:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-58b08bcd418e835fb12353fc89517ea6_l3.png\" height=\"19\" width=\"269\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#69;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#32;&#68;&#32;&#45;&#32;&#84;&#32;&#61;&#32;&#109;&#84;&#32;&#45;&#32;&#84;&#32;&#61;&#32;&#84;&#40;&#109;&#45;&#49;&#41;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>We can define <strong>compensation<\/strong> (multiplier) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> as how much you should multiply the target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> with:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 12px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-414521dcd1b8d940b7ddd2f30a9f6aa9_l3.png\" height=\"12\" width=\"77\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#109;&#45;&#49;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>to recover your fee\/tax costs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/>:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 12px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b3b22a0c9e2ecb286a7b7eaaccefe239_l3.png\" height=\"12\" width=\"58\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#69;&#32;&#61;&#32;&#99;&#84;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>e.g. if you need to charge the customer 1.43 times to breakeven after fees (given a 30% tax\/fees rate), the overhead &#8216;item&#8217; on the bill should be 0.43 (43%) of the target price. <span style=\"color: #0000ff;\">For a &#36;100 item, you&#8217;ll need to bill your customer &#36;43 more just to cover a 30% fees<\/span>.<\/p>\n<hr \/>\n<p>In summary, we have<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ef1cb4142f9bd4f1cc917f21e945eb32_l3.png\" height=\"19\" width=\"175\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#80;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#84;&#32;&#43;&#32;&#69;&#32;&#61;&#32;&#40;&#49;&#43;&#99;&#41;&#84;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> that can be figured out quickly as<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1272084c2e509071617a7919af66ab78_l3.png\" height=\"32\" width=\"42\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> are both bounded between 0 and 1 which adds up to 1:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 14px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ff0a6efe3210279bdf4d15302b53cc9c_l3.png\" height=\"14\" width=\"70\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#114;&#32;&#43;&#32;&#115;&#32;&#61;&#32;&#49;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>Take an example of 30% tax <em><strong>rate<\/strong><\/em> (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-4c78f41c7a7063dfcba3d7dde9ab4766_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#48;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"\/>), the <em><strong>shrink<\/strong><\/em> is 70% (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3e47b3a7b0d0f61960c38e68104a3276_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;&#61;&#48;&#46;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"55\" style=\"vertical-align: 0px;\"\/>), because the factors are complements to each other which adds up to 1.<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 15px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fc1cae5ded0e85acfbef9a61a3849cf8_l3.png\" height=\"15\" width=\"99\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#48;&#46;&#51;&#32;&#43;&#32;&#48;&#46;&#55;&#32;&#61;&#32;&#49;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<hr \/>\n<p>If you want to write it all in terms of <em><strong>shrinkage<\/strong><\/em>\u00a0 <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-37010caf601d0497bfca3a66c07c2c92_l3.png\" height=\"36\" width=\"140\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#115;&#125;&#45;&#49;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#45;&#115;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>Since <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a9a1458450ae56123cf52870871b99b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#45;&#115;&#32;&#61;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"69\" style=\"vertical-align: 0px;\"\/>, we can rewrite the <em><strong>compensation<\/strong><\/em> (factor) in these complement terms <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-76f044d7a56f1a02a3531fad5e65720c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#114;&#44;&#115;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"35\" style=\"vertical-align: -5px;\"\/>, which I think it&#8217;s the easiest way to remember:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1272084c2e509071617a7919af66ab78_l3.png\" height=\"32\" width=\"42\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>or simply the <em><strong>rate\u00a0<\/strong><\/em><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>\u00a0divided by <em><strong>shrinkage\u00a0<\/strong><\/em><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>,<\/p>\n<p>You can also write it in terms of fees\/tax <em><strong>rate<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> in full:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-2efe61357bfae62693439bfdb3f9f97e_l3.png\" height=\"32\" width=\"73\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>e.g. if you have a <span style=\"color: #0000ff;\">30% tax rate<\/span> , you can find the <span style=\"color: #0000ff;\"><em><strong>compensation<\/strong> <\/em>(factor)<\/span> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> by calculating <span style=\"color: #0000ff;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3659d7e24da55dad5e868430ec2c0fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#47;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"27\" style=\"vertical-align: -5px;\"\/><\/span>, because it&#8217;s simply 30% over 70%.