{"id":259,"date":"2021-01-26T22:31:37","date_gmt":"2021-01-26T22:31:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/?post_type=chapter&#038;p=259"},"modified":"2021-05-23T00:41:16","modified_gmt":"2021-05-23T00:41:16","slug":"accounting-rate-of-return","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/chapter\/accounting-rate-of-return\/","title":{"raw":"Discounted Payback","rendered":"Discounted Payback"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Calculate the payback period using discounted cash flows<\/li>\r\n<\/ul>\r\n<\/div>\r\n<img class=\"aligncenter wp-image-1797\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5469\/2021\/01\/17231744\/kieran-wood-UOk1ghQ7juY-unsplash-300x225.jpg\" alt=\"Wooden puzzle\" width=\"500\" height=\"375\" \/>\r\n\r\nWe can improve the payback method by using discounted cash flows instead of the nominal (undiscounted, unadjusted) estimates.\r\n\r\nLet\u2019s review the example:\r\n\r\nJuxtaPos makes interlocking wooden puzzles. One of the machines is old and management is considering either replacing it or refurbishing it. Replacing it will cost $80,000. The new machine would last 10 years and have a residual value of $10,000. Refurbishing the old machine for $56,000 will keep it in service for another 8 years and it will have no residual value at the end of that time.\r\n\r\nYou have estimated production under both scenarios and used those numbers to compute revenue. You have also estimated operating costs and have created the following table of net cash inflows:\r\n<p style=\"text-align: center;\">Net cash inflows (additional cash revenues - additional cash expenses)<\/p>\r\n\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<tbody>\r\n<tr>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\">Refurbish<\/th>\r\n<th class=\"r\" scope=\"col\">Purchase New<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 18,000<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 20,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 16,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 19,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 18,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 12,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 17,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 5<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 10,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 15,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 6<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 13,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 7<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 10,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 8<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 9<\/td>\r\n<td><\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 10 (includes proceeds from sale of machine)<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 12,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 88,000<span class=\"u-sr-only\">Double line<\/span><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 136,000<span class=\"u-sr-only\">Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nNone of these values are adjusted for the time value of money. For instance, $12,000 10 years from now is not the same as $12,000 today.\r\n\r\nLet\u2019s assume JuxtaPos uses a 10% hurdle or discount rate for capital budgeting purposes. If we use a present value table, we find that the factor of 10% and 10 years is 0.386. Multiplying the factor by our $12,000 future value for year 10 gives us a present value of $4,632. That means that if we are to translate all of the future numbers back to Year 0 when we make the initial purchase (beginning of Year 1), the $12,000 future cash flow in Year 10 would be the equivalent of a $4,632 cash flow back at the beginning of Year 1.\r\n<div align=\"left\">\r\n<table class=\"fin-table gridded\">\r\n<thead>\r\n<tr>\r\n<th colspan=\"17\">Present Value of $1<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Periods<\/td>\r\n<td class=\"c highlight-green\">1%<\/td>\r\n<td class=\"c highlight-green\">2%<\/td>\r\n<td class=\"c highlight-green\">3%<\/td>\r\n<td class=\"c highlight-green\">4%<\/td>\r\n<td class=\"c highlight-green\">5%<\/td>\r\n<td class=\"c highlight-green\">6%<\/td>\r\n<td class=\"c highlight-green\">7%<\/td>\r\n<td class=\"c highlight-green\">8%<\/td>\r\n<td class=\"c highlight-green\">9%<\/td>\r\n<td class=\"c highlight-green\">10%<\/td>\r\n<td class=\"c highlight-green\">12%<\/td>\r\n<td class=\"c highlight-green\">14%<\/td>\r\n<td class=\"c highlight-green\">15%<\/td>\r\n<td class=\"c highlight-green\">16%<\/td>\r\n<td class=\"c highlight-green\">18%<\/td>\r\n<td class=\"c highlight-green\">20%<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 1<\/td>\r\n<td class=\"r\">0.990<\/td>\r\n<td class=\"r\">0.980<\/td>\r\n<td class=\"r\">0.971<\/td>\r\n<td class=\"r\">0.962<\/td>\r\n<td class=\"r\">0.952<\/td>\r\n<td class=\"r\">0.943<\/td>\r\n<td class=\"r\">0.935<\/td>\r\n<td class=\"r\">0.926<\/td>\r\n<td class=\"r\">0.917<\/td>\r\n<td class=\"r\">0.909<\/td>\r\n<td class=\"r\">0.893<\/td>\r\n<td class=\"r\">0.877<\/td>\r\n<td class=\"r\">0.870<\/td>\r\n<td class=\"r\">0.862<\/td>\r\n<td class=\"r\">0.847<\/td>\r\n<td class=\"r\">0.833<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 2<\/td>\r\n<td class=\"r\">0.980<\/td>\r\n<td class=\"r\">0.961<\/td>\r\n<td class=\"r\">0.943<\/td>\r\n<td class=\"r\">0.925<\/td>\r\n<td class=\"r\">0.907<\/td>\r\n<td class=\"r\">0.890<\/td>\r\n<td class=\"r\">0.873<\/td>\r\n<td class=\"r\">0.857<\/td>\r\n<td class=\"r\">0.842<\/td>\r\n<td