{"id":267,"date":"2021-01-26T22:33:36","date_gmt":"2021-01-26T22:33:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/?post_type=chapter&#038;p=267"},"modified":"2021-08-13T16:05:34","modified_gmt":"2021-08-13T16:05:34","slug":"profitability-index","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/chapter\/profitability-index\/","title":{"raw":"Internal Rate of Return","rendered":"Internal Rate of Return"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Calculate the internal rate of return<\/li>\r\n<\/ul>\r\n<\/div>\r\nContinuing to use the JuxtaPos scenario where management is considering adding a line of puzzles that necessitates a new machine that will cost $230,000 with an estimated useful life of six years and a residual value of $40,000, let\u2019s see if we can provide a number to management that represents the internal rate of return (IRR) on this project.\r\n\r\nAgain, net annual cash flows are as follows:\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<thead>\r\n<tr class=\"u-sr-only\">\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Amount<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 5<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 50,000<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 6 (includes the $40,000 proceeds from sale)<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nIf these amounts were even, we could look for an annuity table, find a factor that represents the annuity, and then backtrack that number to an approximate interest rate.\r\n\r\nLet\u2019s take a simpler example of an investment of $45,560 that results in an annual cash inflow of $15,000 for four years with no residual value. Is this a good investment? We are trading $45,560 for $60,000 over the next four years.\r\n\r\nIf we look at how the factors in the Present Value of an annuity (a steady stream of future cash flows) are created, we take $45,560 and divide it by the cash flow of $15,000 to get a factor of 3.037 (rounded to the nearest thousandth). On the table, if we follow the row for n=4 across until we find something close to 3.037, we can then extrapolate that the rate of return on this investment is 12%.\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 Ordinary Annuity of $1<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td class=\"c highlight-green\">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\">1.970<\/td>\r\n<td class=\"r\">1.942<\/td>\r\n<td class=\"r\">1.913<\/td>\r\n<td class=\"r\">1.886<\/td>\r\n<td class=\"r\">1.859<\/td>\r\n<td class=\"r\">1.833<\/td>\r\n<td class=\"r\">1.808<\/td>\r\n<td class=\"r\">1.783<\/td>\r\n<td class=\"r\">1.759<\/td>\r\n<td class=\"r\">1.736<\/td>\r\n<td class=\"r\">1.690<\/td>\r\n<td class=\"r\">1.647<\/td>\r\n<td class=\"r\">1.626<\/td>\r\n<td class=\"r\">1.605<\/td>\r\n<td class=\"r\">1.566<\/td>\r\n<td class=\"r\">1.528<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 3<\/td>\r\n<td class=\"r\">2.941<\/td>\r\n<td class=\"r\">2.884<\/td>\r\n<td class=\"r\">2.829<\/td>\r\n<td class=\"r\">2.775<\/td>\r\n<td class=\"r\">2.723<\/td>\r\n<td class=\"r\">2.673<\/td>\r\n<td class=\"r\">2.624<\/td>\r\n<td class=\"r\">2.577<\/td>\r\n<td class=\"r\">2.531<\/td>\r\n<td class=\"r\">2.487<\/td>\r\n<td class=\"r\">2.402<\/td>\r\n<td class=\"r\">2.322<\/td>\r\n<td class=\"r\">2.283<\/td>\r\n<td class=\"r\">2.246<\/td>\r\n<td class=\"r\">2.174<\/td>\r\n<td class=\"r\">2.106<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 4<\/td>\r\n<td class=\"r\">3.902<\/td>\r\n<td class=\"r\">3.808<\/td>\r\n<td class=\"r\">3.717<\/td>\r\n<td class=\"r\">3.630<\/td>\r\n<td class=\"r\">3.546<\/td>\r\n<td class=\"r\">3.465<\/td>\r\n<td class=\"r\">3.387<\/td>\r\n<td class=\"r\">3.312<\/td>\r\n<td class=\"r\">3.240<\/td>\r\n<td class=\"r\">3.170<\/td>\r\n<td class=\"r highlight-green\">3.037<\/td>\r\n<td class=\"r\">2.914<\/td>\r\n<td class=\"r\">2.855<\/td>\r\n<td class=\"r\">2.798<\/td>\r\n<td class=\"r\">2.690<\/td>\r\n<td class=\"r\">2.589<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 5<\/td>\r\n<td class=\"r\">4.853<\/td>\r\n<td class=\"r\">4.713<\/td>\r\n<td class=\"r\">4.580<\/td>\r\n<td class=\"r\">4.452<\/td>\r\n<td class=\"r\">4.329<\/td>\r\n<td class=\"r\">4.212<\/td>\r\n<td class=\"r\">4.100<\/td>\r\n<td class=\"r\">3.993<\/td>\r\n<td class=\"r\">3.890<\/td>\r\n<td class=\"r\">3.791<\/td>\r\n<td class=\"r\">3.605<\/td>\r\n<td class=\"r\">3.433<\/td>\r\n<td class=\"r\">3.352<\/td>\r\n<td class=\"r\">3.274<\/td>\r\n<td class=\"r\">3.127<\/td>\r\n<td class=\"r\">2.991<\/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\">5.795<\/td>\r\n<td class=\"r\">5.601<\/td>\r\n<td class=\"r\">5.417<\/td>\r\n<td class=\"r\">5.242<\/td>\r\n<td class=\"r\">5.076<\/td>\r\n<td class=\"r\">4.917<\/td>\r\n<td class=\"r\">4.767<\/td>\r\n<td class=\"r\">4.623<\/td>\r\n<td class=\"r\">4.486<\/td>\r\n<td class=\"r\">4.355<\/td>\r\n<td class=\"r\">4.111<\/td>\r\n<td class=\"r\">3.889<\/td>\r\n<td class=\"r\">3.784<\/td>\r\n<td class=\"r\">3.685<\/td>\r\n<td class=\"r\">3.489<\/td>\r\n<td class=\"r\">3.326<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 7<\/td>\r\n<td class=\"r\">6.728<\/td>\r\n<td class=\"r\">6.472<\/td>\r\n<td class=\"r\">6.230<\/td>\r\n<td class=\"r\">6.002<\/td>\r\n<td class=\"r\">5.786<\/td>\r\n<td class=\"r\">5.582<\/td>\r\n<td class=\"r\">5.389<\/td>\r\n<td class=\"r\">5.206<\/td>\r\n<td class=\"r\">5.033<\/td>\r\n<td class=\"r\">4.868<\/td>\r\n<td class=\"r\">4.564<\/td>\r\n<td class=\"r\">4.288<\/td>\r\n<td class=\"r\">4.160<\/td>\r\n<td class=\"r\">4.039<\/td>\r\n<td class=\"r\">3.812<\/td>\r\n<td class=\"r\">3.605<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 