<\/p>\n<hr \/>\n<p>To estimate the overhead charge to offset the fee percentage, or <em><strong>compensation<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> by multiplying with the target price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/>:<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\"><span style=\"color: #ff0000;\"><strong>WRONG<\/strong>\u00a0<\/span>way<\/td>\n<td style=\"width: 50%;\"><span style=\"text-decoration-line: line-through;\"><\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 8px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-783b1c81e6581589ec4a6f2a867912c0_l3.png\" height=\"8\" width=\"8\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#114;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\"><span style=\"color: #0000ff;\">CORRECT<\/span>\u00a0way<\/td>\n<td style=\"width: 50%;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-201c7c9fb870777a3cd0c2c1358df06e_l3.png\" height=\"32\" width=\"40\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-size: 1.0625rem;\">The <\/span><em style=\"font-size: 1.0625rem;\"><strong>gap<\/strong> <\/em><span style=\"font-size: 1.0625rem;\">(amount you get shortchanged by computing compensation <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> wrong) is:<\/span><\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 39px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-330396cea3fac7b3b3294e9f5c947f8a_l3.png\" height=\"39\" width=\"233\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#103;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#99;&#45;&#114;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#45;&#114;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#94;&#50;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>The numbers look close enough (for the intuitive but wrong way) when it&#8217;s like around 10%, but your loss (overheads not charged) shoots up (non-linearly) as the fee\/tax percentage goes up beyond 10%!<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 189px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">Fee percentage<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 8px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-783b1c81e6581589ec4a6f2a867912c0_l3.png\" height=\"8\" width=\"8\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#114;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">Correct overhead % to charge<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-19533d89bb6bf095242b313dfc105a01_l3.png\" height=\"32\" width=\"109\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">Undercharged<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 39px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdb40d8fa94335c855575dca83f31383_l3.png\" height=\"39\" width=\"40\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#94;&#50;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">5%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">5.26%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">0.26%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">10%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">11.11%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">1.1%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">20%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">25%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">5%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">30%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">42.86%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">12.86%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">40%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">66.67%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">26.67%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">50%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">100%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">50%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Intuitively, you need to charge DOUBLE the target price if half of it gets taxed to breakeven, NOT adding half of the target price as the overhead! The FULL target price itself is the right overhead to charge for a 50% tax rate!<\/p>\n<p>Since\u00a0the numerator <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is bounded because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fccc780e6814328114cfed369e983691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#32;&#92;&#108;&#101;&#113;&#32;&#114;&#32;&#60;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"\/>, the <strong>denominator<\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-92e4e13afeeb29457d9919571949e79f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#49;&#45;&#114;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"51\" style=\"vertical-align: -5px;\"\/> can blow up (the overhead needed to charge your customer) as it gets small (i.e. high tax\/fee percentage). Here&#8217;s a plot of <\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1d358177846331f976e8ec17aac12ded_l3.png\" height=\"36\" width=\"40\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p>.