Module+18000+III+Explanation+and+Examples

III. Module 18000 Explanation and Examples rrw

Instead of calculating interest one year at a time, it is much simpler to see the **__Future Value__** of the investment using the **__Compound Interest Formula__**. The formula for **__Compound Interest__** is:
 * Interest: **
 * __Simple Interest __** is calculated only on the beginning principle, but **__Compound Interest__** is calculated on the beginning amount plus any interest accumulated in the meantime.


 * P n = P 0 ( 1 + I ) ^ n ||   || where: ||   || P n = Value at the end of n time periods ||
 * ||  ||   ||   || P 0 = Beginning value ||
 * ||  ||   ||   || I = Interest ||
 * ||  ||   ||   || n = Number of periods ||


 * Example of Compound Interest Formula: ** If Sue receives 4% compounded interest on $1,000 for 6 years, what will be the value of her investment at the end of year 6?


 * **P n ** ||   || = ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">P 0 ( 1 + I ) ^ n ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,000 ( 1 + .04) ^ 6 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,000 (1.04) ^ 6 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,265.32 __** ||


 * __<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Present Value __**<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> is the value of your investment today. **__Future Value__** is the value of the same investment at some point in the future.

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">In the above example:


 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Present Value ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,000 __** ||
 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Future Value ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,265.32 __** ||
 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Future Value ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,265.32 __** ||

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **FV** function in Microsoft Excel to solve the above problem:


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=FV(rate,nper,pmt,PV) **

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; nper = Number of periods; pmt = Payment (in our example, this is 0); PV = Present Value


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=FV(.04,6,0,-1000) **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">__$1,265.32__ **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Future Value Formula: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV = PV ( 1 + i ) ^ n ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">where: ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV = Future Value ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV = Present Value ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">i = Interest rate per period ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">n = Number of compounding periods ||


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Example of Future Value Compounded Monthly: **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> If Sue receives 4% interest (compounded monthly) on her $1,000 investment for 6 years, what will be the value of her investment at the end of year 6?


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">i ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">.04 / 12 months per year ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">.0033% per month ||


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">n ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">6 years * 12 months per year ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">72 months ||


 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV ( 1 + i) ^ n ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,000 ( 1 + .0033) ^ 72 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,000 (1.0033) ^ 72 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$1,267.71 __** ||

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **FV** function in <span style="background-color: #008000; color: #ffffff; font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Microsoft Excel <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> to solve the above problem:


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=FV(rate,nper,pmt,PV) **

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; nper = Number of periods; pmt = Payment (in our example, this is 0); PV = Present Value


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=FV(.0033,72,0,-1000) **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">__$1,267.71__ **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Present Value Formula: **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV = FV / ( 1 + i ) ^ n ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">where: ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV = Present Value ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV = Future Value ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">i = Interest rate per period ||
 * ||  ||   ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">n = Number of compounding periods ||


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Example of Present Value Compounded Annually: **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> Camille receives 6% interest (compounded annually) on her investment for 4 years. She knows that her investment will be worth $10,000 at the end of year 4. What is the value of her investment today?


 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV / ( 1 + i) ^ n ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$10,000 / ( 1 + .06) ^ 4 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$10,000 / (1.06) ^ 4 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$7,920.94 __** ||

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **PV** function in <span style="background-color: #008000; color: #ffffff; font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Microsoft Excel <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> to solve the above problem:


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=PV(rate,nper,pmt,FV) **

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; nper = Number of periods; pmt = Payment (in our example, this is 0); FV = Future Value


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=PV(.06,4,0,-10000) **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">__$7,920.94__ **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Example of Present Value Compounded Monthly: **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> Camille receives 6% interest (compounded monthly) on her investment for 4 years. She knows that her investment will be worth $10,000 at the end of year 4. What is the value of her investment today?


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">i ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">.06 / 12 months per year ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">.005% per month ||


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">n ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">4 years * 12 months per year ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">48 months ||


 * **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">PV ** ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">FV / ( 1 + i) ^ n ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$10,000 / ( 1 + .005) ^ 48 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$10,000 / (1.005) ^ 48 ||
 * ||  || <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">= ||   || **__<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">$7,870.98 __** ||

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **PV** function in **<span style="font-family: 'Times New Roman','serif';">Microsoft Excel ** <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> to solve the above problem:


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=PV(rate,nper,pmt,FV) **

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; nper = Number of periods; pmt = Payment (in our example, this is 0); FV = Future Value


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">=PV(.005,48,0,-10000) **


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">__$7,870.98__ **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)

<span style="background-color: #ffff00; font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Notice that __**$7,870.98**__ < __**$7,920.94**__. This means that Camille can get her $10,000 at the end of year 4 with an initial investment of only $7,870.98 if the interest is compounded monthly.

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">A series of future cash flows is called an **__Annuity__**. The following examples will be solved in <span style="background-color: #008000; color: #ffffff; font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**Microsoft Excel** <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> only.


 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Example of Present Value of an Annuity: **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> Sue has invested in a project that is expected to return $500 per year for 3 years. What is the **Present Value** of Sue’s future cash flows if she requires a 10% rate of return?

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **PV** function in **Microsoft Excel** to solve the above problem:

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**=PV(rate,nper,pmt)**

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; nper = Number of periods; pmt = Annuity Payment

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**=PV(.10,3,-500)**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**__$1,243.43__** <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Using the **NPV** (Net Present Value) function in **Microsoft Excel** to solve the above problem:
 * <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Example of Present Value of an Uneven Series of Cash Flows: **<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;"> Camille has invested in a project that is expected to return $500 in year 1; $200 in year 2 and $150 in year 3. What is the **Present Value** of Camille’s future cash flows if she requires a 10% rate of return?

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**=NPV(rate,value1,value2,value3)**

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">Where: rate = Interest; value1 = Cash Flow in 1st year; value2 = Cash Flow in 2nd year; value3 = Cash Flow in 3rd year

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**=NPV(.10,500,200,150)**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 18.6667px;">**__$732.53__** <span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">(Note: the above function must be typed in one cell with no spaces.)

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">References used in the formulas and terms: __http://www.studyfinance.com/lessons/timevalue/index.mv__ __http://www.netmba.com/finance/time-value/future/__ __http://www.netmba.com/finance/time-value/present/__ <span style="font-family: 'Times New Roman','serif'; font-size: 16px;">Hansen, D.R. & Mowen, M.M. (2011). //Cornerstones of Cost Accounting//. Mason, OH: South-Western Cengage Learning.

<span style="font-family: 'Times New Roman','serif'; font-size: 18.6667px;">References used in the Excel functions: __http://www.tvmcalcs.com/calculators/excel_tvm_functions/excel_tvm_functions_page1__ __<span style="font-family: 'Times New Roman','serif';">http://office.microsoft.com/en-us/excel-help/financial-functions-HP005200181.aspx?CTT=3 __