class=\"r\">0.826<\/td>\r\n<td class=\"r\">0.797<\/td>\r\n<td class=\"r\">0.769<\/td>\r\n<td class=\"r\">0.756<\/td>\r\n<td class=\"r\">0.743<\/td>\r\n<td class=\"r\">0.718<\/td>\r\n<td class=\"r\">0.694<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 3<\/td>\r\n<td class=\"r\">0.971<\/td>\r\n<td class=\"r\">0.942<\/td>\r\n<td class=\"r\">0.915<\/td>\r\n<td class=\"r\">0.889<\/td>\r\n<td class=\"r\">0.864<\/td>\r\n<td class=\"r\">0.840<\/td>\r\n<td class=\"r\">0.816<\/td>\r\n<td class=\"r\">0.794<\/td>\r\n<td class=\"r\">0.772<\/td>\r\n<td class=\"r\">0.751<\/td>\r\n<td class=\"r\">0.712<\/td>\r\n<td class=\"r\">0.675<\/td>\r\n<td class=\"r\">0.658<\/td>\r\n<td class=\"r\">0.641<\/td>\r\n<td class=\"r\">0.609<\/td>\r\n<td class=\"r\">0.579<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 4<\/td>\r\n<td class=\"r\">0.961<\/td>\r\n<td class=\"r\">0.924<\/td>\r\n<td class=\"r\">0.888<\/td>\r\n<td class=\"r\">0.855<\/td>\r\n<td class=\"r\">0.823<\/td>\r\n<td class=\"r\">0.792<\/td>\r\n<td class=\"r\">0.763<\/td>\r\n<td class=\"r\">0.735<\/td>\r\n<td class=\"r\">0.708<\/td>\r\n<td class=\"r\">0.683<\/td>\r\n<td class=\"r\">0.636<\/td>\r\n<td class=\"r\">0.592<\/td>\r\n<td class=\"r\">0.572<\/td>\r\n<td class=\"r\">0.552<\/td>\r\n<td class=\"r\">0.516<\/td>\r\n<td class=\"r\">0.482<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 5<\/td>\r\n<td class=\"r\">0.951<\/td>\r\n<td class=\"r\">0.906<\/td>\r\n<td class=\"r\">0.863<\/td>\r\n<td class=\"r\">0.822<\/td>\r\n<td class=\"r\">0.784<\/td>\r\n<td class=\"r\">0.747<\/td>\r\n<td class=\"r\">0.713<\/td>\r\n<td class=\"r\">0.681<\/td>\r\n<td class=\"r\">0.650<\/td>\r\n<td class=\"r\">0.621<\/td>\r\n<td class=\"r\">0.567<\/td>\r\n<td class=\"r\">0.519<\/td>\r\n<td class=\"r\">0.497<\/td>\r\n<td class=\"r\">0.476<\/td>\r\n<td class=\"r\">0.437<\/td>\r\n<td class=\"r\">0.402<\/td>\r\n<\/tr>\r\n<tr aria-hidden=\"true\">\r\n<td colspan=\"17\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 6<\/td>\r\n<td class=\"r\">0.942<\/td>\r\n<td class=\"r\">0.888<\/td>\r\n<td class=\"r\">0.837<\/td>\r\n<td class=\"r\">0.790<\/td>\r\n<td class=\"r\">0.746<\/td>\r\n<td class=\"r\">0.705<\/td>\r\n<td class=\"r\">0.666<\/td>\r\n<td class=\"r\">0.630<\/td>\r\n<td class=\"r\">0.596<\/td>\r\n<td class=\"r\">0.564<\/td>\r\n<td class=\"r\">0.507<\/td>\r\n<td class=\"r\">0.456<\/td>\r\n<td class=\"r\">0.432<\/td>\r\n<td class=\"r\">0.410<\/td>\r\n<td class=\"r\">0.370<\/td>\r\n<td class=\"r\">0.335<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 7<\/td>\r\n<td class=\"r\">0.933<\/td>\r\n<td class=\"r\">0.871<\/td>\r\n<td class=\"r\">0.813<\/td>\r\n<td class=\"r\">0.760<\/td>\r\n<td class=\"r\">0.711<\/td>\r\n<td class=\"r\">0.665<\/td>\r\n<td class=\"r\">0.623<\/td>\r\n<td class=\"r\">0.583<\/td>\r\n<td class=\"r\">0.547<\/td>\r\n<td class=\"r\">0.513<\/td>\r\n<td class=\"r\">0.452<\/td>\r\n<td class=\"r\">0.400<\/td>\r\n<td class=\"r\">0.376<\/td>\r\n<td class=\"r\">0.354<\/td>\r\n<td class=\"r\">0.314<\/td>\r\n<td class=\"r\">0.279<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 8<\/td>\r\n<td class=\"r\">0.923<\/td>\r\n<td class=\"r\">0.853<\/td>\r\n<td class=\"r\">0.789<\/td>\r\n<td class=\"r\">0.731<\/td>\r\n<td class=\"r\">0.677<\/td>\r\n<td class=\"r\">0.627<\/td>\r\n<td class=\"r\">0.582<\/td>\r\n<td class=\"r\">0.540<\/td>\r\n<td class=\"r\">0.502<\/td>\r\n<td class=\"r\">0.467<\/td>\r\n<td class=\"r\">0.404<\/td>\r\n<td class=\"r\">0.351<\/td>\r\n<td class=\"r\">0.327<\/td>\r\n<td class=\"r\">0.305<\/td>\r\n<td class=\"r\">0.266<\/td>\r\n<td class=\"r\">0.233<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 9<\/td>\r\n<td class=\"r\">0.914<\/td>\r\n<td class=\"r\">0.837<\/td>\r\n<td class=\"r\">0.766<\/td>\r\n<td class=\"r\">0.703<\/td>\r\n<td class=\"r\">0.645<\/td>\r\n<td class=\"r\">0.592<\/td>\r\n<td class=\"r\">0.544<\/td>\r\n<td class=\"r\">0.500<\/td>\r\n<td class=\"r\">0.460<\/td>\r\n<td class=\"r\">0.424<\/td>\r\n<td class=\"r\">0.361<\/td>\r\n<td class=\"r\">0.308<\/td>\r\n<td class=\"r\">0.284<\/td>\r\n<td class=\"r\">0.263<\/td>\r\n<td class=\"r\">0.225<\/td>\r\n<td class=\"r\">0.194<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 10<\/td>\r\n<td class=\"r\">0.905<\/td>\r\n<td class=\"r\">0.820<\/td>\r\n<td class=\"r\">0.744<\/td>\r\n<td class=\"r\">0.676<\/td>\r\n<td class=\"r\">0.614<\/td>\r\n<td class=\"r\">0.558<\/td>\r\n<td class=\"r\">0.508<\/td>\r\n<td class=\"r\">0.463<\/td>\r\n<td class=\"r\">0.422<\/td>\r\n<td class=\"r highlight-green\">0.386<\/td>\r\n<td class=\"r\">0.322<\/td>\r\n<td class=\"r\">0.270<\/td>\r\n<td class=\"r\">0.247<\/td>\r\n<td class=\"r\">0.227<\/td>\r\n<td class=\"r\">0.191<\/td>\r\n<td class=\"r\">0.162<\/td>\r\n<\/tr>\r\n<tr aria-hidden=\"true\">\r\n<td colspan=\"17\"><\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 11<\/td>\r\n<td class=\"r\">0.896<\/td>\r\n<td class=\"r\">0.804<\/td>\r\n<td class=\"r\">0.722<\/td>\r\n<td class=\"r\">0.650<\/td>\r\n<td class=\"r\">0.585<\/td>\r\n<td class=\"r\">0.527<\/td>\r\n<td class=\"r\">0.475<\/td>\r\n<td class=\"r\">0.429<\/td>\r\n<td class=\"r\">0.388<\/td>\r\n<td class=\"r\">0.350<\/td>\r\n<td class=\"r\">0.287<\/td>\r\n<td class=\"r\">0.237<\/td>\r\n<td class=\"r\">0.215<\/td>\r\n<td class=\"r\">0.195<\/td>\r\n<td class=\"r\">0.162<\/td>\r\n<td class=\"r\">0.135<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 12<\/td>\r\n<td class=\"r\">0.887<\/td>\r\n<td class=\"r\">0.788<\/td>\r\n<td class=\"r\">0.701<\/td>\r\n<td class=\"r\">0.625<\/td>\r\n<td class=\"r\">0.557<\/td>\r\n<td class=\"r\">0.497<\/td>\r\n<td class=\"r\">0.444<\/td>\r\n<td class=\"r\">0.397<\/td>\r\n<td class=\"r\">0.356<\/td>\r\n<td