8<\/td>\r\n<td class=\"r\">7.652<\/td>\r\n<td class=\"r\">7.325<\/td>\r\n<td class=\"r\">7.020<\/td>\r\n<td class=\"r\">6.733<\/td>\r\n<td class=\"r\">6.463<\/td>\r\n<td class=\"r\">6.210<\/td>\r\n<td class=\"r\">5.971<\/td>\r\n<td class=\"r\">5.747<\/td>\r\n<td class=\"r\">5.535<\/td>\r\n<td class=\"r\">5.335<\/td>\r\n<td class=\"r\">4.968<\/td>\r\n<td class=\"r\">4.639<\/td>\r\n<td class=\"r\">4.487<\/td>\r\n<td class=\"r\">4.344<\/td>\r\n<td class=\"r\">4.078<\/td>\r\n<td class=\"r\">3.837<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 9<\/td>\r\n<td class=\"r\">8.566<\/td>\r\n<td class=\"r\">8.162<\/td>\r\n<td class=\"r\">7.786<\/td>\r\n<td class=\"r\">7.435<\/td>\r\n<td class=\"r\">7.108<\/td>\r\n<td class=\"r\">6.802<\/td>\r\n<td class=\"r\">6.515<\/td>\r\n<td class=\"r\">6.247<\/td>\r\n<td class=\"r\">5.995<\/td>\r\n<td class=\"r\">5.759<\/td>\r\n<td class=\"r\">5.328<\/td>\r\n<td class=\"r\">4.946<\/td>\r\n<td class=\"r\">4.772<\/td>\r\n<td class=\"r\">4.607<\/td>\r\n<td class=\"r\">4.303<\/td>\r\n<td class=\"r\">4.031<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 10<\/td>\r\n<td class=\"r\">9.471<\/td>\r\n<td class=\"r\">8.983<\/td>\r\n<td class=\"r\">8.530<\/td>\r\n<td class=\"r\">8.111<\/td>\r\n<td class=\"r\">7.722<\/td>\r\n<td class=\"r\">7.360<\/td>\r\n<td class=\"r\">7.024<\/td>\r\n<td class=\"r\">6.710<\/td>\r\n<td class=\"r\">6.418<\/td>\r\n<td class=\"r\">6.145<\/td>\r\n<td class=\"r\">5.650<\/td>\r\n<td class=\"r\">5.216<\/td>\r\n<td class=\"r\">5.019<\/td>\r\n<td class=\"r\">4.833<\/td>\r\n<td class=\"r\">4.494<\/td>\r\n<td class=\"r\">4.192<\/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\">10.368<\/td>\r\n<td class=\"r\">9.787<\/td>\r\n<td class=\"r\">9.253<\/td>\r\n<td class=\"r\">8.760<\/td>\r\n<td class=\"r\">8.306<\/td>\r\n<td class=\"r\">7.887<\/td>\r\n<td class=\"r\">7.499<\/td>\r\n<td class=\"r\">7.139<\/td>\r\n<td class=\"r\">6.805<\/td>\r\n<td class=\"r\">6.495<\/td>\r\n<td class=\"r\">5.938<\/td>\r\n<td class=\"r\">5.453<\/td>\r\n<td class=\"r\">5.234<\/td>\r\n<td class=\"r\">5.029<\/td>\r\n<td class=\"r\">4.656<\/td>\r\n<td class=\"r\">4.327<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 12<\/td>\r\n<td class=\"r\">11.255<\/td>\r\n<td class=\"r\">10.575<\/td>\r\n<td class=\"r\">9.954<\/td>\r\n<td class=\"r\">9.385<\/td>\r\n<td class=\"r\">8.863<\/td>\r\n<td class=\"r\">8.384<\/td>\r\n<td class=\"r\">7.943<\/td>\r\n<td class=\"r\">7.536<\/td>\r\n<td class=\"r\">7.161<\/td>\r\n<td class=\"r\">6.814<\/td>\r\n<td class=\"r\">6.194<\/td>\r\n<td class=\"r\">5.660<\/td>\r\n<td class=\"r\">5.421<\/td>\r\n<td class=\"r\">5.197<\/td>\r\n<td class=\"r\">4.793<\/td>\r\n<td class=\"r\">4.439<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 13<\/td>\r\n<td class=\"r\">12.134<\/td>\r\n<td class=\"r\">11.348<\/td>\r\n<td class=\"r\">10.635<\/td>\r\n<td class=\"r\">9.986<\/td>\r\n<td class=\"r\">9.394<\/td>\r\n<td class=\"r\">8.853<\/td>\r\n<td class=\"r\">8.358<\/td>\r\n<td class=\"r\">7.904<\/td>\r\n<td class=\"r\">7.487<\/td>\r\n<td class=\"r\">7.103<\/td>\r\n<td class=\"r\">6.424<\/td>\r\n<td class=\"r\">5.842<\/td>\r\n<td class=\"r\">5.583<\/td>\r\n<td class=\"r\">5.342<\/td>\r\n<td class=\"r\">4.910<\/td>\r\n<td class=\"r\">4.533<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 14<\/td>\r\n<td class=\"r\">13.004<\/td>\r\n<td class=\"r\">12.106<\/td>\r\n<td class=\"r\">11.296<\/td>\r\n<td class=\"r\">10.563<\/td>\r\n<td class=\"r\">9.899<\/td>\r\n<td class=\"r\">9.295<\/td>\r\n<td class=\"r\">8.745<\/td>\r\n<td class=\"r\">8.244<\/td>\r\n<td class=\"r\">7.786<\/td>\r\n<td class=\"r\">7.367<\/td>\r\n<td class=\"r\">6.628<\/td>\r\n<td class=\"r\">6.002<\/td>\r\n<td class=\"r\">5.724<\/td>\r\n<td class=\"r\">5.468<\/td>\r\n<td class=\"r\">5.008<\/td>\r\n<td class=\"r\">4.611<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nWe could prove this by looking at it from a slightly different vantage point. What if we invested $45,560 with a promised return of $15,000 over the next four years (basically, an annuity) and we knew it was a 12% return on investment (ROI)? We could discount each of the future cash flows according to the PV of $1 tables and compare it to our initial investment like this:\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 class=\"c highlight-green\">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 highlight-green\">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 highlight-green\">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 highlight-green\">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 highlight-green\">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\">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\n&nbsp;\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<thead>\r\n<tr class=\"u-sr-only\">\r\n<th scope=\"col\">Year<\/th>\r\n<th scope=\"col\">Amount<\/th>\r\n<th scope=\"col\">Factor<\/th>\r\n<th scope=\"col\">Total<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\r\n<td class=\"r\">0.893<\/td>\r\n<td class=\"r\">$13,395<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\r\n<td class=\"r\">0.797<\/td>\r\n<td class=\"r\">$11,955<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\r\n<td class=\"r\">0.712<\/td>\r\n<td class=\"r\">$10,680<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\r\n<td class=\"r\">0.636<\/td>\r\n<td class=\"r\">$9,540<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total present value of cash inflows<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r\">$45,570<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Initial investment<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r\"><span style=\"color: #ff0000;\">($45,560)<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Net present value of project<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$10<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\nNotice that the NPV is very close to zero (rounding prevents it from coming out to exactly zero). This means that the present value of each of these future cash flows is equal to our initial investment if our alternative is a 12% ROI.