{"id":486,"date":"2020-04-28T11:37:18","date_gmt":"2020-04-28T15:37:18","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/?post_type=chapter&p=486"},"modified":"2021-06-29T11:49:39","modified_gmt":"2021-06-29T15:49:39","slug":"multiple-cash-flows","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/businessmathematics\/chapter\/multiple-cash-flows\/","title":{"raw":"4.5 Multiple Cash Flows","rendered":"4.5 Multiple Cash Flows"},"content":{"raw":"Up to this point, you have considered situations that have only a single loan or deposit and a repayment. There are, however, many cases in which there are many inflows and\/or outflows to a particular individual or company. For example, consider the company that is developing a business and needs cash inflows (such as loans) early in its life and will balance these inflows with outflows later.\r\n\r\n \r\n

Example 4.5.1<\/h2>\r\nSuppose, for instance, that a builder plans to finance a project through a bank and will borrow $150,000 now and $100,000 in three months, then repay $50,000 in <\/strong>six months and the rest in one year's time. Interest is to be paid on the outstanding balance at 12% compounded monthly.\r\n\r\n\"Timeline\r\n\r\nThen you can find the size of the last payment (denoted by x\u00a0 above) by following through an account and adding interest every month.\r\n\r\nCash inflows to the builder are positive.\r\n\r\n\r\n\r\n\r\n\r\n\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 (months)<\/strong><\/td>\r\nInterest<\/strong><\/td>\r\nCash Flow<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
0<\/td>\r\n0.00<\/td>\r\n$150,000.00<\/td>\r\n$150,000.00<\/td>\r\n<\/tr>\r\n
1<\/td>\r\n1,500.00<\/td>\r\n0.00<\/td>\r\n151,500.00<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n1,515.00<\/td>\r\n0.00<\/td>\r\n153,015.00<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n1,530.15<\/td>\r\n100,000.00<\/td>\r\n254,545.15<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n2,545.45<\/td>\r\n0.00<\/td>\r\n257,090.60<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n2,570.91<\/td>\r\n0.00<\/td>\r\n259,661.51<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n2,596.62<\/td>\r\n-50,000.00<\/td>\r\n212,258.12<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n2,122.58<\/td>\r\n0.00<\/td>\r\n214,380.70<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n2,143.81<\/td>\r\n0.00<\/td>\r\n216,524.51<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n2,165.25<\/td>\r\n0.00<\/td>\r\n218,689.76<\/td>\r\n<\/tr>\r\n
10<\/td>\r\n2,186.90<\/td>\r\n0.00<\/td>\r\n220,876.65<\/td>\r\n<\/tr>\r\n
11<\/td>\r\n2,208.77<\/td>\r\n0.00<\/td>\r\n223,085.42<\/td>\r\n<\/tr>\r\n
12<\/td>\r\n2,230.85<\/td>\r\n0.00<\/td>\r\n225,316.27<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n \r\n\r\nA shorter way to check the account is to accumulate the future value on the outstanding balance <\/em>only at the time of cash flows. <\/em>For the above account, then, the result is as follows:\r\n\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Time (months)<\/strong><\/td>\r\nInterest<\/strong><\/td>\r\nCash Flow<\/strong><\/td>\r\nBalance<\/strong><\/td>\r\n<\/tr>\r\n<\/thead>\r\n
0<\/td>\r\n<\/td>\r\n$150,000<\/td>\r\n$150,000<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n[latex]$150,000(1.01)^3=$154,545.15[\/latex]<\/td>\r\n100,000.00<\/td>\r\n254,545.15<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n[latex]$254,545.15(1.01)^3=262,258.12[\/latex]<\/td>\r\n-50,000<\/td>\r\n212,258.12<\/td>\r\n<\/tr>\r\n
12<\/td>\r\n[latex]$212,258.12\u00d7(1.01)^6=225,316.27[\/latex]<\/td>\r\n-225,316.27<\/td>\r\n0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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\"]","rendered":"

