{"id":845,"date":"2020-05-25T15:19:06","date_gmt":"2020-05-25T19:19:06","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=845"},"modified":"2025-06-04T16:45:13","modified_gmt":"2025-06-04T20:45:13","slug":"payback","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/payback\/","title":{"raw":"6.6 Payback","rendered":"6.6 Payback"},"content":{"raw":"The payback period <\/em>of an investment is the length of time it takes to recover the initial investment. The shorter the time needed, the better the investment by this criterion. Unless stated otherwise, the time will be calculated using the undiscounted cash flows.\r\n

Example 6.6.1<\/h2>\r\nSuppose that an investment of $20,000 will produce cash inflows of $2,000 in the first year and $6,000 annually for many years after that. Then the payback period of this investment is four years, since by accumulating the inflows you can obtain the following table:\r\n\r\n \r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time (yr)<\/strong><\/td>\r\nCash Flow<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n-$20,000<\/td>\r\n-$20,000<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n2,000<\/td>\r\n-18,000<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n6,000<\/td>\r\n-12,000<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n6,000<\/td>\r\n-6,000<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n6,000<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe payback is at four years.\r\n

Example 6.6.2<\/h2>\r\nWhat if the final cash flow in year four was $10,000?\u00a0\u00a0 Then we would have the following:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time (yr)<\/strong><\/td>\r\nCash Flow<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n-$20,000<\/td>\r\n-$20,000<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n2,000<\/td>\r\n-18,000<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n6,000<\/td>\r\n-12,000<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n6,000<\/td>\r\n-6,000<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n10,000<\/td>\r\n4,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nIn this case, convention says that we treat all inflows and outflows as taking place uniformly throughout the year, so payback is:\r\n\r\n[latex]\\begin{align*}\r\n\r\n\\textrm{Payback}&=\\frac{\\textrm{-Balance at that year}}{\\textrm{Cash flow at the next year}}\\\\\r\n\r\n&=\\frac{$6,000}{$10,000}\\\\\r\n\r\n& = 3.6 \\textrm{ years}\r\n\r\n\\end{align*}[\/latex]\r\n\r\n<\/div>\r\n \r\n\r\nNote that no allowance is made for the exact timing of flows (if the inflows were $5,000 a year the same result would have been obtained) or for the size of cash flows after the payback period. Also, there is no mention of a rate of return, <\/strong>although a short payback period usually indicates a high rate of return.\r\n\r\nIf the investment is not paid back exactly at the end of a year, and, if the cash flows could reasonably be assumed to occur uniformly throughout the year, then you can estimate the payback period by adding the fraction of the last year needed to recover the investment. This is an approximation, but it is a useful tool.\r\n<\/span>\r\n\r\nSuppose that in Example 6.8 above the investment required had been $21,500. Then the payback period would have been extended to 4.25 years since the additional $1,500 would have to be earned in the 5th year and would require 1,500\/6,000 = 0.25 years, so that the payback period would be 4 + 0.25 = 4.25 years.\r\n\r\nIf the cash flows were given on a monthly basis there would be no need to estimate a part of a month - the time could be given to the end of the first month at which the recovery is complete.\r\n\r\nThe payback period is one of the simplest measures of investment effectiveness. Its benefits are that it is easily understood, easily calculated and that it provides some assessment of the risk to which a company is exposed in an investment. Investments which require a long period before the investment is recovered are generally felt to carry a higher risk, since predictions of cash flows are more likely to be in error if they are for times far in the future.\r\n\r\n \r\n
\r\n

Knowledge Check 6.4<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nComplete the tables and calculations below to obtain the payback periods for the restaurant OPTIONS A and B given in Knowledge Check 6.3.\r\n\r\nOPTION A ($30,000 invested at time 0)\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time<\/strong><\/td>\r\nInflow<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/tr>\r\n
0<\/td>\r\n-$30,0000<\/td>\r\n<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n12,000<\/td>\r\n<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n12,000<\/td>\r\n<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n12,000<\/td>\r\n<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTime needed beyond end of second year:\r\n\r\nAmount needed\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ?\r\n\r\nAmount in year three\u00a0 ?\r\n\r\n \r\n\r\n<\/div>\r\n<\/div>\r\n \r\n

Your Own Notes<\/h2>\r\n
    \r\n \t
  • Are there any notes you want to take from this section? Is there anything you'd like to copy and paste below?<\/li>\r\n \t
  • These notes are for you only (they will not be stored anywhere)<\/li>\r\n \t
  • Make sure to download them at the end to use as a reference<\/li>\r\n<\/ul>\r\n[h5p id=\"1\"]\r\n\r\n ","rendered":"

    The payback period <\/em>of an investment is the length of time it takes to recover the initial investment. The shorter the time needed, the better the investment by this criterion. Unless stated otherwise, the time will be calculated using the undiscounted cash flows.<\/p>\n