\r\n\r\nB\r\n\r\nLet's go back to JuxtaPos. Because the cash flows are not uniform, we can\u2019t use the PV of an annuity table to back our way into the IRR. We might be able to come up with a reasonable estimate though. The average annual net cash flow is $57,500\u00a0 (total of $345,000 divided by six years). Dividing the initial investment of $230,000 by the average annual net cash flow of $57,500, we get a factor of 4.0. On the table for the row n=6, we see that the factor of 4.0 would fall somewhere between 12% and 14%.\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 Ordinary Annuity of $1<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td class=\"c highlight-green\">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\">1.970<\/td>\r\n<td class=\"r\">1.942<\/td>\r\n<td class=\"r\">1.913<\/td>\r\n<td class=\"r\">1.886<\/td>\r\n<td class=\"r\">1.859<\/td>\r\n<td class=\"r\">1.833<\/td>\r\n<td class=\"r\">1.808<\/td>\r\n<td class=\"r\">1.783<\/td>\r\n<td class=\"r\">1.759<\/td>\r\n<td class=\"r\">1.736<\/td>\r\n<td class=\"r\">1.690<\/td>\r\n<td class=\"r\">1.647<\/td>\r\n<td class=\"r\">1.626<\/td>\r\n<td class=\"r\">1.605<\/td>\r\n<td class=\"r\">1.566<\/td>\r\n<td class=\"r\">1.528<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 3<\/td>\r\n<td class=\"r\">2.941<\/td>\r\n<td class=\"r\">2.884<\/td>\r\n<td class=\"r\">2.829<\/td>\r\n<td class=\"r\">2.775<\/td>\r\n<td class=\"r\">2.723<\/td>\r\n<td class=\"r\">2.673<\/td>\r\n<td class=\"r\">2.624<\/td>\r\n<td class=\"r\">2.577<\/td>\r\n<td class=\"r\">2.531<\/td>\r\n<td class=\"r\">2.487<\/td>\r\n<td class=\"r\">2.402<\/td>\r\n<td class=\"r\">2.322<\/td>\r\n<td class=\"r\">2.283<\/td>\r\n<td class=\"r\">2.246<\/td>\r\n<td class=\"r\">2.174<\/td>\r\n<td class=\"r\">2.106<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 4<\/td>\r\n<td class=\"r\">3.902<\/td>\r\n<td class=\"r\">3.808<\/td>\r\n<td class=\"r\">3.717<\/td>\r\n<td class=\"r\">3.630<\/td>\r\n<td class=\"r\">3.546<\/td>\r\n<td class=\"r\">3.465<\/td>\r\n<td class=\"r\">3.387<\/td>\r\n<td class=\"r\">3.312<\/td>\r\n<td class=\"r\">3.240<\/td>\r\n<td class=\"r\">3.170<\/td>\r\n<td class=\"r\">3.037<\/td>\r\n<td class=\"r\">2.914<\/td>\r\n<td class=\"r\">2.855<\/td>\r\n<td class=\"r\">2.798<\/td>\r\n<td class=\"r\">2.690<\/td>\r\n<td class=\"r\">2.589<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 5<\/td>\r\n<td class=\"r\">4.853<\/td>\r\n<td class=\"r\">4.713<\/td>\r\n<td class=\"r\">4.580<\/td>\r\n<td class=\"r\">4.452<\/td>\r\n<td class=\"r\">4.329<\/td>\r\n<td class=\"r\">4.212<\/td>\r\n<td class=\"r\">4.100<\/td>\r\n<td class=\"r\">3.993<\/td>\r\n<td class=\"r\">3.890<\/td>\r\n<td class=\"r\">3.791<\/td>\r\n<td class=\"r\">3.605<\/td>\r\n<td class=\"r\">3.433<\/td>\r\n<td class=\"r\">3.352<\/td>\r\n<td class=\"r\">3.274<\/td>\r\n<td class=\"r\">3.127<\/td>\r\n<td class=\"r\">2.991<\/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\">5.795<\/td>\r\n<td class=\"r\">5.601<\/td>\r\n<td class=\"r\">5.417<\/td>\r\n<td class=\"r\">5.242<\/td>\r\n<td class=\"r\">5.076<\/td>\r\n<td class=\"r\">4.917<\/td>\r\n<td class=\"r\">4.767<\/td>\r\n<td class=\"r\">4.623<\/td>\r\n<td class=\"r\">4.486<\/td>\r\n<td class=\"r\">4.355<\/td>\r\n<td class=\"r highlight-green\">4.111<\/td>\r\n<td class=\"r highlight-green\">3.889<\/td>\r\n<td class=\"r\">3.784<\/td>\r\n<td class=\"r\">3.685<\/td>\r\n<td class=\"r\">3.489<\/td>\r\n<td class=\"r\">3.326<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 7<\/td>\r\n<td class=\"r\">6.728<\/td>\r\n<td class=\"r\">6.472<\/td>\r\n<td class=\"r\">6.230<\/td>\r\n<td class=\"r\">6.002<\/td>\r\n<td class=\"r\">5.786<\/td>\r\n<td class=\"r\">5.582<\/td>\r\n<td class=\"r\">5.389<\/td>\r\n<td class=\"r\">5.206<\/td>\r\n<td class=\"r\">5.033<\/td>\r\n<td class=\"r\">4.868<\/td>\r\n<td class=\"r\">4.564<\/td>\r\n<td class=\"r\">4.288<\/td>\r\n<td class=\"r\">4.160<\/td>\r\n<td class=\"r\">4.039<\/td>\r\n<td class=\"r\">3.812<\/td>\r\n<td class=\"r\">3.605<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 8<\/td>\r\n<td class=\"r\">7.652<\/td>\r\n<td class=\"r\">7.325<\/td>\r\n<td class=\"r\">7.020<\/td>\r\n<td class=\"r\">6.733<\/td>\r\n<td class=\"r\">6.463<\/td>\r\n<td class=\"r\">6.210<\/td>\r\n<td class=\"r\">5.971<\/td>\r\n<td class=\"r\">5.747<\/td>\r\n<td class=\"r\">5.535<\/td>\r\n<td class=\"r\">5.335<\/td>\r\n<td class=\"r\">4.968<\/td>\r\n<td class=\"r\">4.639<\/td>\r\n<td class=\"r\">4.487<\/td>\r\n<td class=\"r\">4.344<\/td>\r\n<td class=\"r\">4.078<\/td>\r\n<td class=\"r\">3.837<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 9<\/td>\r\n<td class=\"r\">8.566<\/td>\r\n<td class=\"r\">8.162<\/td>\r\n<td class=\"r\">7.786<\/td>\r\n<td class=\"r\">7.435<\/td>\r\n<td class=\"r\">7.108<\/td>\r\n<td class=\"r\">6.802<\/td>\r\n<td class=\"r\">6.515<\/td>\r\n<td class=\"r\">6.247<\/td>\r\n<td class=\"r\">5.995<\/td>\r\n<td class=\"r\">5.759<\/td>\r\n<td class=\"r\">5.328<\/td>\r\n<td class=\"r\">4.946<\/td>\r\n<td class=\"r\">4.772<\/td>\r\n<td class=\"r\">4.607<\/td>\r\n<td class=\"r\">4.303<\/td>\r\n<td class=\"r\">4.031<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 