    Up to this point, you have considered situations that have only a single loan or deposit and a repayment. There are, however, many cases in which there are many inflows and\/or outflows to a particular individual or company. For example, consider the company that is developing a business and needs cash inflows (such as loans) early in its life and will balance these inflows with outflows later.<\/p>\n

     <\/p>\n

    Example 4.5.1<\/h2>\n

    Suppose, for instance, that a builder plans to finance a project through a bank and will borrow $150,000 now and $100,000 in three months, then repay $50,000 in <\/strong>six months and the rest in one year’s time. Interest is to be paid on the outstanding balance at 12% compounded monthly.<\/p>\n

    \"Timeline<\/p>\n

    Then you can find the size of the last payment (denoted by x\u00a0 above) by following through an account and adding interest every month.<\/p>\n

    Cash inflows to the builder are positive.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
    Time (months)<\/strong><\/td>\nInterest<\/strong><\/td>\nCash Flow<\/strong><\/td>\nBalance<\/strong><\/td>\n<\/tr>\n<\/thead>\n
    0<\/td>\n0.00<\/td>\n$150,000.00<\/td>\n$150,000.00<\/td>\n<\/tr>\n
    1<\/td>\n1,500.00<\/td>\n0.00<\/td>\n151,500.00<\/td>\n<\/tr>\n
    2<\/td>\n1,515.00<\/td>\n0.00<\/td>\n153,015.00<\/td>\n<\/tr>\n
    3<\/td>\n1,530.15<\/td>\n100,000.00<\/td>\n254,545.15<\/td>\n<\/tr>\n
    4<\/td>\n2,545.45<\/td>\n0.00<\/td>\n257,090.60<\/td>\n<\/tr>\n
    5<\/td>\n2,570.91<\/td>\n0.00<\/td>\n259,661.51<\/td>\n<\/tr>\n
    6<\/td>\n2,596.62<\/td>\n-50,000.00<\/td>\n212,258.12<\/td>\n<\/tr>\n
    7<\/td>\n2,122.58<\/td>\n0.00<\/td>\n214,380.70<\/td>\n<\/tr>\n
    8<\/td>\n2,143.81<\/td>\n0.00<\/td>\n216,524.51<\/td>\n<\/tr>\n
    9<\/td>\n2,165.25<\/td>\n0.00<\/td>\n218,689.76<\/td>\n<\/tr>\n
    10<\/td>\n2,186.90<\/td>\n0.00<\/td>\n220,876.65<\/td>\n<\/tr>\n
    11<\/td>\n2,208.77<\/td>\n0.00<\/td>\n223,085.42<\/td>\n<\/tr>\n
    12<\/td>\n2,230.85<\/td>\n0.00<\/td>\n225,316.27<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

     <\/p>\n

    A shorter way to check the account is to accumulate the future value on the outstanding balance <\/em>only at the time of cash flows. <\/em>For the above account, then, the result is as follows:<\/p>\n

     <\/p>\n\n\n\n\n\n\n\n\n
    Time (months)<\/strong><\/td>\nInterest<\/strong><\/td>\nCash Flow<\/strong><\/td>\nBalance<\/strong><\/td>\n<\/tr>\n<\/thead>\n
    0<\/td>\n<\/td>\n$150,000<\/td>\n$150,000<\/td>\n<\/tr>\n
    3<\/td>\n[latex]$150,000(1.01)^3=$154,545.15[\/latex]<\/td>\n100,000.00<\/td>\n254,545.15<\/td>\n<\/tr>\n
    6<\/td>\n[latex]$254,545.15(1.01)^3=262,258.12[\/latex]<\/td>\n-50,000<\/td>\n212,258.12<\/td>\n<\/tr>\n
    12<\/td>\n[latex]$212,258.12\u00d7(1.01)^6=225,316.27[\/latex]<\/td>\n-225,316.27<\/td>\n0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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