Build a Model Spreadsheet a. Find the FV of $1,000 invested to earn 10% after 5 years. Answer this question by using a math formula and also by using the Excel function wizard. Note: Use a mathematical formula to compute the value in cell E9 and then use the wizard to conpute the value in cell E10. It is generally easiest to fill in the wizard menus by clicking on one of the menu slots to activate the cursor in that slot and then clicking on the input cell where the item is given. Then, hit the tab key to move down to the next menu slot. Experiment by changing the input values to see how quickly the output values change. b. Now create a table that shows the FV at 0%,5%, and 20% for 0,1,2,3,4, and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results. Begin by typing in the row and column labels as shown below. We could fill in the table by inserting formulas in all the cells, but a better way is to use an Excel data table. Note that the Row Input Cell is D7 and the Column Input Cell is D8, and we set Cell B28 equal to Cell E9. Then,select (highlight) the To create the graph, first select the range C29:E34. Then click the chart wizard. Then follow the menu. It is easy to make a chart, but a lot of detailed steps are involved to format it so that it's "pretty." Pretty charts are generally not necessary to get the picture, though. Note that as the last item in the charfy menu you are asked if you want to put the chart on the worksheet or on a separate tab. This is a matter of taste. We put the chart right on the spreadsheet so we could see how changes in the data lead to changes in the graph. Note that the inputs to the data table, hence to the graph, are now in the row and column heads. Change the 20% in Cell E28 to 0.1 (or 10% ), then to 0.3, then to 0.5, etc., to see how the table and the chart change. c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. Again, work the problem with a formula and also by using the function wizard. \begin{tabular}{l|l|l|} \hline Inputs: & & \\ & FV= & 1000 \\ & i= & 10% \\ \hline & n= & 5 \\ \hline Formula: & PV=FV/(1+I)n= & \\ \hline Wizard (PV): & \\ \hline \end{tabular} Note: In the wizard's menu, use zero for PMTS because there are no periodic payments. Also, set the FV with a negative sign so that the PV will appear as a positive number. d. A security has a cost of $1,000 and will return $2,000 after 5 years. What rate of return does the security provide? Wizard (Rate): Note: Ilso worn for Pemt eince there are no nerindis navmente Note that the PV is oiven a Problem Sheet2 Sheet3 + Note: Use zero for Pmt since there are no periodic payments. Note that the PV is given a negative sign because it is an outflow (cost to buy the security). Also, note that you must scroll down the menu to complete the inputs. e. Suppose California's population is 30 million people, and its population is expected to grow by 2% f. Find the PV of an annuity that pays $1,000 at the end of each of the next 5 years if the interest rate is 15%. Then find the FV of that same annuity. \begin{tabular}{|r|} \hline 51,000 \\ \hline 5 \\ \hline 15% \end{tabular} 108 g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary annuity? 111 For the PV, each payment would be received one period sooner, hence would be discounted back one 112 less year. This would make the PV larger. We can find the PV of the annuity due by finding the PV of 113 an ordinary annuity and then multiplying it by (1+i). 117 Exactly the same adjustment is made to find the FV of the annuity due. \begin{tabular}{|l|l|l|l|} \hline 118 & & & \\ 119 & FV annuity due = & \\ 120 & & \\ 121 & & & \\ \hline 122 & h. What would the FV and the PV for problems a and c be if \end{tabular} 122 h. What would the FV and the PV for problems a and c be if the interest rate were 10% with 123 semiannual compounding rather than 10% with annual compounding? L. Find the PV and the FV of an Investment that makes the following end-of-year payments. The interest rate is 8%. To find the PV, use the NPV function: Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore, we must find this FV by some other method. Probably the easiest procedure is to simply compound each payment, then sum them, as is done below. Note that since the payments are received at the end of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0 years. Build a Model Spreadsheet a. Find the FV of $1,000 invested to earn 10% after 