class=\"r\">0.319<\/td>\r\n<td class=\"r\">0.257<\/td>\r\n<td class=\"r\">0.208<\/td>\r\n<td class=\"r\">0.187<\/td>\r\n<td class=\"r\">0.168<\/td>\r\n<td class=\"r\">0.137<\/td>\r\n<td class=\"r\">0.112<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 13<\/td>\r\n<td class=\"r\">0.879<\/td>\r\n<td class=\"r\">0.773<\/td>\r\n<td class=\"r\">0.681<\/td>\r\n<td class=\"r\">0.601<\/td>\r\n<td class=\"r\">0.530<\/td>\r\n<td class=\"r\">0.469<\/td>\r\n<td class=\"r\">0.415<\/td>\r\n<td class=\"r\">0.368<\/td>\r\n<td class=\"r\">0.326<\/td>\r\n<td class=\"r\">0.290<\/td>\r\n<td class=\"r\">0.229<\/td>\r\n<td class=\"r\">0.182<\/td>\r\n<td class=\"r\">0.163<\/td>\r\n<td class=\"r\">0.145<\/td>\r\n<td class=\"r\">0.116<\/td>\r\n<td class=\"r\">0.093<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 14<\/td>\r\n<td class=\"r\">0.870<\/td>\r\n<td class=\"r\">0.758<\/td>\r\n<td class=\"r\">0.661<\/td>\r\n<td class=\"r\">0.577<\/td>\r\n<td class=\"r\">0.505<\/td>\r\n<td class=\"r\">0.442<\/td>\r\n<td class=\"r\">0.388<\/td>\r\n<td class=\"r\">0.340<\/td>\r\n<td class=\"r\">0.299<\/td>\r\n<td class=\"r\">0.263<\/td>\r\n<td class=\"r\">0.205<\/td>\r\n<td class=\"r\">0.160<\/td>\r\n<td class=\"r\">0.141<\/td>\r\n<td class=\"r\">0.125<\/td>\r\n<td class=\"r\">0.099<\/td>\r\n<td class=\"r\">0.078<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nMore precisely (because factors in the tables are rounded), the present value of $12,000 at 10% for 10 years is $4,626.5194732\u2026 which we could round to $4,626.52.\r\n\r\nIf we were to invest that amount in a mutual fund that gave us an annual return of 10%, we would see the following results:\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<tbody>\r\n<tr>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\">BOY<\/th>\r\n<th class=\"r\" scope=\"col\">interest<\/th>\r\n<th class=\"r\" scope=\"col\">EOY<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 4,626.52<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 462.65<\/td>\r\n<td class=\"r\">$\u00a0 5,089.17<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 5,089.17<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 508.92<\/td>\r\n<td class=\"r\">$\u00a0 5,598.09<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a05,598.09<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 559.81<\/td>\r\n<td class=\"r\">$\u00a0 6,157.90<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a06,157.90<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 615.79<\/td>\r\n<td class=\"r\">$\u00a0 6,773.69<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 5<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a06,773.69<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 677.37<\/td>\r\n<td class=\"r\">$\u00a0 7,451.06<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 6<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 7,451.06<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 745.11<\/td>\r\n<td class=\"r\">$\u00a0 8,196.17<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 7<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a08,196.17<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 819.62<\/td>\r\n<td class=\"r\">$\u00a0 9,015.79<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 8<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 9,015.79<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 901.58<\/td>\r\n<td class=\"r\">$\u00a0 9,917.37<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 9<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a09,917.37<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 991.74<\/td>\r\n<td class=\"r\">$\u00a010,909.11<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 10<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 10,909.11<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a01,090.91<\/td>\r\n<td class=\"r\">$\u00a012,000.02<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nIn other words, $4,626.52 invested at 10% today will grow to $12,000.02 at the end of the tenth year. So, the present value of $12,000 is $4,626.52. The future value of $4,626.52 invested at 10% for 10 years is $12,000.02.\r\n\r\nIf we apply this logic to all of the cash flow numbers, using 10% as our discount rate and the appropriate number of years for each cash inflow, we get the following table of discounted cash flows:\r\n<p style=\"text-align: center;\">Discounted net cash inflows<\/p>\r\n\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<tbody>\r\n<tr>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\">Refurbish<\/th>\r\n<th class=\"r\" scope=\"col\">Purchase New<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td>PV Year 1<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a016,364<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a018,182<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 2<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a013,223<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a015,702<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 3<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a010,518<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a013,524<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 4<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8,196<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0\u00a0 11,611<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 5<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6,209<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 9,314<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 6<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4,516<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 