10<\/td>\r\n<td class=\"r\">9.471<\/td>\r\n<td class=\"r\">8.983<\/td>\r\n<td class=\"r\">8.530<\/td>\r\n<td class=\"r\">8.111<\/td>\r\n<td class=\"r\">7.722<\/td>\r\n<td class=\"r\">7.360<\/td>\r\n<td class=\"r\">7.024<\/td>\r\n<td class=\"r\">6.710<\/td>\r\n<td class=\"r\">6.418<\/td>\r\n<td class=\"r\">6.145<\/td>\r\n<td class=\"r\">5.650<\/td>\r\n<td class=\"r\">5.216<\/td>\r\n<td class=\"r\">5.019<\/td>\r\n<td class=\"r\">4.833<\/td>\r\n<td class=\"r\">4.494<\/td>\r\n<td class=\"r\">4.192<\/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\">10.368<\/td>\r\n<td class=\"r\">9.787<\/td>\r\n<td class=\"r\">9.253<\/td>\r\n<td class=\"r\">8.760<\/td>\r\n<td class=\"r\">8.306<\/td>\r\n<td class=\"r\">7.887<\/td>\r\n<td class=\"r\">7.499<\/td>\r\n<td class=\"r\">7.139<\/td>\r\n<td class=\"r\">6.805<\/td>\r\n<td class=\"r\">6.495<\/td>\r\n<td class=\"r\">5.938<\/td>\r\n<td class=\"r\">5.453<\/td>\r\n<td class=\"r\">5.234<\/td>\r\n<td class=\"r\">5.029<\/td>\r\n<td class=\"r\">4.656<\/td>\r\n<td class=\"r\">4.327<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 12<\/td>\r\n<td class=\"r\">11.255<\/td>\r\n<td class=\"r\">10.575<\/td>\r\n<td class=\"r\">9.954<\/td>\r\n<td class=\"r\">9.385<\/td>\r\n<td class=\"r\">8.863<\/td>\r\n<td class=\"r\">8.384<\/td>\r\n<td class=\"r\">7.943<\/td>\r\n<td class=\"r\">7.536<\/td>\r\n<td class=\"r\">7.161<\/td>\r\n<td class=\"r\">6.814<\/td>\r\n<td class=\"r\">6.194<\/td>\r\n<td class=\"r\">5.660<\/td>\r\n<td class=\"r\">5.421<\/td>\r\n<td class=\"r\">5.197<\/td>\r\n<td class=\"r\">4.793<\/td>\r\n<td class=\"r\">4.439<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 13<\/td>\r\n<td class=\"r\">12.134<\/td>\r\n<td class=\"r\">11.348<\/td>\r\n<td class=\"r\">10.635<\/td>\r\n<td class=\"r\">9.986<\/td>\r\n<td class=\"r\">9.394<\/td>\r\n<td class=\"r\">8.853<\/td>\r\n<td class=\"r\">8.358<\/td>\r\n<td class=\"r\">7.904<\/td>\r\n<td class=\"r\">7.487<\/td>\r\n<td class=\"r\">7.103<\/td>\r\n<td class=\"r\">6.424<\/td>\r\n<td class=\"r\">5.842<\/td>\r\n<td class=\"r\">5.583<\/td>\r\n<td class=\"r\">5.342<\/td>\r\n<td class=\"r\">4.910<\/td>\r\n<td class=\"r\">4.533<\/td>\r\n<\/tr>\r\n<tr>\r\n<td class=\"r\">Period 14<\/td>\r\n<td class=\"r\">13.004<\/td>\r\n<td class=\"r\">12.106<\/td>\r\n<td class=\"r\">11.296<\/td>\r\n<td class=\"r\">10.563<\/td>\r\n<td class=\"r\">9.899<\/td>\r\n<td class=\"r\">9.295<\/td>\r\n<td class=\"r\">8.745<\/td>\r\n<td class=\"r\">8.244<\/td>\r\n<td class=\"r\">7.786<\/td>\r\n<td class=\"r\">7.367<\/td>\r\n<td class=\"r\">6.628<\/td>\r\n<td class=\"r\">6.002<\/td>\r\n<td class=\"r\">5.724<\/td>\r\n<td class=\"r\">5.468<\/td>\r\n<td class=\"r\">5.008<\/td>\r\n<td class=\"r\">4.611<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nWe could estimate the IRR then at 13%.\r\n\r\nWe could also use a simple Excel formula to calculate IRR:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/lh5.googleusercontent.com\/JjsygxOjwbaOW0IrQGKzQGbicjikri8USLfLTV8QhDk9TZEOaU059MgA5BkuIYZVVnGJdhke5KIMnlHJwYZQB-qHmj8l9x5MHrDOcbM6-ItvIbdy5SaPmoQB89R9LwUNtaaWUZSe\" alt=\"Screenshot of Excel showing an IRR calculation.\" width=\"441\" height=\"360\" \/>\r\n\r\nAnd by recalculating our NPV analysis using 13% (the factors are not in the table above) we find that the NPV of the project at 13% is more or less equal to the initial investment, proving that the IRR is right around 13%.\r\n\r\nNet cash inflows (additional cash revenues - additional cash expenses)\u00a0 \u00a0 \u00a0 \u00a0 \u00a013%\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<thead>\r\n<tr class=\"u-sr-only\">\r\n<th scope=\"col\">Year<\/th>\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Factor<\/th>\r\n<th scope=\"col\">Total<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.8850<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 53,100<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.7830<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 46,980<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.6930<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 38,115<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.6130<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 33,715<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 5<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 50,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.5430<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 27,150<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 6<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.4800<\/td>\r\n<td class=\"r\">$\u00a0 \u00a0 31,200<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total present value of cash inflows<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0230,260<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Initial investment<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r\">$\u00a0(230,000)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Net present value of project<\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 260<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\nThe IRR is the actual rate of return or Return on Investment (ROI) of the project. If our hurdle rate is 15%, then this project at 13% does not rise to the level of an acceptable endeavor.\r\n\r\nBefore we calculate the profitability index on this project, check your understanding of the IRR.