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Finance Homework
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Ch 02 P 26 Build a Model Chapter 2. Ch 02 P 26 Build a Model a. Find the FV of $1,000 invested to earn 10% after 5 years. Answer this q math formula and also by using the Excel function wizard. Inputs: PV = 1000 i = 10% n = 5 Formula: FV = PV(1+I)^n = $ 1,610.51 Wizard (FV): $6,105.10 Note: When you use the wizard and fill in the menu items, the result is the formula line if you put the pointer on cell E12. Put the pointer on E12 and wizard (fx) to see the completed menu. Finally, it is generally easiest to f clicking on one of the menu slots to activate the cursor in that slot and the where the item is given. Then, hit the tab key to move down to the next menu Experiment by changing the input values to see how quickly the output values b. Now create a table that shows the FV at 0%, 5%, and 20% for 0, 1, 2, 3, create a graph with years on the horizontal axis and FV on the vertical Begin by typing in the row and column labels as shown below. We could fill in formulas in all the cells, but a better way is to use an Excel data table as used the data table procedure. Note that the Row Input Cell is D9 and the Co and we set Cell B32 equal to Cell E11. Then, we selected (highlighted) the r Data, Table, and filled in the menu items to complete the table. Years (D10): Interest Rate (D9) $ 1,610.51 0% 5% 60% 0 $1,000.00 $1,000.00 $1,000.00 1 $1,000.00 $1,050.00 $1,600.00 2 $1,000.00 $1,102.50 $2,560.00 3 $1,000.00 $1,157.63 $4,096.00 4 $1,000.00 $1,215.51 $6,553.60 5 $1,000.00 $1,276.28 $10,485.76 To create the graph, first select the range C33:E38. Then click the chart wi It is easy to make a chart, but a lot of detailed steps are involved to forma charts are generally not necessary to get the picture, though. Note that as t menu you are asked if you want to put the chart on the worksheet or on a sepa of taste. We put the chart right on the spreadsheet so we could see how chan changes in the graph. Note that the inputs to the data table, hence to the graph, are now in the ro Change the 10% in Cell E32 to .2 (or 20%), then to .3, then to .5, etc., to s changes. $10,000.00 $12,000.00
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Assignments for Advanced Corporate Finance
Transcript of Finance Homework
Time Value of Money, Build a Model
ProblemCh 02 P 26 Build a Model4/6/03Chapter 2. Ch 02 P 26 Build a Modela. Find the FV of $1,000 invested to earn 10% after 5 years. Answer this question by using amath formula and also by using the Excel function wizard.Inputs:PV =1000i =10%n =5Formula:FV = PV(1+I)^n =$1,610.51Wizard (FV):$6,105.10Note: When you use the wizard and fill in the menu items, the result is the formula you see on theformula line if you put the pointer on cell E12. Put the pointer on E12 and then click the functionwizard (fx) to see the completed menu. Finally, it is generally easiest to fill in the wizard menus byclicking on one of the menu slots to activate the cursor in that slot and then clicking on the input cellwhere 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. Thencreate 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 insertingformulas in all the cells, but a better way is to use an Excel data table as described in 07model. Weused the data table procedure. Note that the Row Input Cell is D9 and the Column Input Cell is D10,and we set Cell B32 equal to Cell E11. Then, we selected (highlighted) the range B32:E38, then clickedData, Table, and filled in the menu items to complete the table.Years (D10):Interest Rate (D9)$1,610.510%5%60%0$1,000.00$1,000.00$1,000.001$1,000.00$1,050.00$1,600.002$1,000.00$1,102.50$2,560.003$1,000.00$1,157.63$4,096.004$1,000.00$1,215.51$6,553.605$1,000.00$1,276.28$10,485.76To create the graph, first select the range C33:E38. 