7,338<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 7<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3,079<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 5,132<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 8<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1,866<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 3,266<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 9<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0-<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 2,120<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>PV Year 10<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0-<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 4,627<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a063,971<span class=\"u-sr-only\">Double line<\/span><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a090,816<span class=\"u-sr-only\">Double line<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\nApplying these numbers to our payback analysis, we find that the amount of time it takes for the refurbish option to pay for itself is 5 years 4 months:\r\n<p style=\"text-align: center;\">Refurbish<\/p>\r\n\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<tbody>\r\n<tr>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\">% of cash flows<\/th>\r\n<th class=\"r\" scope=\"col\">months<\/th>\r\n<th class=\"r\" scope=\"col\">years<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td>Cost to refurbish<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 56,000<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 1<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(16,364)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 39,636<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 2<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(13,223)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 26,413<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 3<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(10,518)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 15,895<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 4<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 (8,196)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0\u00a0 7,699<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 5<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0\u00a0(6,209)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0\u00a0 1,489<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 6<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 (1,489)<\/td>\r\n<td class=\"r\">33%<\/td>\r\n<td class=\"r\">4.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 0.33<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nAnd the payback period for a new machine is 6 years 10 months.\r\n<p style=\"text-align: center;\">Purchase<\/p>\r\n\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<tbody>\r\n<tr>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\"><\/th>\r\n<th class=\"r\" scope=\"col\">% of cash flows<\/th>\r\n<th class=\"r\" scope=\"col\">months<\/th>\r\n<th class=\"r\" scope=\"col\">years<\/th>\r\n<\/tr>\r\n<\/tbody>\r\n<tbody>\r\n<tr>\r\n<td>Cost to purchase<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 80,000<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 1<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 (18,182)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 61,818<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 2<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 (15,702)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 46,116<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 3<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 (13,524)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 32,592<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 4<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 (11,611)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 20,981<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 5<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(9,314)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 11,667<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 6<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(7,338)<\/td>\r\n<td class=\"r\">100%<\/td>\r\n<td class=\"r\">12.0<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a04,329<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Recaptured YR 7<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(4,329)<\/td>\r\n<td class=\"r\">84%<\/td>\r\n<td class=\"r\">10.1<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 0.84<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Left to recapture<\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (0)<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\nThis is an improvement over the simple payback method, but still does not take into account the overall rate of return and it does not address cash flows that occur after the payback period.\r\n\r\nBefore we address those issues, check your understanding of the payback method using discounted cash flows.\r\n<div class=\"textbox tryit\">\r\n<h3>Practice Question<\/h3>\r\n[ohm_question hide_question_numbers=1]221580[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Calculate the payback period using discounted cash flows<\/li>\n<\/ul>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-1797\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5469\/2021\/01\/17231744\/kieran-wood-UOk1ghQ7juY-unsplash-300x225.jpg\" alt=\"Wooden puzzle\" width=\"500\" height=\"375\" \/><\/p>\n<p>We can improve the payback method by using discounted cash flows instead of the nominal (undiscounted, unadjusted) estimates.