<\/p>\n<p><a href=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-2096\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png 300w, https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/p>\n<p>e.g. <span style=\"color: #0000ff;\">A 66.6% imports tax rate means giving two cars to the government when you import one<\/span>!<\/p>\n<p>To push it to the extreme, 90% tax rate would mean 900% overhead, which means if you buy one car, you give the government 9 cars, assuming they don&#8217;t tax themselves. Your estimates are off by 10 times if you use the wrong method to compute the excess <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> making up for the tax that gets charged.<\/p>\n<p>If people can think in terms of the excess you will need to earn EXTRA to offset the tax rate, you will think twice about letting the government dip in another 2% or so. That&#8217;s why welfare-state through taxes can be highly counter-productive when it get past certain point.<\/p>\n<hr \/>\n<p style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Advanced analysis for the intrigued<\/span><\/p>\n<p>Just for fun, let&#8217;s investigate the impractical case (<span style=\"color: #ff0000;\">communist tyrants<\/span>) when tax rates gets to 100% and above (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-3e5b31f3d23b27941e85a59e250ad3df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#32;&#92;&#103;&#101;&#113;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -3px;\"\/>):<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 189px;\" border=\"1\">\n<tbody>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">Fee percentage<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 8px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-783b1c81e6581589ec4a6f2a867912c0_l3.png\" height=\"8\" width=\"8\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#114;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">Correct overhead % to charge<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-19533d89bb6bf095242b313dfc105a01_l3.png\" height=\"32\" width=\"109\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">Undercharged<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 39px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdb40d8fa94335c855575dca83f31383_l3.png\" height=\"39\" width=\"40\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#94;&#50;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-072a6eba2cde371eb2be2123067bc11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 47.8494%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-07dec7a1515c6a9db51b9134ffb1250c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 25.0672%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-072a6eba2cde371eb2be2123067bc11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">90%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\">900%<\/td>\n<td style=\"width: 25.0672%; height: 27px;\">810%<\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">100%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ac47b919d94a96e82a20265519dbcd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 25.0672%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ac47b919d94a96e82a20265519dbcd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"\/><\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\">200%<\/td>\n<td style=\"width: 47.8494%; height: 27px;\"><span style=\"color: #808080;\">-200%<\/span><\/td>\n<td style=\"width: 25.0672%; height: 27px;\"><span style=\"color: #808080;\">-400%<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 27.0833%;\">300%<\/td>\n<td style=\"width: 47.8494%;\"><span style=\"color: #808080;\">-150%<\/span><\/td>\n<td style=\"width: 25.0672%;\"><span style=\"color: #808080;\">-450%<\/span><\/td>\n<\/tr>\n<tr style=\"height: 27px;\">\n<td style=\"width: 27.0833%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-072a6eba2cde371eb2be2123067bc11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 47.8494%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-07dec7a1515c6a9db51b9134ffb1250c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 25.0672%; height: 27px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-072a6eba2cde371eb2be2123067bc11b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#100;&#111;&#116;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"3\" style=\"vertical-align: 0px;\"\/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 27.0833%;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ac47b919d94a96e82a20265519dbcd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"\/><\/td>\n<td style=\"width: 47.8494%;\"><span style=\"color: #808080;\">-100%<br \/>\n<\/span><\/td>\n<td style=\"width: 25.0672%;\"><span style=\"color: #808080;\">&#8211;<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ac47b919d94a96e82a20265519dbcd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#105;&#110;&#102;&#116;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"\/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>When charged 100% tax rate, the government seize any gains from your production. There&#8217;s never enough overhead you can charge your customer to breakeven.