5 years. Answer this question by using a math formula and also by using the Excel function wizard. Note: Use a mathematical formula to compute the value in cell E9 and then use the wizard to conpute the value in cell E10. It is generally easiest to fill in the wizard menus by clicking on one of the menu slots to activate the cursor in that slot and then clicking on the input cell where the item is given. Then, hit the tab key to move down to the next menu slot. Experiment by changing the input values to see how quickly the output values change. b. Now create a table that shows the FV at 0%,5%, and 20% for 0,1,2,3,4, and 5 years. Then create a graph with years on the horizontal axis and FV on the vertical axis to display your results. Begin by typing in the row and column labels as shown below. We could fill in the table by inserting formulas in all the cells, but a better way is to use an Excel data table. Note that the Row Input Cell is D7 and the Column Input Cell is D8, and we set Cell B28 equal to Cell E9. Then,select (highlight) the To create the graph, first select the range C29:E34. Then click the chart wizard. Then follow the menu. It is easy to make a chart, but a lot of detailed steps are involved to format it so that it's "pretty." Pretty charts are generally not necessary to get the picture, though. Note that as the last item in the charfy menu you are asked if you want to put the chart on the worksheet or on a separate tab. This is a matter of taste. We put the chart right on the spreadsheet so we could see how changes in the data lead to changes in the graph. Note that the inputs to the data table, hence to the graph, are now in the row and column heads. Change the 20% in Cell E28 to 0.1 (or 10% ), then to 0.3, then to 0.5, etc., to see how the table and the chart change. c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. Again, work the problem with a formula and also by using the function wizard. \begin{tabular}{l|l|l|} \hline Inputs: & & \\ & FV= & 1000 \\ & i= & 10% \\ \hline & n= & 5 \\ \hline Formula: & PV=FV/(1+I)n= & \\ \hline Wizard (PV): & \\ \hline \end{tabular} Note: In the wizard's menu, use zero for PMTS because there are no periodic payments. Also, set the FV with a negative sign so that the PV will appear as a positive number. d. A security has a cost of $1,000 and will return $2,000 after 5 years. What rate of return does the security provide? Wizard (Rate): Note: Ilso worn for Pemt eince there are no nerindis navmente Note that the PV is oiven a Problem Sheet2 Sheet3 + Note: Use zero for Pmt since there are no periodic payments. Note that the PV is given a negative sign because it is an outflow (cost to buy the security). Also, note that you must scroll down the menu to complete the inputs. e. Suppose California's population is 30 million people, and its population is expected to grow by 2% f. Find the PV of an annuity that pays $1,000 at the end of each of the next 5 years if the interest rate is 15%. Then find the FV of that same annuity. \begin{tabular}{|r|} \hline 51,000 \\ \hline 5 \\ \hline 15% \end{tabular} 108 g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinary annuity? 111 For the PV, each payment would be received one period sooner, hence would be discounted back one 112 less year. This would make the PV larger. We can find the PV of the annuity due by finding the PV of 113 an ordinary annuity and then multiplying it by (1+i). 117 Exactly the same adjustment is made to find the FV of the annuity due. \begin{tabular}{|l|l|l|l|} \hline 118 & & & \\ 119 & FV annuity due = & \\ 120 & & \\ 121 & & & \\ \hline 122 & h. What would the FV and the PV for problems a and c be if \end{tabular} 122 h. What would the FV and the PV for problems a and c be if the interest rate were 10% with 123 semiannual compounding rather than 10% with annual compounding? L. Find the PV and the FV of an Investment that makes the following end-of-year payments. The interest rate is 8%. To find the PV, use the NPV function: Excel does not have a function for the sum of the future values for a set of uneven payments. Therefore, we must find this FV by some other method. Probably the easiest procedure is to simply compound each payment, then sum them, as is done below. Note that since the payments are received at the end of each year, the first payment is compounded for 2 years, the second for 1 year, and the third for 0 years