\r\n<div class=\"textbox tryit\">\r\n<h3>Practice Question<\/h3>\r\n[ohm_question hide_question_numbers=1]221585[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Calculate the internal rate of return<\/li>\n<\/ul>\n<\/div>\n<p>Continuing to use the JuxtaPos scenario where management is considering adding a line of puzzles that necessitates a new machine that will cost $230,000 with an estimated useful life of six years and a residual value of $40,000, let\u2019s see if we can provide a number to management that represents the internal rate of return (IRR) on this project.<\/p>\n<p>Again, net annual cash flows are as follows:<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<thead>\n<tr class=\"u-sr-only\">\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Amount<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<\/tr>\n<tr>\n<td>Year 5<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 50,000<\/td>\n<\/tr>\n<tr>\n<td>Year 6 (includes the $40,000 proceeds from sale)<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>If these amounts were even, we could look for an annuity table, find a factor that represents the annuity, and then backtrack that number to an approximate interest rate.<\/p>\n<p>Let\u2019s take a simpler example of an investment of $45,560 that results in an annual cash inflow of $15,000 for four years with no residual value. Is this a good investment? We are trading $45,560 for $60,000 over the next four years.<\/p>\n<p>If we look at how the factors in the Present Value of an annuity (a steady stream of future cash flows) are created, we take $45,560 and divide it by the cash flow of $15,000 to get a factor of 3.037 (rounded to the nearest thousandth). On the table, if we follow the row for n=4 across until we find something close to 3.037, we can then extrapolate that the rate of return on this investment is 12%.<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table gridded\">\n<thead>\n<tr>\n<th colspan=\"17\">Present Value of Ordinary Annuity of $1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"c highlight-green\">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\">1.970<\/td>\n<td class=\"r\">1.942<\/td>\n<td class=\"r\">1.913<\/td>\n<td class=\"r\">1.886<\/td>\n<td class=\"r\">1.859<\/td>\n<td class=\"r\">1.833<\/td>\n<td class=\"r\">1.808<\/td>\n<td class=\"r\">1.783<\/td>\n<td class=\"r\">1.759<\/td>\n<td class=\"r\">1.736<\/td>\n<td class=\"r\">1.690<\/td>\n<td class=\"r\">1.647<\/td>\n<td class=\"r\">1.626<\/td>\n<td class=\"r\">1.605<\/td>\n<td class=\"r\">1.566<\/td>\n<td class=\"r\">1.528<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 3<\/td>\n<td class=\"r\">2.941<\/td>\n<td class=\"r\">2.884<\/td>\n<td class=\"r\">2.829<\/td>\n<td class=\"r\">2.775<\/td>\n<td class=\"r\">2.723<\/td>\n<td class=\"r\">2.673<\/td>\n<td class=\"r\">2.624<\/td>\n<td class=\"r\">2.577<\/td>\n<td class=\"r\">2.531<\/td>\n<td class=\"r\">2.487<\/td>\n<td class=\"r\">2.402<\/td>\n<td class=\"r\">2.322<\/td>\n<td class=\"r\">2.283<\/td>\n<td class=\"r\">2.246<\/td>\n<td class=\"r\">2.174<\/td>\n<td class=\"r\">2.106<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 4<\/td>\n<td class=\"r\">3.902<\/td>\n<td class=\"r\">3.808<\/td>\n<td class=\"r\">3.717<\/td>\n<td class=\"r\">3.630<\/td>\n<td class=\"r\">3.546<\/td>\n<td class=\"r\">3.465<\/td>\n<td class=\"r\">3.387<\/td>\n<td class=\"r\">3.312<\/td>\n<td class=\"r\">3.240<\/td>\n<td class=\"r\">3.170<\/td>\n<td class=\"r highlight-green\">3.037<\/td>\n<td class=\"r\">2.914<\/td>\n<td class=\"r\">2.855<\/td>\n<td class=\"r\">2.798<\/td>\n<td class=\"r\">2.690<\/td>\n<td class=\"r\">2.589<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 5<\/td>\n<td class=\"r\">4.853<\/td>\n<td class=\"r\">4.713<\/td>\n<td class=\"r\">4.580<\/td>\n<td class=\"r\">4.452<\/td>\n<td class=\"r\">4.329<\/td>\n<td class=\"r\">4.212<\/td>\n<td class=\"r\">4.100<\/td>\n<td class=\"r\">3.993<\/td>\n<td class=\"r\">3.890<\/td>\n<td class=\"r\">3.791<\/td>\n<td class=\"r\">3.605<\/td>\n<td class=\"r\">3.433<\/td>\n<td class=\"r\">3.352<\/td>\n<td class=\"r\">3.274<\/td>\n<td class=\"r\">3.127<\/td>\n<td class=\"r\">2.991<\/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\">5.795<\/td>\n<td class=\"r\">5.601<\/td>\n<td class=\"r\">5.417<\/td>\n<td class=\"r\">5.242<\/td>\n<td class=\"r\">5.076<\/td>\n<td class=\"r\">4.917<\/td>\n<td class=\"r\">4.767<\/td>\n<td class=\"r\">4.623<\/td>\n<td class=\"r\">4.486<\/td>\n<td class=\"r\">4.355<\/td>\n<td class=\"r\">4.111<\/td>\n<td class=\"r\">3.889<\/td>\n<td class=\"r\">3.784<\/td>\n<td class=\"r\">3.685<\/td>\n<td class=\"r\">3.489<\/td>\n<td class=\"r\">3.326<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 7<\/td>\n<td class=\"r\">6.728<\/td>\n<td class=\"r\">6.472<\/td>\n<td class=\"r\">6.230<\/td>\n<td class=\"r\">6.002<\/td>\n<td class=\"r\">5.786<\/td>\n<td class=\"r\">5.582<\/td>\n<td class=\"r\">5.389<\/td>\n<td class=\"r\">5.206<\/td>\n<td class=\"r\">5.033<\/td>\n<td class=\"r\">4.868<\/td>\n<td class=\"r\">4.564<\/td>\n<td class=\"r\">4.288<\/td>\n<td class=\"r\">4.160<\/td>\n<td class=\"r\">4.039<\/td>\n<td class=\"r\">3.812<\/td>\n<td class=\"r\">3.605<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 8<\/td>\n<td class=\"r\">7.652<\/td>\n<td class=\"r\">7.325<\/td>\n<td class=\"r\">7.020<\/td>\n<td class=\"r\">6.733<\/td>\n<td class=\"r\">6.463<\/td>\n<td class=\"r\">6.210<\/td>\n<td class=\"r\">5.971<\/td>\n<td class=\"r\">5.747<\/td>\n<td class=\"r\">5.535<\/td>\n<td class=\"r\">5.335<\/td>\n<td class=\"r\">4.968<\/td>\n<td class=\"r\">4.639<\/td>\n<td class=\"r\">4.487<\/td>\n<td class=\"r\">4.344<\/td>\n<td class=\"r\">4.078<\/td>\n<td class=\"r\">3.837<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 9<\/td>\n<td class=\"r\">8.566<\/td>\n<td class=\"r\">8.162<\/td>\n<td class=\"r\">7.786<\/td>\n<td class=\"r\">7.435<\/td>\n<td