<\/p>\n<p>The more perverted case is what happens when you go above 100%, say at 200% tax rate? When you sell &#36;100 worth of stuff, you pay the government &#36;200 to do so. You are paying a &#36;100 penalty to work\/produce &#36;100 for the government. Twisted!<\/p>\n<p>Then how do we explain the negative numbers in the <em><strong>compensation<\/strong><\/em>\u00a0(factor) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>? In reality, it means you ALWAYS make a loss no matter what.\u00a0There&#8217;s no way you can bill your customer to make up for the loss.<\/p>\n<p>In the unrealistic (unicorn) case, if the benevolent crazy dictator is willing and able to compensate your losses (at the sales tax rate), aka giving you money back every time you lose money,<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-f84312e54af886389b43753ce99395bb_l3.png\" height=\"19\" width=\"103\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#80;&#32;&#61;&#32;&#40;&#49;&#43;&#99;&#41;&#84;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>means the the <em><strong>magnifier<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-b83a15ff02efdd0095c33027b3f754fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#40;&#49;&#43;&#99;&#41;&#32;&#60;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -5px;\"\/> for sure when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-70c2a277bdda711d11a766c823dd6cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#32;&#92;&#103;&#101;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -3px;\"\/>. It&#8217;s illustrated in the graph as a deadzone <\/p>\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7a2d9340a15549ab407bdb3594d4d8db_l3.png\" height=\"32\" width=\"121\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#45;&#49;&#32;&#60;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#60;&#32;&#48;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p>:<\/p>\n<p><a href=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-extended.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-2098\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-extended.png\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-extended.png 300w, https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-extended-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>which you can verify the same by solving this inequality<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 32px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-748d58d2cb73157285abca8a90d50033_l3.png\" height=\"32\" width=\"121\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#45;&#49;&#32;&#60;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#92;&#108;&#101;&#113;&#32;&#48;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>and realize you get <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-368b9975f8b0abb5f3122f352eb66e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#45;&#49;&#32;&#92;&#103;&#101;&#32;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"71\" style=\"vertical-align: -3px;\"\/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-17b09adedd682a382224268947386285_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#40;&#49;&#45;&#114;&#41;&#32;&#92;&#108;&#101;&#113;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"84\" style=\"vertical-align: -5px;\"\/>, which boils down to saying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ba40666975c4ae9797cf7bd1b85608a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#32;&#92;&#103;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: -3px;\"\/> which is a contradiction.<\/p>\n<p>That means to achieve target earnings <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> under tax rates above 100%, you should charge the customer negative amounts (i.e. giving away goods + money) in order to get the negative taxes (subsidy).<\/p>\n<p>e.g. At 300% tax rate (<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1630959f4de9845bc173eb05f47d52e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"\/>), it your sticker price (also target price) is &#36;100, you&#8217;ll need to GIVE the customer &#36;50 so the government will triple match your loss as a subsidy (which is &#36;150), which is enough to cover the &#36;50 giveaway (to the customer) plus\u00a0the &#36;100 so you&#8217;ll breakeven.<\/p>\n<p>Having negative tax (subsidy) is a perverse incentive. Forget about maintaining a target earning (same as the original sticker price for the goods you are selling), just lose (give away) money as fast as you can to suck up as much subsidy as you can before the system collapse.<\/p>\n<p>I still fondly recall my economics 301 (intermediate microeconomics professors) <a href=\"http:\/\/www.ssc.wisc.edu\/~jmontgom\/\">James Montgomery<\/a> saying that &#8220;if you can graph it, it can possibly happen&#8221; in the lecture.