{"id":265,"date":"2021-01-26T22:33:18","date_gmt":"2021-01-26T22:33:18","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/?post_type=chapter&#038;p=265"},"modified":"2021-08-13T16:00:12","modified_gmt":"2021-08-13T16:00:12","slug":"net-present-value","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/chapter\/net-present-value\/","title":{"raw":"Net Present Value","rendered":"Net Present Value"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Calculate the net present value of a capital project<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo calculate the net present value of a capital project, start with the nominal cash flows. We\u2019ll be using 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 $40,000. Management is using the weighted average cost of capital of 15% as a hurdle rate\r\n\r\nNet annual cash flows are as follows:\r\n<div align=\"left\">\r\n<table class=\"fin-table acctstatement fw\">\r\n<thead>\r\n<tr class=\"u-sr-only\">\r\n<th scope=\"col\">Description<\/th>\r\n<th scope=\"col\">Amount<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td>Year 1<\/td>\r\n<td class=\"r\">$\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&nbsp;\r\n\r\n<\/div>\r\nNext, using Excel, a financial calculator, or a PV table (as shown below), calculate the net present value of each cash flow. Use the factors from the 15% column.\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\">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\">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<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 60,000<\/td>\r\n<td class=\"r\">times the factor of\u00a0 \u00a0 0.8700<\/td>\r\n<td class=\"r\">= $52,200<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 2<\/td>\r\n<td class=\"r\">\u00a0 60,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.7560<\/td>\r\n<td class=\"r\">$ 45,360<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 3<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.6580<\/td>\r\n<td class=\"r\">$ 36,190<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 4<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.5720<\/td>\r\n<td class=\"r\">$ 31,460<\/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<td class=\"r\">\u00a0 \u00a0 0.4970<\/td>\r\n<td class=\"r\">$ 24,850<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Year 6<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\r\n<td class=\"r\">\u00a0 \u00a0 0.4320<\/td>\r\n<td class=\"r\">$ 28,080<\/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 218,140<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n\r\nThen subtract the initial investment:\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>Initial investment<\/td>\r\n<td class=\"r\">$ (230,000)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Net present value of project<\/td>\r\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 (11,860)<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\nThis negative net present value tells us that the present value of all future cash flows, discounted at 15%, is less than the original price of the project, so it is as if we are spending $230,000 today and immediately receiving back only $218,140. In other words, the company is losing money on this project.\r\n\r\nHere is an NPV problem worked out on video:\r\n\r\n<iframe src=\"\/\/plugin.3playmedia.com\/show?mf=6352604&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=HFFkFMfotT0&amp;video_target=tpm-plugin-91e8k4yz-HFFkFMfotT0\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe>\r\n\r\nYou can view the <a href=\"https:\/\/oerfiles.s3.us-west-2.amazonaws.com\/Managerial+Accounting\/Transcripts\/NetPresentValue_transcript.txt\" target=\"_blank\" rel=\"noopener\">transcript for \"Net Present Value (NPV)\" here (opens in new window)<\/a>.\r\n\r\nBefore we calculate the Internal Rate of Return (IRR) on this project, check your understanding of the NPV method.\r\n<div class=\"textbox tryit\">\r\n<h3>Practice Question<\/h3>\r\n[ohm_question hide_question_numbers=1]221584[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Calculate the net present value of a capital project<\/li>\n<\/ul>\n<\/div>\n<p>To calculate the net present value of a capital project, start with the nominal cash flows. We\u2019ll be using 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 $40,000. Management is using the weighted average cost of capital of 15% as a hurdle rate<\/p>\n<p>Net annual cash flows are as follows:<\/p>\n<div style=\"text-align: left;\">\n<table class=\"fin-table acctstatement fw\">\n<thead>\n<tr class=\"u-sr-only\">\n<th scope=\"col\">Description<\/th>\n<th scope=\"col\">Amount<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Year 1<\/td>\n<td class=\"r\">$\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<p>&nbsp;<\/p>\n<\/div>\n<p>Next, using Excel, a financial calculator, or a PV table (as shown below), calculate the net present value of each cash flow. Use the factors from the 15% column.