class=\"r\">7.108<\/td>\n<td class=\"r\">6.802<\/td>\n<td class=\"r\">6.515<\/td>\n<td class=\"r\">6.247<\/td>\n<td class=\"r\">5.995<\/td>\n<td class=\"r\">5.759<\/td>\n<td class=\"r\">5.328<\/td>\n<td class=\"r\">4.946<\/td>\n<td class=\"r\">4.772<\/td>\n<td class=\"r\">4.607<\/td>\n<td class=\"r\">4.303<\/td>\n<td class=\"r\">4.031<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 10<\/td>\n<td class=\"r\">9.471<\/td>\n<td class=\"r\">8.983<\/td>\n<td class=\"r\">8.530<\/td>\n<td class=\"r\">8.111<\/td>\n<td class=\"r\">7.722<\/td>\n<td class=\"r\">7.360<\/td>\n<td class=\"r\">7.024<\/td>\n<td class=\"r\">6.710<\/td>\n<td class=\"r\">6.418<\/td>\n<td class=\"r\">6.145<\/td>\n<td class=\"r\">5.650<\/td>\n<td class=\"r\">5.216<\/td>\n<td class=\"r\">5.019<\/td>\n<td class=\"r\">4.833<\/td>\n<td class=\"r\">4.494<\/td>\n<td class=\"r\">4.192<\/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\">10.368<\/td>\n<td class=\"r\">9.787<\/td>\n<td class=\"r\">9.253<\/td>\n<td class=\"r\">8.760<\/td>\n<td class=\"r\">8.306<\/td>\n<td class=\"r\">7.887<\/td>\n<td class=\"r\">7.499<\/td>\n<td class=\"r\">7.139<\/td>\n<td class=\"r\">6.805<\/td>\n<td class=\"r\">6.495<\/td>\n<td class=\"r\">5.938<\/td>\n<td class=\"r\">5.453<\/td>\n<td class=\"r\">5.234<\/td>\n<td class=\"r\">5.029<\/td>\n<td class=\"r\">4.656<\/td>\n<td class=\"r\">4.327<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 12<\/td>\n<td class=\"r\">11.255<\/td>\n<td class=\"r\">10.575<\/td>\n<td class=\"r\">9.954<\/td>\n<td class=\"r\">9.385<\/td>\n<td class=\"r\">8.863<\/td>\n<td class=\"r\">8.384<\/td>\n<td class=\"r\">7.943<\/td>\n<td class=\"r\">7.536<\/td>\n<td class=\"r\">7.161<\/td>\n<td class=\"r\">6.814<\/td>\n<td class=\"r\">6.194<\/td>\n<td class=\"r\">5.660<\/td>\n<td class=\"r\">5.421<\/td>\n<td class=\"r\">5.197<\/td>\n<td class=\"r\">4.793<\/td>\n<td class=\"r\">4.439<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 13<\/td>\n<td class=\"r\">12.134<\/td>\n<td class=\"r\">11.348<\/td>\n<td class=\"r\">10.635<\/td>\n<td class=\"r\">9.986<\/td>\n<td class=\"r\">9.394<\/td>\n<td class=\"r\">8.853<\/td>\n<td class=\"r\">8.358<\/td>\n<td class=\"r\">7.904<\/td>\n<td class=\"r\">7.487<\/td>\n<td class=\"r\">7.103<\/td>\n<td class=\"r\">6.424<\/td>\n<td class=\"r\">5.842<\/td>\n<td class=\"r\">5.583<\/td>\n<td class=\"r\">5.342<\/td>\n<td class=\"r\">4.910<\/td>\n<td class=\"r\">4.533<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 14<\/td>\n<td class=\"r\">13.004<\/td>\n<td class=\"r\">12.106<\/td>\n<td class=\"r\">11.296<\/td>\n<td class=\"r\">10.563<\/td>\n<td class=\"r\">9.899<\/td>\n<td class=\"r\">9.295<\/td>\n<td class=\"r\">8.745<\/td>\n<td class=\"r\">8.244<\/td>\n<td class=\"r\">7.786<\/td>\n<td class=\"r\">7.367<\/td>\n<td class=\"r\">6.628<\/td>\n<td class=\"r\">6.002<\/td>\n<td class=\"r\">5.724<\/td>\n<td class=\"r\">5.468<\/td>\n<td class=\"r\">5.008<\/td>\n<td class=\"r\">4.611<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>We could prove this by looking at it from a slightly different vantage point. What if we invested $45,560 with a promised return of $15,000 over the next four years (basically, an annuity) and we knew it was a 12% return on investment (ROI)? We could discount each of the future cash flows according to the PV of $1 tables and compare it to our initial investment like this:<\/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 class=\"c highlight-green\">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 highlight-green\">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 highlight-green\">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 highlight-green\">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 highlight-green\">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\">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>&nbsp;<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<thead>\n<tr class=\"u-sr-only\">\n<th scope=\"col\">Year<\/th>\n<th scope=\"col\">Amount<\/th>\n<th scope=\"col\">Factor<\/th>\n<th scope=\"col\">Total<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\n<td class=\"r\">0.893<\/td>\n<td class=\"r\">$13,395<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\n<td class=\"r\">0.797<\/td>\n<td class=\"r\">$11,955<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\n<td class=\"r\">0.712<\/td>\n<td class=\"r\">$10,680<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">$ \u00a0 \u00a0 \u00a0 \u00a0 15,000.00<\/td>\n<td class=\"r\">0.636<\/td>\n<td class=\"r\">$9,540<\/td>\n<\/tr>\n<tr>\n<td>Total present value of cash inflows<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r\">$45,570<\/td>\n<\/tr>\n<tr>\n<td>Initial investment<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r\"><span style=\"color: #ff0000;\">($45,560)<\/span><\/td>\n<\/tr>\n<tr>\n<td>Net present value of project<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$10<span class=\"u-sr-only\">Double line<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Notice that the NPV is very close to zero (rounding prevents it from coming out to exactly zero). This means that the present value of each of these future cash flows is equal to our initial investment if our alternative is a 12% ROI.<\/p>\n<p>B<\/p>\n<p>Let&#8217;s go back to JuxtaPos. Because the cash flows are not uniform, we can\u2019t use the PV of an annuity table to back our way into the IRR. We might be able to come up with a reasonable estimate though. The average annual net cash flow is $57,500\u00a0 (total of $345,000 divided by six years). Dividing the initial investment of $230,000 by the average annual net cash flow of $57,500, we get a factor of 4.0. On the table for the row n=6, we see that the factor of 4.0 would fall somewhere between 12% and 14%.