Question

5.1 An Investment offers $10,000 per year for 15 years, with the first payment occurring 1 year from now. If the require retum is 7.5 percent. a. What is the value of the investment? (3%) b. What would the value be if the payments occurred for 30 year? (2%) c. For 60 year? (2%) d. Forever? (3%)

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Answer 1

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ABC Cla .00.0 Book1 - Microsoft Excel Home Insert Formulas Page Layout Data Review View Developer X n! % Cut AutoSum- Calibri 16 Α Α΄ Wrap Text Accounting Fill Paste En Copy Format Painter B I U - Merge & Center $ % +0.00 .00 0 Insert Delete Format Conditional Format Cell Formatting as Table Styles Styles 2 Clear Sort & Find & Filter - Select Number Cells Editing V H - J K P Clipboard Font Alignment E26 fx =SUM(E11:E25) A B C D E F G 1 Answer) 2 I will help you understand the question by both the formulae and by annual calculation 3 Since the payment is made at the beginning of next year (2nd). It can be taken as at the end of 1st year 4 5 10000 10000 10000 6 Current Year 1 2 3 7 L M N 0 Formulae P=PMT((1-(1/(1+r)n) /r)) where PMT Annual Payment Rate of interest n No of period 10000(1-(1/(1+.075)^15))/.075)) $ 88,271.20 5 8 9 A) Annual Calculation 10 Year Annual Payment 11 1 10000 12 2 10000 13 3 10000 14 4 10000 15 10000 16 6 10000 17 7 10000 18 8 10000 19 9 10000 20 10 10000 21 11 10000 22 12 10000 23 13 10000 24 14 10000 25 15 10000 [email protected]% Discounted Cash flow 0.930233 9302.33 0.865333 8653.33 0.804961 8049.61 0.748801 7488.01 0.696559 6965.59 0.647962 6479.62 0.602755 6027.55 0.560702 5607.02 0.521583 5215.83 0.485194 4851.94 0.451343 4513.43 0.419854 4198.54 0.390562 3905.62 0.363313 3633.13 0.337966 3379.66 $ 88,271.20 Sheets Sheet6 26 Sheet1 Sheet2 Sheet3 Sheet4 IIII Ready HE 90% U + SD wa 2:19 PM 7/7/2020 M

ABC Cla .00.0 Book1 - Microsoft Excel Home Insert Page Layout Formulas Data Review View Developer X ! % Cut Σ AutoSum και Calibri 16 Α Α΄ Wrap Text Accounting Fill Paste En Copy Format Painter B I U Merge & Center $ % +0.00 .00 0 Insert Delete Format Conditional Format Cell Formatting as Table Styles Styles 2 Clear Sort & Find & Filter - Select Editing Cells V - J K L M N 0 P Q 32 = Clipboard Font Alignment Number B39 for =10000*((1-(1/(1+0.075)^60))/0.075) A B С D E F G H 23 13 10000 0.390562 3905.62 24 14 10000 0.363313 3633.13 25 15 10000 0.337966 3379.66 26 $ 88,271.20 27 28 This shows that the Value will be same by both the formulaes. Now let's use the formuale for remaining part of the question 29 30 B) If payment occurred for 30 Years 31 10000((1-(1/(1+.075)^30)7.075)) 33 = $ 118,103.86 34 35 36 C) If payment occurred for 60 Years 37 38 = 10000/(1-(1/(1+.075-60))/.075)) 39 = $ 131,593.81 40 41 D) Forever (It means for Perpetuity) 42 43 = Annual Payment/ 44 = 10000/0.075 45 $ 133,333.33 46 47 Sheet1 Sheet2 Sheet3 Sheet4 Sheets Sheet6 IIII Ready 90% + D. wa 2:20 PM 7/7/2020 M

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