<\/p>\n<p>Let\u2019s review the example:<\/p>\n<p>JuxtaPos makes interlocking wooden puzzles. One of the machines is old and management is considering either replacing it or refurbishing it. Replacing it will cost $80,000. The new machine would last 10 years and have a residual value of $10,000. Refurbishing the old machine for $56,000 will keep it in service for another 8 years and it will have no residual value at the end of that time.<\/p>\n<p>You have estimated production under both scenarios and used those numbers to compute revenue. You have also estimated operating costs and have created the following table of net cash inflows:<\/p>\n<p style=\"text-align: center;\">Net cash inflows (additional cash revenues &#8211; additional cash expenses)<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<tbody>\n<tr>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\">Refurbish<\/th>\n<th class=\"r\" scope=\"col\">Purchase New<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 18,000<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 20,000<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 16,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 19,000<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 14,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 18,000<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 12,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 17,000<\/td>\n<\/tr>\n<tr>\n<td>Year 5<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 10,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 15,000<\/td>\n<\/tr>\n<tr>\n<td>Year 6<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 13,000<\/td>\n<\/tr>\n<tr>\n<td>Year 7<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 10,000<\/td>\n<\/tr>\n<tr>\n<td>Year 8<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 7,000<\/td>\n<\/tr>\n<tr>\n<td>Year 9<\/td>\n<td><\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 5,000<\/td>\n<\/tr>\n<tr>\n<td>Year 10 (includes proceeds from sale of machine)<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 12,000<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 88,000<span class=\"u-sr-only\">Double line<\/span><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 136,000<span class=\"u-sr-only\">Double line<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>None of these values are adjusted for the time value of money. For instance, $12,000 10 years from now is not the same as $12,000 today.<\/p>\n<p>Let\u2019s assume JuxtaPos uses a 10% hurdle or discount rate for capital budgeting purposes. If we use a present value table, we find that the factor of 10% and 10 years is 0.386. Multiplying the factor by our $12,000 future value for year 10 gives us a present value of $4,632. That means that if we are to translate all of the future numbers back to Year 0 when we make the initial purchase (beginning of Year 1), the $12,000 future cash flow in Year 10 would be the equivalent of a $4,632 cash flow back at the beginning of Year 1.<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table gridded\">\n<thead>\n<tr>\n<th colspan=\"17\">Present Value of $1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Periods<\/td>\n<td class=\"c highlight-green\">1%<\/td>\n<td class=\"c highlight-green\">2%<\/td>\n<td class=\"c highlight-green\">3%<\/td>\n<td class=\"c highlight-green\">4%<\/td>\n<td class=\"c highlight-green\">5%<\/td>\n<td class=\"c highlight-green\">6%<\/td>\n<td class=\"c highlight-green\">7%<\/td>\n<td class=\"c highlight-green\">8%<\/td>\n<td class=\"c highlight-green\">9%<\/td>\n<td class=\"c highlight-green\">10%<\/td>\n<td class=\"c highlight-green\">12%<\/td>\n<td class=\"c highlight-green\">14%<\/td>\n<td class=\"c highlight-green\">15%<\/td>\n<td class=\"c highlight-green\">16%<\/td>\n<td class=\"c highlight-green\">18%<\/td>\n<td class=\"c highlight-green\">20%<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 1<\/td>\n<td class=\"r\">0.990<\/td>\n<td class=\"r\">0.980<\/td>\n<td class=\"r\">0.971<\/td>\n<td class=\"r\">0.962<\/td>\n<td class=\"r\">0.952<\/td>\n<td class=\"r\">0.943<\/td>\n<td class=\"r\">0.935<\/td>\n<td class=\"r\">0.926<\/td>\n<td class=\"r\">0.917<\/td>\n<td class=\"r\">0.909<\/td>\n<td class=\"r\">0.893<\/td>\n<td class=\"r\">0.877<\/td>\n<td class=\"r\">0.870<\/td>\n<td class=\"r\">0.862<\/td>\n<td class=\"r\">0.847<\/td>\n<td class=\"r\">0.833<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 2<\/td>\n<td class=\"r\">0.980<\/td>\n<td class=\"r\">0.961<\/td>\n<td class=\"r\">0.943<\/td>\n<td class=\"r\">0.925<\/td>\n<td class=\"r\">0.907<\/td>\n<td class=\"r\">0.890<\/td>\n<td class=\"r\">0.873<\/td>\n<td class=\"r\">0.857<\/td>\n<td class=\"r\">0.842<\/td>\n<td class=\"r\">0.826<\/td>\n<td class=\"r\">0.797<\/td>\n<td class=\"r\">0.769<\/td>\n<td class=\"r\">0.756<\/td>\n<td class=\"r\">0.743<\/td>\n<td class=\"r\">0.718<\/td>\n<td class=\"r\">0.694<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 3<\/td>\n<td class=\"r\">0.971<\/td>\n<td class=\"r\">0.942<\/td>\n<td class=\"r\">0.915<\/td>\n<td class=\"r\">0.889<\/td>\n<td class=\"r\">0.864<\/td>\n<td class=\"r\">0.840<\/td>\n<td class=\"r\">0.816<\/td>\n<td class=\"r\">0.794<\/td>\n<td class=\"r\">0.772<\/td>\n<td class=\"r\">0.751<\/td>\n<td class=\"r\">0.712<\/td>\n<td class=\"r\">0.675<\/td>\n<td class=\"r\">0.658<\/td>\n<td class=\"r\">0.641<\/td>\n<td class=\"r\">0.609<\/td>\n<td class=\"r\">0.579<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 4<\/td>\n<td class=\"r\">0.961<\/td>\n<td