<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table gridded\">\n<thead>\n<tr>\n<th colspan=\"17\">Present Value of Ordinary Annuity of $1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td class=\"c highlight-green\">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\">1.970<\/td>\n<td class=\"r\">1.942<\/td>\n<td class=\"r\">1.913<\/td>\n<td class=\"r\">1.886<\/td>\n<td class=\"r\">1.859<\/td>\n<td class=\"r\">1.833<\/td>\n<td class=\"r\">1.808<\/td>\n<td class=\"r\">1.783<\/td>\n<td class=\"r\">1.759<\/td>\n<td class=\"r\">1.736<\/td>\n<td class=\"r\">1.690<\/td>\n<td class=\"r\">1.647<\/td>\n<td class=\"r\">1.626<\/td>\n<td class=\"r\">1.605<\/td>\n<td class=\"r\">1.566<\/td>\n<td class=\"r\">1.528<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 3<\/td>\n<td class=\"r\">2.941<\/td>\n<td class=\"r\">2.884<\/td>\n<td class=\"r\">2.829<\/td>\n<td class=\"r\">2.775<\/td>\n<td class=\"r\">2.723<\/td>\n<td class=\"r\">2.673<\/td>\n<td class=\"r\">2.624<\/td>\n<td class=\"r\">2.577<\/td>\n<td class=\"r\">2.531<\/td>\n<td class=\"r\">2.487<\/td>\n<td class=\"r\">2.402<\/td>\n<td class=\"r\">2.322<\/td>\n<td class=\"r\">2.283<\/td>\n<td class=\"r\">2.246<\/td>\n<td class=\"r\">2.174<\/td>\n<td class=\"r\">2.106<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 4<\/td>\n<td class=\"r\">3.902<\/td>\n<td class=\"r\">3.808<\/td>\n<td class=\"r\">3.717<\/td>\n<td class=\"r\">3.630<\/td>\n<td class=\"r\">3.546<\/td>\n<td class=\"r\">3.465<\/td>\n<td class=\"r\">3.387<\/td>\n<td class=\"r\">3.312<\/td>\n<td class=\"r\">3.240<\/td>\n<td class=\"r\">3.170<\/td>\n<td class=\"r\">3.037<\/td>\n<td class=\"r\">2.914<\/td>\n<td class=\"r\">2.855<\/td>\n<td class=\"r\">2.798<\/td>\n<td class=\"r\">2.690<\/td>\n<td class=\"r\">2.589<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 5<\/td>\n<td class=\"r\">4.853<\/td>\n<td class=\"r\">4.713<\/td>\n<td class=\"r\">4.580<\/td>\n<td class=\"r\">4.452<\/td>\n<td class=\"r\">4.329<\/td>\n<td class=\"r\">4.212<\/td>\n<td class=\"r\">4.100<\/td>\n<td class=\"r\">3.993<\/td>\n<td class=\"r\">3.890<\/td>\n<td class=\"r\">3.791<\/td>\n<td class=\"r\">3.605<\/td>\n<td class=\"r\">3.433<\/td>\n<td class=\"r\">3.352<\/td>\n<td class=\"r\">3.274<\/td>\n<td class=\"r\">3.127<\/td>\n<td class=\"r\">2.991<\/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\">5.795<\/td>\n<td class=\"r\">5.601<\/td>\n<td class=\"r\">5.417<\/td>\n<td class=\"r\">5.242<\/td>\n<td class=\"r\">5.076<\/td>\n<td class=\"r\">4.917<\/td>\n<td class=\"r\">4.767<\/td>\n<td class=\"r\">4.623<\/td>\n<td class=\"r\">4.486<\/td>\n<td class=\"r\">4.355<\/td>\n<td class=\"r highlight-green\">4.111<\/td>\n<td class=\"r highlight-green\">3.889<\/td>\n<td class=\"r\">3.784<\/td>\n<td class=\"r\">3.685<\/td>\n<td class=\"r\">3.489<\/td>\n<td class=\"r\">3.326<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 7<\/td>\n<td class=\"r\">6.728<\/td>\n<td class=\"r\">6.472<\/td>\n<td class=\"r\">6.230<\/td>\n<td class=\"r\">6.002<\/td>\n<td class=\"r\">5.786<\/td>\n<td class=\"r\">5.582<\/td>\n<td class=\"r\">5.389<\/td>\n<td class=\"r\">5.206<\/td>\n<td class=\"r\">5.033<\/td>\n<td class=\"r\">4.868<\/td>\n<td class=\"r\">4.564<\/td>\n<td class=\"r\">4.288<\/td>\n<td class=\"r\">4.160<\/td>\n<td class=\"r\">4.039<\/td>\n<td class=\"r\">3.812<\/td>\n<td class=\"r\">3.605<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 8<\/td>\n<td class=\"r\">7.652<\/td>\n<td class=\"r\">7.325<\/td>\n<td class=\"r\">7.020<\/td>\n<td class=\"r\">6.733<\/td>\n<td class=\"r\">6.463<\/td>\n<td class=\"r\">6.210<\/td>\n<td class=\"r\">5.971<\/td>\n<td class=\"r\">5.747<\/td>\n<td class=\"r\">5.535<\/td>\n<td class=\"r\">5.335<\/td>\n<td class=\"r\">4.968<\/td>\n<td class=\"r\">4.639<\/td>\n<td class=\"r\">4.487<\/td>\n<td class=\"r\">4.344<\/td>\n<td class=\"r\">4.078<\/td>\n<td class=\"r\">3.837<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 9<\/td>\n<td class=\"r\">8.566<\/td>\n<td class=\"r\">8.162<\/td>\n<td class=\"r\">7.786<\/td>\n<td class=\"r\">7.435<\/td>\n<td class=\"r\">7.108<\/td>\n<td class=\"r\">6.802<\/td>\n<td class=\"r\">6.515<\/td>\n<td class=\"r\">6.247<\/td>\n<td class=\"r\">5.995<\/td>\n<td class=\"r\">5.759<\/td>\n<td class=\"r\">5.328<\/td>\n<td class=\"r\">4.946<\/td>\n<td class=\"r\">4.772<\/td>\n<td class=\"r\">4.607<\/td>\n<td class=\"r\">4.303<\/td>\n<td class=\"r\">4.031<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 10<\/td>\n<td class=\"r\">9.471<\/td>\n<td class=\"r\">8.983<\/td>\n<td class=\"r\">8.530<\/td>\n<td class=\"r\">8.111<\/td>\n<td class=\"r\">7.722<\/td>\n<td class=\"r\">7.360<\/td>\n<td class=\"r\">7.024<\/td>\n<td class=\"r\">6.710<\/td>\n<td class=\"r\">6.418<\/td>\n<td class=\"r\">6.145<\/td>\n<td class=\"r\">5.650<\/td>\n<td class=\"r\">5.216<\/td>\n<td class=\"r\">5.019<\/td>\n<td class=\"r\">4.833<\/td>\n<td class=\"r\">4.494<\/td>\n<td class=\"r\">4.192<\/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\">10.368<\/td>\n<td class=\"r\">9.787<\/td>\n<td class=\"r\">9.253<\/td>\n<td class=\"r\">8.760<\/td>\n<td class=\"r\">8.306<\/td>\n<td class=\"r\">7.887<\/td>\n<td class=\"r\">7.499<\/td>\n<td class=\"r\">7.139<\/td>\n<td class=\"r\">6.805<\/td>\n<td class=\"r\">6.495<\/td>\n<td class=\"r\">5.938<\/td>\n<td class=\"r\">5.453<\/td>\n<td class=\"r\">5.234<\/td>\n<td class=\"r\">5.029<\/td>\n<td class=\"r\">4.656<\/td>\n<td class=\"r\">4.327<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 12<\/td>\n<td class=\"r\">11.255<\/td>\n<td