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">Even more sophisticated math for the geeks<\/p>\n<p>Remember from above, the <em><strong>magnification<\/strong> <\/em>factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fdc40b8ad1cdad0aab9d632215459d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"\/> can be rewritten as the reciprocal of <em><strong>shrinkage<\/strong><\/em> factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-1edc883862ceed1a21913f60358e31d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>?<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-a1148e8b6b8932a9732ed014b10f2b76_l3.png\" height=\"36\" width=\"117\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#109;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#115;&#125;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#45;&#114;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>which reminds me of geometric series<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 36px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-eae3ff66b2d7c8fa24fc00b64ba6a0f9_l3.png\" height=\"36\" width=\"221\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#61;&#32;&#49;&#32;&#43;&#32;&#114;&#32;&#43;&#32;&#114;&#94;&#50;&#32;&#43;&#32;&#114;&#94;&#51;&#32;&#43;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#125;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>given <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-26b0821dac6bd862f875c208c179bf04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#124;&#114;&#124;&#32;&#60;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"48\" style=\"vertical-align: -5px;\"\/>? For non-perverted cases, we are considering <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-fccc780e6814328114cfed369e983691_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#32;&#92;&#108;&#101;&#113;&#32;&#114;&#32;&#60;&#32;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: -3px;\"\/>, which is well within the domain.<\/p>\n<p>This gives an idea of approximating the compensation factor <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-5b74155e288dcbd9545bd0f71b42e49d_l3.png\" height=\"19\" width=\"257\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#109;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#49;&#43;&#99;&#32;&#61;&#32;&#49;&#32;&#43;&#32;&#114;&#32;&#43;&#32;&#114;&#94;&#50;&#32;&#43;&#32;&#114;&#94;&#51;&#32;&#43;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>which after taking <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-69a7c7fb1023d315f416440bca10d849_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\"\/> off both sides:<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 19px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-34924936d27eeace22c1cca081013238_l3.png\" height=\"19\" width=\"157\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#99;&#32;&#61;&#32;&#114;&#32;&#43;&#32;&#114;&#94;&#50;&#32;&#43;&#32;&#114;&#94;&#51;&#32;&#43;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>This explains exactly why people are <span style=\"color: #ff0000;\"><strong>wrong to just assume <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-276a76eafbebc4494deafceec7cc4ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> is just <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/>, because their false intuition kept ONLY the first order term<\/strong><\/span> in the power series approximation!<\/p>\n<p>The gap (how much they are off with the WRONG way), is<\/p>\n<p style=\"text-align: center;\">\n<p class=\"ql-center-displayed-equation\" style=\"line-height: 39px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-ff9728d5cd821d053feeb10151d3bd88_l3.png\" height=\"39\" width=\"256\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#103;&#32;&#92;&#101;&#113;&#117;&#105;&#118;&#32;&#99;&#45;&#114;&#32;&#61;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#94;&#50;&#125;&#123;&#49;&#45;&#114;&#125;&#32;&#61;&#32;&#114;&#94;&#50;&#32;&#43;&#32;&#114;&#94;&#51;&#32;&#43;&#32;&#92;&#99;&#100;&#111;&#116;&#115;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/p>\n<p>So while <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-9679c4ebf5bc2a9e5002caed08127404_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#49;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"30\" style=\"vertical-align: 0px;\"\/> dies fast enough (0.01) by 2nd order term,\u00a0<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-47e2e44d6642621ea3983c8c69d794e3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#57;&#94;&#50;&#61;&#48;&#46;&#56;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"85\" style=\"vertical-align: 0px;\"\/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-27084402b68ea0d48abc9f31fdd79c56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#57;&#94;&#51;&#32;&#61;&#32;&#48;&#46;&#55;&#50;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"95\" style=\"vertical-align: 0px;\"\/> &#8230; are still very significant up to say 6th order term which makes it off by a factor of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bc05bacb87e850792d6e14d3855d7bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"\/>.