class=\"r\">0.924<\/td>\n<td class=\"r\">0.888<\/td>\n<td class=\"r\">0.855<\/td>\n<td class=\"r\">0.823<\/td>\n<td class=\"r\">0.792<\/td>\n<td class=\"r\">0.763<\/td>\n<td class=\"r\">0.735<\/td>\n<td class=\"r\">0.708<\/td>\n<td class=\"r\">0.683<\/td>\n<td class=\"r\">0.636<\/td>\n<td class=\"r\">0.592<\/td>\n<td class=\"r\">0.572<\/td>\n<td class=\"r\">0.552<\/td>\n<td class=\"r\">0.516<\/td>\n<td class=\"r\">0.482<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 5<\/td>\n<td class=\"r\">0.951<\/td>\n<td class=\"r\">0.906<\/td>\n<td class=\"r\">0.863<\/td>\n<td class=\"r\">0.822<\/td>\n<td class=\"r\">0.784<\/td>\n<td class=\"r\">0.747<\/td>\n<td class=\"r\">0.713<\/td>\n<td class=\"r\">0.681<\/td>\n<td class=\"r\">0.650<\/td>\n<td class=\"r\">0.621<\/td>\n<td class=\"r\">0.567<\/td>\n<td class=\"r\">0.519<\/td>\n<td class=\"r\">0.497<\/td>\n<td class=\"r\">0.476<\/td>\n<td class=\"r\">0.437<\/td>\n<td class=\"r\">0.402<\/td>\n<\/tr>\n<tr aria-hidden=\"true\">\n<td colspan=\"17\"><\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 6<\/td>\n<td class=\"r\">0.942<\/td>\n<td class=\"r\">0.888<\/td>\n<td class=\"r\">0.837<\/td>\n<td class=\"r\">0.790<\/td>\n<td class=\"r\">0.746<\/td>\n<td class=\"r\">0.705<\/td>\n<td class=\"r\">0.666<\/td>\n<td class=\"r\">0.630<\/td>\n<td class=\"r\">0.596<\/td>\n<td class=\"r\">0.564<\/td>\n<td class=\"r\">0.507<\/td>\n<td class=\"r\">0.456<\/td>\n<td class=\"r\">0.432<\/td>\n<td class=\"r\">0.410<\/td>\n<td class=\"r\">0.370<\/td>\n<td class=\"r\">0.335<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 7<\/td>\n<td class=\"r\">0.933<\/td>\n<td class=\"r\">0.871<\/td>\n<td class=\"r\">0.813<\/td>\n<td class=\"r\">0.760<\/td>\n<td class=\"r\">0.711<\/td>\n<td class=\"r\">0.665<\/td>\n<td class=\"r\">0.623<\/td>\n<td class=\"r\">0.583<\/td>\n<td class=\"r\">0.547<\/td>\n<td class=\"r\">0.513<\/td>\n<td class=\"r\">0.452<\/td>\n<td class=\"r\">0.400<\/td>\n<td class=\"r\">0.376<\/td>\n<td class=\"r\">0.354<\/td>\n<td class=\"r\">0.314<\/td>\n<td class=\"r\">0.279<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 8<\/td>\n<td class=\"r\">0.923<\/td>\n<td class=\"r\">0.853<\/td>\n<td class=\"r\">0.789<\/td>\n<td class=\"r\">0.731<\/td>\n<td class=\"r\">0.677<\/td>\n<td class=\"r\">0.627<\/td>\n<td class=\"r\">0.582<\/td>\n<td class=\"r\">0.540<\/td>\n<td class=\"r\">0.502<\/td>\n<td class=\"r\">0.467<\/td>\n<td class=\"r\">0.404<\/td>\n<td class=\"r\">0.351<\/td>\n<td class=\"r\">0.327<\/td>\n<td class=\"r\">0.305<\/td>\n<td class=\"r\">0.266<\/td>\n<td class=\"r\">0.233<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 9<\/td>\n<td class=\"r\">0.914<\/td>\n<td class=\"r\">0.837<\/td>\n<td class=\"r\">0.766<\/td>\n<td class=\"r\">0.703<\/td>\n<td class=\"r\">0.645<\/td>\n<td class=\"r\">0.592<\/td>\n<td class=\"r\">0.544<\/td>\n<td class=\"r\">0.500<\/td>\n<td class=\"r\">0.460<\/td>\n<td class=\"r\">0.424<\/td>\n<td class=\"r\">0.361<\/td>\n<td class=\"r\">0.308<\/td>\n<td class=\"r\">0.284<\/td>\n<td class=\"r\">0.263<\/td>\n<td class=\"r\">0.225<\/td>\n<td class=\"r\">0.194<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 10<\/td>\n<td class=\"r\">0.905<\/td>\n<td class=\"r\">0.820<\/td>\n<td class=\"r\">0.744<\/td>\n<td class=\"r\">0.676<\/td>\n<td class=\"r\">0.614<\/td>\n<td class=\"r\">0.558<\/td>\n<td class=\"r\">0.508<\/td>\n<td class=\"r\">0.463<\/td>\n<td class=\"r\">0.422<\/td>\n<td class=\"r highlight-green\">0.386<\/td>\n<td class=\"r\">0.322<\/td>\n<td class=\"r\">0.270<\/td>\n<td class=\"r\">0.247<\/td>\n<td class=\"r\">0.227<\/td>\n<td class=\"r\">0.191<\/td>\n<td class=\"r\">0.162<\/td>\n<\/tr>\n<tr aria-hidden=\"true\">\n<td colspan=\"17\"><\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 11<\/td>\n<td class=\"r\">0.896<\/td>\n<td class=\"r\">0.804<\/td>\n<td class=\"r\">0.722<\/td>\n<td class=\"r\">0.650<\/td>\n<td class=\"r\">0.585<\/td>\n<td class=\"r\">0.527<\/td>\n<td class=\"r\">0.475<\/td>\n<td class=\"r\">0.429<\/td>\n<td class=\"r\">0.388<\/td>\n<td class=\"r\">0.350<\/td>\n<td class=\"r\">0.287<\/td>\n<td class=\"r\">0.237<\/td>\n<td class=\"r\">0.215<\/td>\n<td class=\"r\">0.195<\/td>\n<td class=\"r\">0.162<\/td>\n<td class=\"r\">0.135<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 12<\/td>\n<td class=\"r\">0.887<\/td>\n<td class=\"r\">0.788<\/td>\n<td class=\"r\">0.701<\/td>\n<td class=\"r\">0.625<\/td>\n<td class=\"r\">0.557<\/td>\n<td class=\"r\">0.497<\/td>\n<td class=\"r\">0.444<\/td>\n<td class=\"r\">0.397<\/td>\n<td class=\"r\">0.356<\/td>\n<td class=\"r\">0.319<\/td>\n<td class=\"r\">0.257<\/td>\n<td class=\"r\">0.208<\/td>\n<td class=\"r\">0.187<\/td>\n<td class=\"r\">0.168<\/td>\n<td class=\"r\">0.137<\/td>\n<td class=\"r\">0.112<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 13<\/td>\n<td class=\"r\">0.879<\/td>\n<td class=\"r\">0.773<\/td>\n<td class=\"r\">0.681<\/td>\n<td class=\"r\">0.601<\/td>\n<td class=\"r\">0.530<\/td>\n<td class=\"r\">0.469<\/td>\n<td class=\"r\">0.415<\/td>\n<td class=\"r\">0.368<\/td>\n<td class=\"r\">0.326<\/td>\n<td class=\"r\">0.290<\/td>\n<td class=\"r\">0.229<\/td>\n<td class=\"r\">0.182<\/td>\n<td class=\"r\">0.163<\/td>\n<td class=\"r\">0.145<\/td>\n<td class=\"r\">0.116<\/td>\n<td class=\"r\">0.093<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 14<\/td>\n<td class=\"r\">0.870<\/td>\n<td class=\"r\">0.758<\/td>\n<td class=\"r\">0.661<\/td>\n<td class=\"r\">0.577<\/td>\n<td class=\"r\">0.505<\/td>\n<td class=\"r\">0.442<\/td>\n<td class=\"r\">0.388<\/td>\n<td class=\"r\">0.340<\/td>\n<td class=\"r\">0.299<\/td>\n<td class=\"r\">0.263<\/td>\n<td class=\"r\">0.205<\/td>\n<td class=\"r\">0.160<\/td>\n<td class=\"r\">0.141<\/td>\n<td class=\"r\">0.125<\/td>\n<td class=\"r\">0.099<\/td>\n<td class=\"r\">0.078<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>More precisely (because factors in the tables are rounded), the present value of $12,000 at 10% for 10 years is $4,626.5194732\u2026 which we could round to $4,626.52.