class=\"r\">10.575<\/td>\n<td class=\"r\">9.954<\/td>\n<td class=\"r\">9.385<\/td>\n<td class=\"r\">8.863<\/td>\n<td class=\"r\">8.384<\/td>\n<td class=\"r\">7.943<\/td>\n<td class=\"r\">7.536<\/td>\n<td class=\"r\">7.161<\/td>\n<td class=\"r\">6.814<\/td>\n<td class=\"r\">6.194<\/td>\n<td class=\"r\">5.660<\/td>\n<td class=\"r\">5.421<\/td>\n<td class=\"r\">5.197<\/td>\n<td class=\"r\">4.793<\/td>\n<td class=\"r\">4.439<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 13<\/td>\n<td class=\"r\">12.134<\/td>\n<td class=\"r\">11.348<\/td>\n<td class=\"r\">10.635<\/td>\n<td class=\"r\">9.986<\/td>\n<td class=\"r\">9.394<\/td>\n<td class=\"r\">8.853<\/td>\n<td class=\"r\">8.358<\/td>\n<td class=\"r\">7.904<\/td>\n<td class=\"r\">7.487<\/td>\n<td class=\"r\">7.103<\/td>\n<td class=\"r\">6.424<\/td>\n<td class=\"r\">5.842<\/td>\n<td class=\"r\">5.583<\/td>\n<td class=\"r\">5.342<\/td>\n<td class=\"r\">4.910<\/td>\n<td class=\"r\">4.533<\/td>\n<\/tr>\n<tr>\n<td class=\"r\">Period 14<\/td>\n<td class=\"r\">13.004<\/td>\n<td class=\"r\">12.106<\/td>\n<td class=\"r\">11.296<\/td>\n<td class=\"r\">10.563<\/td>\n<td class=\"r\">9.899<\/td>\n<td class=\"r\">9.295<\/td>\n<td class=\"r\">8.745<\/td>\n<td class=\"r\">8.244<\/td>\n<td class=\"r\">7.786<\/td>\n<td class=\"r\">7.367<\/td>\n<td class=\"r\">6.628<\/td>\n<td class=\"r\">6.002<\/td>\n<td class=\"r\">5.724<\/td>\n<td class=\"r\">5.468<\/td>\n<td class=\"r\">5.008<\/td>\n<td class=\"r\">4.611<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>We could estimate the IRR then at 13%.<\/p>\n<p>We could also use a simple Excel formula to calculate IRR:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/lh5.googleusercontent.com\/JjsygxOjwbaOW0IrQGKzQGbicjikri8USLfLTV8QhDk9TZEOaU059MgA5BkuIYZVVnGJdhke5KIMnlHJwYZQB-qHmj8l9x5MHrDOcbM6-ItvIbdy5SaPmoQB89R9LwUNtaaWUZSe\" alt=\"Screenshot of Excel showing an IRR calculation.\" width=\"441\" height=\"360\" \/><\/p>\n<p>And by recalculating our NPV analysis using 13% (the factors are not in the table above) we find that the NPV of the project at 13% is more or less equal to the initial investment, proving that the IRR is right around 13%.<\/p>\n<p>Net cash inflows (additional cash revenues &#8211; additional cash expenses)\u00a0 \u00a0 \u00a0 \u00a0 \u00a013%<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<thead>\n<tr class=\"u-sr-only\">\n<th scope=\"col\">Year<\/th>\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Factor<\/th>\n<th scope=\"col\">Total<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.8850<\/td>\n<td class=\"r\">$\u00a0 \u00a0 53,100<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 60,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.7830<\/td>\n<td class=\"r\">$\u00a0 \u00a0 46,980<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.6930<\/td>\n<td class=\"r\">$\u00a0 \u00a0 38,115<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.6130<\/td>\n<td class=\"r\">$\u00a0 \u00a0 33,715<\/td>\n<\/tr>\n<tr>\n<td>Year 5<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 50,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.5430<\/td>\n<td class=\"r\">$\u00a0 \u00a0 27,150<\/td>\n<\/tr>\n<tr>\n<td>Year 6<\/td>\n<td class=\"r\">$\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.4800<\/td>\n<td class=\"r\">$\u00a0 \u00a0 31,200<\/td>\n<\/tr>\n<tr>\n<td>Total present value of cash inflows<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r line-single\"><span class=\"u-sr-only\">Single Line<\/span>$\u00a0 \u00a0230,260<\/td>\n<\/tr>\n<tr>\n<td>Initial investment<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r\">$\u00a0(230,000)<\/td>\n<\/tr>\n<tr>\n<td>Net present value of project<\/td>\n<td><\/td>\n<td><\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 \u00a0 \u00a0 260<span class=\"u-sr-only\">Double line<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The IRR is the actual rate of return or Return on Investment (ROI) of the project. If our hurdle rate is 15%, then this project at 13% does not rise to the level of an acceptable endeavor.<\/p>\n<p>Before we calculate the profitability index on this project, check your understanding of the IRR.<\/p>\n<div class=\"textbox tryit\">\n<h3>Practice Question<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm221585\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=221585&theme=oea&iframe_resize_id=ohm221585\" 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-267\">\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>Internal Rate of Return. <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>\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":17,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Internal Rate of Return\",\"author\":\"Joseph Cooke\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"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-267","chapter","type-chapter","status-publish","hentry"],"part":37,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/users\/364389"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/267\/revisions"}],"predecessor-version":[{"id":2596,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/267\/revisions\/2596"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/parts\/37"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/267\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/media?parent=267"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapter-type?post=267"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/contributor?post=267"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/license?post=267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}