Calculate amount to invest to meet objectives. Use the worksheet. Mary Bender is

Question

Calculate amount to invest to meet objectives. Use the worksheet. Mary Bender is now employed as the managing editor of a well-know business journal. Although she thoroughly enhoys her job and the people she works with, what she would really like to do is open a bookstore of her own. She would like to open her store in about eight years and figures she'll need about $50,000 in capital to do so. Giben that Mary thinks she can make about 10 percent on her money, use Worksheet to answer the following.

a. How much would Mary have to invest today, in one lump sum, to end up with $50,000 in eight years?

b. If she's starting from scratch, how much would she have to put away annually to accumulate the needed capital in eight years?

c. If she already has $10,000 socked away, how much would she have to put away annually to accumuate the required capital in eight years?

d. Given that Mary has an idea of how much she needs to save, explain how she could use an investment plan to help reach her objective.

DETERMINING AMOUNT OF INVESTMENT CAPITAL Financial goa 1. Targeted Financial Goal (see Note 1) 2. Projected Average Return on Investments 6 Finding a Lump Sum Investment: 3. Future Value Factor, from Appendix A based on return on investment of years to target date and a projected average 6 1.000 4. Required Lump Sum Investment line 1 ÷ line 3 Making a Series of Investments over Time: 5. 6. B. Amount of Initial Investment, if any (see Note 2) Future Value Factor, from Appendix A based years of target date and a projected average return on investment of 6 1.000 7. Terminal Value of Initial Investment line 5 x line 6 B. Balance to Come from Savings Plan line 1 line 7 Future Value Annuity Factor, from Appendix B 9. years to target date and a projected average based return on investment of Series of Annual Investments Required over Time * line 8 ÷ line 9 6 0.00 10 Note 1: The "targeted financial goal" is the amount of money you want to accumulate by some target date in the future. Note 2: If you're starting from scratch-i.e., there is no initial investment-enter zero on line 5, skip lines 6 and 7, and then use the total targeted financial goal (from line 1) as the amount to be funded from a savings plan; now proceed with the rest of the worksheet.

Explanation / Answer

a. Total time period = 8 years. Return on Investment = 10%. Amount required after eight years = $50,000

Present Value Factor of 10% return can be calculated as follows = 1 / (1+0.10)8 = 0.4665.

Amount of Lumpsum investment required today can be calculated as follows:

Lumpsum Investment = Amount required after eight years x Present value Factor of 10% return

= $50,000 x .4665

= $23,325.

NOTE: The same can be rechecked by adding 10% each year to the lumpsum amount calculated by us till 8 years. Total Amount will be $50,000

b. In the second part of the question, Mary will be investing equal amount each year for 8 years and therefore for calculating the equated amount for each year we will have to divide $50,000 by Cumulative Present Value Factor on 10% return.

Cumulative Present value Factor = [1/(1+0.10)1 + 1/(1+0.10)2 + 1/(1+1.10)3 + ................+ 1/(1+0.10)8 ]

Using the calculator for the same we get Cumulative Present Value Factor to be 5.35 (Rounded to 2 decimal places)

Amount required annually to be put away = Amount required after 8 years / Cumulative Present Value Factor.

= $50,000 / 5.35

= $9,345.80 annually.

c. In the third part of the question, Mary is already having $10,000 socked away for investing in the capital of the business. However, it is to noted that this $10,000 will be having less value after eight years and therefore first we will have to calculate the present value of these $10,000 and then subtract the same from $50,000 for arriving at the actual amount needed for capital.

Present Valur Factor of 10% return = 1/(1+0.10)8 = 0.4665.

Present value of $10,000 = $10,000 x .4665 = $4,665.

This means that $10,000 of todaay will have a value of only $4,665 after eight years.

Amount further required for meeting the capital = $50,000 - $4665 = $45,335.

Now for calculating the equated annual investment required to be made we will Divide $45,335 by cumulative Present Value Factor of 10% return.

From part b we know that Cumulative Present Value Factor = 5.35

Therefore, amount required to be put away annually = $45,335 / 5.35 = $8473.83 annually.

  

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