<\/p>\n<p>If we were to invest that amount in a mutual fund that gave us an annual return of 10%, we would see the following results:<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<tbody>\n<tr>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\">BOY<\/th>\n<th class=\"r\" scope=\"col\">interest<\/th>\n<th class=\"r\" scope=\"col\">EOY<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 4,626.52<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 462.65<\/td>\n<td class=\"r\">$\u00a0 5,089.17<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 5,089.17<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 508.92<\/td>\n<td class=\"r\">$\u00a0 5,598.09<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a05,598.09<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 559.81<\/td>\n<td class=\"r\">$\u00a0 6,157.90<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a06,157.90<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 615.79<\/td>\n<td class=\"r\">$\u00a0 6,773.69<\/td>\n<\/tr>\n<tr>\n<td>Year 5<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a06,773.69<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 677.37<\/td>\n<td class=\"r\">$\u00a0 7,451.06<\/td>\n<\/tr>\n<tr>\n<td>Year 6<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 7,451.06<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 745.11<\/td>\n<td class=\"r\">$\u00a0 8,196.17<\/td>\n<\/tr>\n<tr>\n<td>Year 7<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a08,196.17<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 819.62<\/td>\n<td class=\"r\">$\u00a0 9,015.79<\/td>\n<\/tr>\n<tr>\n<td>Year 8<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 9,015.79<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 901.58<\/td>\n<td class=\"r\">$\u00a0 9,917.37<\/td>\n<\/tr>\n<tr>\n<td>Year 9<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a09,917.37<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 991.74<\/td>\n<td class=\"r\">$\u00a010,909.11<\/td>\n<\/tr>\n<tr>\n<td>Year 10<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 10,909.11<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a01,090.91<\/td>\n<td class=\"r\">$\u00a012,000.02<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In other words, $4,626.52 invested at 10% today will grow to $12,000.02 at the end of the tenth year. So, the present value of $12,000 is $4,626.52. The future value of $4,626.52 invested at 10% for 10 years is $12,000.02.<\/p>\n<p>If we apply this logic to all of the cash flow numbers, using 10% as our discount rate and the appropriate number of years for each cash inflow, we get the following table of discounted cash flows:<\/p>\n<p style=\"text-align: center;\">Discounted net cash inflows<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<tbody>\n<tr>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\">Refurbish<\/th>\n<th class=\"r\" scope=\"col\">Purchase New<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>PV Year 1<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a0\u00a016,364<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a018,182<\/td>\n<\/tr>\n<tr>\n<td>PV Year 2<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0\u00a013,223<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a015,702<\/td>\n<\/tr>\n<tr>\n<td>PV Year 3<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a010,518<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a013,524<\/td>\n<\/tr>\n<tr>\n<td>PV Year 4<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8,196<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0\u00a0 11,611<\/td>\n<\/tr>\n<tr>\n<td>PV Year 5<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 6,209<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 9,314<\/td>\n<\/tr>\n<tr>\n<td>PV Year 6<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 4,516<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 7,338<\/td>\n<\/tr>\n<tr>\n<td>PV Year 7<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3,079<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 5,132<\/td>\n<\/tr>\n<tr>\n<td>PV Year 8<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 1,866<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 3,266<\/td>\n<\/tr>\n<tr>\n<td>PV Year 9<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8211;<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 2,120<\/td>\n<\/tr>\n<tr>\n<td>PV Year 10<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0&#8211;<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 4,627<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a063,971<span class=\"u-sr-only\">Double line<\/span><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a090,816<span class=\"u-sr-only\">Double line<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>Applying these numbers to our payback analysis, we find that the amount of time it takes for the refurbish option to pay for itself is 5 years 4 months:<\/p>\n<p style=\"text-align: center;\">Refurbish<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<tbody>\n<tr>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\">% of cash flows<\/th>\n<th class=\"r\" scope=\"col\">months<\/th>\n<th class=\"r\" scope=\"col\">years<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Cost to refurbish<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 