Calculating the Amount of Monthly Investment - Case Study Example

Finance assignment Table of Contents Table of Contents 2 Background 3 Present value of investment 3 Conclusion 8 Reference 9 Bibliography 10 Background My friend Mr A, currently 25 years of age is planning to start investment for his retirement from his next birthday i.e. at the age of 26. He is working in a private limited company and is drawing a monthly salary of $5000. The retirement age in the company is 65 years. He plans to get married in another 5 years. After retirement he wants to draw $8000 every month till the age of 75. He owns property that he has given out on rent. Therefore, the other monthly expenses after retirement will be taken care of from this source. Other than this retirement investment he has made some equity investment. Therefore, the investment in shares will take care of any capital expenses like funding the higher educations needs of the children. At present his monthly salary is sufficient of taking care of his monthly expenses. But with the passage of time the value of money will fall. The post-tax retirement drawings have been taken as $8000, higher than the present monthly salary, for incorporating the inflationary effect. Present value of investment Mr A can invest money for his retirement for a period of 30 years, starting from the time he reaches the age of 26 till his last serving year in office. He has chalked out the monthly drawings of $8000 keeping in mind the factor of inflation. The rate of inflation in US has been forecasted at 1.2% for the month of January 2011 (Financial Forecast Center, LLC, n.d.). If this inflation rate is adjusted with the current annual salary of Mr A then this comes to- = 60000*(1+0.012) ^40 = $96687.82 From this the monthly figure after adjustment of inflation is obtained as $8057. This has been rounded off to $8000. This means that even if the value of money falls due to inflation the real value of his monthly drawings will remain constant. Mr A wants to draw this amount as monthly annuities after a period of 40 years. Now the present value of this amount must be less due to the concept of “time value of money”. According to the time value concept the value of an amount receivable over a period of say 10 years must be less today. Therefore the amount of monthly drawings for the various time periods must be adjusted with interest rate to calculate the present value. Here the interest rate used is “compound interest”. If the interest is paid only on the amount of principal then this is referred as “simple interest” but when interest is paid on the amount of interest earned previously it is called compound interest. The comparison between the values of different periods of time cannot be done without adjusting the amounts with the compound interest rate (UT Department of Finance, 2010). This concept is used while deciding about the worthiness of an investment or withdrawal of investment. The method is primarily used for estimating whether the lump sum withdrawal of pension amount will be better as compared to monthly withdrawals. Assuming that the annual rate of interest is 6 percent, in the first place, the present value of the amount of drawings till the point of retirement has been calculated. This has been done by discounting the monthly annuity streams after retirement with the monthly discount rate. The monthly discount rate is- = 6/ 12 = 0.5%. The calculation of present value of drawings by discounting the monthly drawings of each month is a very tedious process as this will amount to reiterating the process for 10 years i.e. for the number of periods of 120. For this reason the present value annuity formula has been used for calculating the present value of the drawings at the point of retirement. This is given as- P = A / i [1- 1/ (1+i) ^n] P is the present value of the investment A is the amount of monthly drawings i is the monthly interest rate n is the number of periods (Chandra, 2008, pp.167). From the above equation the present value of drawings is calculated as- P = 8000 / 0.005 [1-1/ (1+0.005) ^120] = $720587.62 Now one needs to calculate the amount of monthly investment that will help him reach this amount of investment at the end of 30 years. To accumulate this amount at the end of 15 years Mr A has to contribute monthly for his service tenure of 40 years. As the contributions are monthly the number of periods for which the investment is made is calculated as- = 40*12 = 480 If Mr A makes monthly contributions for 480 periods then by the end of his working life his monthly contributions will add up to the desired sum. The future value of the monthly investments has been calculated as $720587. But Mr A needs to contribute less than this sum. This is because of the underlying time value concept. The value of $720587 is after a period of 40 years however its value as on the current date will be lower. This is based on the premise that the value of $100 is today is not the same as its value after 10 years. For this reason the accumulated monthly contributions that Mr A has to make will be less then the future value of the investment. Therefore one has to compute the future value of the monthly instalments to equate this with $720587. Technically this is termed as calculating the “future value of annuity”. Here a formula is used which is stated as- FVA = A / i [(1+i) ^n -1] FVA is the future value of the annuity investment A is the monthly annuity n is the number of periods (Booker, 2006, pp.1-49) From the above formula the present value of the amount of $720587 is calculated as- 720587 = A/ 0.005 * [1+ 005) ^480 -1)] A = 720587 * 0.005 / [(1+0.005) ^ 480-1] = $362 Another way of finding it is by using “PMT” function in Excel. The result obtained in both the case is similar. The amount of $362 signifies that if Mr A makes monthly contributions equivalent to this amount then by the end of investment period i.e. 40 years the monthly contributions together with interest will add up to $720587. This monthly contribution is nearly equal to 7 percent of his current monthly salary. Normally an individual can save around 10 percent of his salary but the amount of retirement investment has been capped at less than this amount as Mr A wants to invest certain portion of his monthly income in shares as well. He has a good knowledge about the financial markets and therefore can identify the undervalued stocks. But as income from this source is volatile he wants to invest a portion of his monthly salary whereby he can derive a fixed return. The total amount contributed by Mr A towards his pension is- = 362*480 = $173679 The amount accumulated at the end of 40 years is higher than the monthly contributions. The difference between the two amounts gives the interest earned on the monthly contributions. This is equal to- =720587 – 173679 = $546908 On the monthly contributions made towards the retirement, Mr A will receive interest of $546908. This is more than the contributions made by him towards this investment. The reason for this is explained by the concept of time value of money. Conclusion The amounts at different time periods are not comparable. To make decision with regard to the investment it is important to discount the cash flows to the current date. This is done by using the present and future value formulae on time value. This can be used for calculating the amount that has to be invested over a period of time to be able to draw a fixed monthly amount for the desired number of years. For Mr A the amount that will enable him to draw $8000 on a monthly basis for 10 years is obtained as $720587. To accumulate this amount he will have to invest $362 on a monthly basis for a period of 40 years starting from the age of 26 till his last year in office. His monthly contributions will add up to $720587 by the time he reaches the age of 65. This amount is inclusive of the interest accumulated on the amount over the years. Here one also receives interest on the amount of accumulated interest over the years. Reference Booker, J. 2006. Financial Planning Fundamentals. CCH Canadian Limited. Chandra, P. 2008. Investment Planning. Tata McGraw-Hill. Financial Forecast Center, LLC. No date. U.S. Inflation Rate Forecast. Available at: http://www.forecasts.org/inflation.htm [Accessed on August 21, 2010]. UT Department of Finance. 2010. How can one compare amounts in different time periods?. The Time Value of Money. Available at: http://itc.utk.edu/spotlight/archive/murphy/MBA_Prep_Summer_Tech.ppt [Accessed on August 21, 2010]. Bibliography USA TODAY. 2010. Federal pay ahead of private industry. Available at: http://www.usatoday.com/news/nation/2010-03-04-federal-pay_N.htm Kuhlemeyer, A.G. 2004. Time Value of Money. Pearson Education Limited. Available at: http://www.sis.pitt.edu/~gray/ITMgnt/lectures/finance/tvomPearsonEd.ppt Annexure- Annual rate 0.06 Monthly drawings ($) 8000 Years 10 Periods 120 Monthly rate 0.005 Present Value of this investment (at age of 65) $720,587.63 Investment period 40 Number of periods 480 Monthly contribution ($) (362) FVA = A / i [(1+i)^n -1]   Monthly contribution (Using formula) ($) 362 Read More