    Example 6.6.1<\/h2>\n

    Suppose that an investment of $20,000 will produce cash inflows of $2,000 in the first year and $6,000 annually for many years after that. Then the payback period of this investment is four years, since by accumulating the inflows you can obtain the following table:<\/p>\n

     <\/p>\n

    \n\n\n\n\n\n\n\n\n
    Time (yr)<\/strong><\/td>\nCash Flow<\/strong><\/td>\nBalance<\/strong><\/td>\n<\/tr>\n
    0<\/td>\n-$20,000<\/td>\n-$20,000<\/td>\n<\/tr>\n
    1<\/td>\n2,000<\/td>\n-18,000<\/td>\n<\/tr>\n
    2<\/td>\n6,000<\/td>\n-12,000<\/td>\n<\/tr>\n
    3<\/td>\n6,000<\/td>\n-6,000<\/td>\n<\/tr>\n
    4<\/td>\n6,000<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    The payback is at four years.<\/p>\n

    Example 6.6.2<\/h2>\n

    What if the final cash flow in year four was $10,000?\u00a0\u00a0 Then we would have the following:<\/p>\n\n\n\n\n\n\n\n\n
    Time (yr)<\/strong><\/td>\nCash Flow<\/strong><\/td>\nBalance<\/strong><\/td>\n<\/tr>\n
    0<\/td>\n-$20,000<\/td>\n-$20,000<\/td>\n<\/tr>\n
    1<\/td>\n2,000<\/td>\n-18,000<\/td>\n<\/tr>\n
    2<\/td>\n6,000<\/td>\n-12,000<\/td>\n<\/tr>\n
    3<\/td>\n6,000<\/td>\n-6,000<\/td>\n<\/tr>\n
    4<\/td>\n10,000<\/td>\n4,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    In this case, convention says that we treat all inflows and outflows as taking place uniformly throughout the year, so payback is:<\/p>\n

    [latex]\\begin{align*} \\textrm{Payback}&=\\frac{\\textrm{-Balance at that year}}{\\textrm{Cash flow at the next year}}\\\\ &=\\frac{$6,000}{$10,000}\\\\ & = 3.6 \\textrm{ years} \\end{align*}[\/latex]<\/p>\n<\/div>\n

     <\/p>\n

    Note that no allowance is made for the exact timing of flows (if the inflows were $5,000 a year the same result would have been obtained) or for the size of cash flows after the payback period. Also, there is no mention of a rate of return, <\/strong>although a short payback period usually indicates a high rate of return.<\/p>\n

    If the investment is not paid back exactly at the end of a year, and, if the cash flows could reasonably be assumed to occur uniformly throughout the year, then you can estimate the payback period by adding the fraction of the last year needed to recover the investment. This is an approximation, but it is a useful tool.
    \n<\/span><\/p>\n

    Suppose that in Example 6.8 above the investment required had been $21,500. Then the payback period would have been extended to 4.25 years since the additional $1,500 would have to be earned in the 5th year and would require 1,500\/6,000 = 0.25 years, so that the payback period would be 4 + 0.25 = 4.25 years.<\/p>\n

    If the cash flows were given on a monthly basis there would be no need to estimate a part of a month – the time could be given to the end of the first month at which the recovery is complete.<\/p>\n

    The payback period is one of the simplest measures of investment effectiveness. Its benefits are that it is easily understood, easily calculated and that it provides some assessment of the risk to which a company is exposed in an investment. Investments which require a long period before the investment is recovered are generally felt to carry a higher risk, since predictions of cash flows are more likely to be in error if they are for times far in the future.<\/p>\n

     <\/p>\n

    \n
    \n

    Knowledge Check 6.4<\/p>\n<\/header>\n

    \n

    Complete the tables and calculations below to obtain the payback periods for the restaurant OPTIONS A and B given in Knowledge Check 6.3.<\/p>\n

    OPTION A ($30,000 invested at time 0)<\/p>\n\n\n\n\n\n\n\n
    Time<\/strong><\/td>\nInflow<\/strong><\/td>\nBalance<\/strong><\/td>\n<\/tr>\n
    0<\/td>\n-$30,0000<\/td>\n<\/td>\n<\/tr>\n
    1<\/td>\n12,000<\/td>\n<\/td>\n<\/tr>\n
    2<\/td>\n12,000<\/td>\n<\/td>\n<\/tr>\n
    3<\/td>\n12,000<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    Time needed beyond end of second year:<\/p>\n

    Amount needed\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 = \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 ?<\/p>\n

    Amount in year three\u00a0 ?<\/p>\n

     <\/p>\n<\/div>\n<\/div>\n

     <\/p>\n

    Your Own Notes<\/h2>\n
      \n
    • Are there any notes you want to take from this section? Is there anything you’d like to copy and paste below?<\/li>\n
    • These notes are for you only (they will not be stored anywhere)<\/li>\n
    • Make sure to download them at the end to use as a reference<\/li>\n<\/ul>\n
      \n