56,000<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 1<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(16,364)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 39,636<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 2<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(13,223)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 26,413<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 3<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(10,518)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 15,895<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 4<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 (8,196)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0\u00a0 7,699<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 5<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0\u00a0(6,209)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0\u00a0 1,489<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 6<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 (1,489)<\/td>\n<td class=\"r\">33%<\/td>\n<td class=\"r\">4.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 0.33<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 0<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>And the payback period for a new machine is 6 years 10 months.<\/p>\n<p style=\"text-align: center;\">Purchase<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<tbody>\n<tr>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\"><\/th>\n<th class=\"r\" scope=\"col\">% of cash flows<\/th>\n<th class=\"r\" scope=\"col\">months<\/th>\n<th class=\"r\" scope=\"col\">years<\/th>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Cost to purchase<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 80,000<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 1<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 (18,182)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 61,818<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 2<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 (15,702)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 46,116<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 3<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 (13,524)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 32,592<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 4<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 (11,611)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 20,981<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 5<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(9,314)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 11,667<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 6<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(7,338)<\/td>\n<td class=\"r\">100%<\/td>\n<td class=\"r\">12.0<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 1.00<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 \u00a04,329<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Recaptured YR 7<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0(4,329)<\/td>\n<td class=\"r\">84%<\/td>\n<td class=\"r\">10.1<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 0.84<\/td>\n<\/tr>\n<tr>\n<td>Left to recapture<\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (0)<\/td>\n<td><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>This is an improvement over the simple payback method, but still does not take into account the overall rate of return and it does not address cash flows that occur after the payback period.<\/p>\n<p>Before we address those issues, check your understanding of the payback method using discounted cash flows.<\/p>\n<div class=\"textbox tryit\">\n<h3>Practice Question<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm221580\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=221580&theme=oea&iframe_resize_id=ohm221580\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-259\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Discounted Payback. <strong>Authored by<\/strong>: Joseph Cooke. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Wooden puzzle. <strong>Provided by<\/strong>: Unsplash. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/unsplash.com\/photos\/UOk1ghQ7juY\">https:\/\/unsplash.com\/photos\/UOk1ghQ7juY<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":364389,"menu_order":14,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Discounted Payback\",\"author\":\"Joseph Cooke\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Wooden puzzle\",\"author\":\"\",\"organization\":\"Unsplash\",\"url\":\"https:\/\/unsplash.com\/photos\/UOk1ghQ7juY\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-259","chapter","type-chapter","status-publish","hentry"],"part":37,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/259","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/wp\/v2\/users\/364389"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/259\/revisions"}],"predecessor-version":[{"id":1894,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/259\/revisions\/1894"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/parts\/37"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/259\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/wp\/v2\/media?parent=259"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/pressbooks\/v2\/chapter-type?post=259"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/wp\/v2\/contributor?post=259"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-clinton-managerialaccounting\/wp-json\/wp\/v2\/license?post=259"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}