<\/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\">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\">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<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 60,000<\/td>\n<td class=\"r\">times the factor of\u00a0 \u00a0 0.8700<\/td>\n<td class=\"r\">= $52,200<\/td>\n<\/tr>\n<tr>\n<td>Year 2<\/td>\n<td class=\"r\">\u00a0 60,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.7560<\/td>\n<td class=\"r\">$ 45,360<\/td>\n<\/tr>\n<tr>\n<td>Year 3<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.6580<\/td>\n<td class=\"r\">$ 36,190<\/td>\n<\/tr>\n<tr>\n<td>Year 4<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 55,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.5720<\/td>\n<td class=\"r\">$ 31,460<\/td>\n<\/tr>\n<tr>\n<td>Year 5<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 50,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.4970<\/td>\n<td class=\"r\">$ 24,850<\/td>\n<\/tr>\n<tr>\n<td>Year 6<\/td>\n<td class=\"r\">\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 65,000<\/td>\n<td class=\"r\">\u00a0 \u00a0 0.4320<\/td>\n<td class=\"r\">$ 28,080<\/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 218,140<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Then subtract the initial investment:<\/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>Initial investment<\/td>\n<td class=\"r\">$ (230,000)<\/td>\n<\/tr>\n<tr>\n<td>Net present value of project<\/td>\n<td class=\"r line-single line-double\"><span class=\"u-sr-only\">Single Line<\/span>$ \u00a0 (11,860)<span class=\"u-sr-only\">Double line<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<p>This negative net present value tells us that the present value of all future cash flows, discounted at 15%, is less than the original price of the project, so it is as if we are spending $230,000 today and immediately receiving back only $218,140. In other words, the company is losing money on this project.<\/p>\n<p>Here is an NPV problem worked out on video:<\/p>\n<p><iframe loading=\"lazy\" src=\"\/\/plugin.3playmedia.com\/show?mf=6352604&amp;p3sdk_version=1.10.1&amp;p=20361&amp;pt=375&amp;video_id=HFFkFMfotT0&amp;video_target=tpm-plugin-91e8k4yz-HFFkFMfotT0\" width=\"800px\" height=\"450px\" frameborder=\"0\" marginwidth=\"0px\" marginheight=\"0px\"><\/iframe><\/p>\n<p>You can view the <a href=\"https:\/\/oerfiles.s3.us-west-2.amazonaws.com\/Managerial+Accounting\/Transcripts\/NetPresentValue_transcript.txt\" target=\"_blank\" rel=\"noopener\">transcript for &#8220;Net Present Value (NPV)&#8221; here (opens in new window)<\/a>.<\/p>\n<p>Before we calculate the Internal Rate of Return (IRR) on this project, check your understanding of the NPV method.<\/p>\n<div class=\"textbox tryit\">\n<h3>Practice Question<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm221584\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=221584&theme=oea&iframe_resize_id=ohm221584\" 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-265\">\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>Net Present Value. <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\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Net Present Value (NPV). <strong>Provided by<\/strong>: Edspira. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/HFFkFMfotT0\">https:\/\/youtu.be\/HFFkFMfotT0<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/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":16,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Net Present Value\",\"author\":\"Joseph Cooke\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"copyrighted_video\",\"description\":\"Net Present Value (NPV)\",\"author\":\"\",\"organization\":\"Edspira\",\"url\":\"https:\/\/youtu.be\/HFFkFMfotT0\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-265","chapter","type-chapter","status-publish","hentry"],"part":37,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/265","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":13,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/265\/revisions"}],"predecessor-version":[{"id":2594,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapters\/265\/revisions\/2594"}],"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\/265\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/media?parent=265"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/pressbooks\/v2\/chapter-type?post=265"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/contributor?post=265"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-managerialaccounting\/wp-json\/wp\/v2\/license?post=265"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}