<\/p>\n<p>Yes, you are off by 1% when the tax rate is 10%, but you can be wrong by a factor of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-bc05bacb87e850792d6e14d3855d7bf0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\"\/> times if you just multiplied the tax rate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"\/> with the <em><strong>target<\/strong> <\/em>price <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#84;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"\/> to estimate the amount of <em><strong>excess<\/strong><\/em> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-638a7387bd72763290cc777a9b509c38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#69;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"\/> to collect to make up for the fees!<\/p>\n<hr \/>\n<p>Summary<\/p>\n<ul>\n<li>The total damage (bill) you should charge your customer can be calculated by dividing the <em><strong>target<\/strong> <\/em>amount (of money you want to home free with) by the shrinkage, which is (1 &#8211; tax rate).\u00a0<span style=\"color: #0000ff;\">e.g. 30% tax rate means 70% shrinkage. <span style=\"text-decoration: underline;\">Divide<\/span> the <em><strong>target<\/strong> <\/em>by 0.7 to get the final bill<\/span><\/li>\n<li>A shortcut to calculate how much you should put in (by multiplying with the target price) for an charge item on the bill to make up for the fees is (tax rate)\/(shrinkage)\u00a0<span style=\"color: #0000ff;\">e.g. 30% tax rate means 70% shrinkage. <span style=\"text-decoration: underline;\">Multiply<\/span> the <em><strong>target<\/strong> <\/em>by 30\/70 (or 3\/7, which is 42%) to get the <em><strong>excess<\/strong><\/em> which covers the fee.<\/span><\/li>\n<li>Do NOT attempt to use the rule of thumb to calculate the <strong><em>excess<\/em><\/strong>\u00a0by just multiplying with the tax rate unless it&#8217;s 10% or less. The &#8216;rule of thumb&#8217; assumed <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/ql-cache\/quicklatex.com-19db2644cdc31d7e9f0115deb1e187cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#94;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"15\" style=\"vertical-align: 0px;\"\/> (and thus the higher powers) are insignificant, which is nowhere true for 0.1 and above based on this graph!<a href=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png\"><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-2096\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r.png 300w, https:\/\/wonghoi.humgar.com\/blog\/wp-content\/uploads\/2020\/10\/r-over-1-r-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/li>\n<\/ul>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_2056\" class=\"pvc_stats all  \" data-element-id=\"2056\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>It&#8217;s very common to have a percentage fee (called tax rate below) slapped on our earnings: Commissions (e.g. eBay final value fees) Sales Tax Incremental income taxable within the same bracket. Many adults cannot directly figure out how much EXTRA &hellip; <a href=\"https:\/\/wonghoi.humgar.com\/blog\/2020\/10\/17\/mathematics-of-calculating-overheads-to-charge\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n<div class=\"pvc_clear\"><\/div>\n<p id=\"pvc_stats_2056\" class=\"pvc_stats all  \" data-element-id=\"2056\" style=\"\"><i class=\"pvc-stats-icon medium\" aria-hidden=\"true\"><svg aria-hidden=\"true\" focusable=\"false\" data-prefix=\"far\" data-icon=\"chart-bar\" role=\"img\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 512 512\" class=\"svg-inline--fa fa-chart-bar fa-w-16 fa-2x\"><path fill=\"currentColor\" d=\"M396.8 352h22.4c6.4 0 12.8-6.4 12.8-12.8V108.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v230.4c0 6.4 6.4 12.8 12.8 12.8zm-192 0h22.4c6.4 0 12.8-6.4 12.8-12.8V140.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v198.4c0 6.4 6.4 12.8 12.8 12.8zm96 0h22.4c6.4 0 12.8-6.4 12.8-12.8V204.8c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v134.4c0 6.4 6.4 12.8 12.8 12.8zM496 400H48V80c0-8.84-7.16-16-16-16H16C7.16 64 0 71.16 0 80v336c0 17.67 14.33 32 32 32h464c8.84 0 16-7.16 16-16v-16c0-8.84-7.16-16-16-16zm-387.2-48h22.4c6.4 0 12.8-6.4 12.8-12.8v-70.4c0-6.4-6.4-12.8-12.8-12.8h-22.4c-6.4 0-12.8 6.4-12.8 12.8v70.4c0 6.4 6.4 12.8 12.8 12.8z\" class=\"\"><\/path><\/svg><\/i> <img loading=\"lazy\" decoding=\"async\" width=\"16\" height=\"16\" alt=\"Loading\" src=\"https:\/\/wonghoi.humgar.com\/blog\/wp-content\/plugins\/page-views-count\/ajax-loader-2x.gif\" border=0 \/><\/p>\n<div class=\"pvc_clear\"><\/div>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[47,43,46],"tags":[],"class_list":["post-2056","post","type-post","status-publish","format-standard","hentry","category-ebay","category-economics","category-layman-mathematics"],"_links":{"self":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2056","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/comments?post=2056"}],"version-history":[{"count":94,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2056\/revisions"}],"predecessor-version":[{"id":2581,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/posts\/2056\/revisions\/2581"}],"wp:attachment":[{"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/media?parent=2056"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/categories?post=2056"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wonghoi.humgar.com\/blog\/wp-json\/wp\/v2\/tags?post=2056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}