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." Prettycharts are generally not necessary to get the picture, though. Note that as the last item in the chartmenu you are asked if you want to put the chart on the worksheet or on a separate tab. This is a matterof taste. We put the chart right on the spreadsheet so we could see how changes in the data lead tochanges 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 10% in Cell E32 to .2 (or 20%), then to .3, then to .5, etc., to see how the table and the chartchanges.c. Find the PV of $1,000 due in 5 years if the discount rate is 10%. Again, work the problem witha formula and also by using the function wizard.Inputs:FV =1000i =10%n =5Formula:FV = FV/(1+I)^n =$620.92Wizard (PV):$620.92Note: 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 thesecurity provide?Inputs:PV =-1000FV =2000i =?n =5Wizard (Rate):14.87%Note: Use zero for Pmt since there are no periodic payments. Note that the PV is given anegative sign because it is an outflow (cost to buy the security). Also, note that you mustscroll down the menu to complete the inputs.e. Suppose Californias population is 30 million people, and its population is expected to grow by 2%per year. How long would it take for the population to double?Inputs:PV =-30FV =60i = growth rate2%n =?Wizard (NPER):= Years to double.f. Find the PV of an annuity that pays $1,000 at the end of each of the next 5 years if the interest rateis 15%. Then find the FV of that same annuity.Inputs:Pmt$1,000n5i15%PV: Use function wizard (PV)PV =-$3,352.16FV: Use function wizard (FV)FV =-$6,742.38g. How would the PV and FV of the annuity change if it were an annuity due rather than an ordinaryannuity?For the PV, each payment would be received one period sooner, hence would be discounted back oneless year. This would make the PV larger. We can find the PV of the annuity due by finding the PV ofan ordinary annuity and then multiplying it by (1 + i).PV annuity due =-$3,352.16x115%=-$3,854.98Exactly the same adjustment is made to find the FV of the annuity due.FV annuity due =-$6,742.38x115%=-$7,753.74h. What would the FV and the PV for problems a and c be if the interest rate were 10% withsemiannual compounding rather than 10% with annual compounding?Part a. FV with semiannual compounding:Orig. Inputs:New Inputs:Inputs:PV =10001000i =10%5%n =510Formula:FV = PV(1+I)^n =$1,610.51$1,628.89Wizard (FV):$1,610.51$1,628.89Part c. PV with semiannual compounding:Orig. Inputs:New Inputs:Inputs:FV =10001000i =10%5%n =510Formula:FV = FV/(1+I)^n =$620.92$613.91Wizard (PV):$620.92$613.91i. Find the PV and the FV of an investment that makes the following end-of-year payments. Theinterest rate is 8%.YearPayment110022003400Rate =8%To find the PV, use the NPV function:PV =$581.59Excel 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 simplycompound each payment, then sum them, as is done below. Note that since the payments are receivedat the end of each year, the first payment is compounded for 2 years, the second for 1 year, and thethird for 0 years.YearPaymentx(1 + I )^(n-t)=FV11001.17116.6422001.08216.0034001.00400.00Sum =$732.64An alternative procedure for finding the FV would be to find the PV of the series using the NPVfunction, then compound that amount, as is done below:PV =$581.59FV of PV =$732.64j. Suppose you bought a house and took out a mortgage for $50,000. The interest rate is 8%, andyou must amortize the loan over 10 years with equal end-of-year payments. Set up an amortizationschedule that shows the annual payments and the amount of each payment that goes to pay off theprincipal and the amount that constitutes interest expense to the borrower and interest income tothe lender.Original amount of mortgage:50000Term of mortgage:10Interest rate:0.08Annual payment (use PMT function):-$7,451.47YearBeg. Amt.PmtInterestPrincipalEnd. Bal.150000$7,451.47$4,000.00$3,451.47$46,548.532$46,548.53$7,451.47$3,723.88$3,727.59$42,820.933$42,820.93$7,451.47$3,425.67$4,025.80$38,795.134$38,795.13$7,451.47$3,103.61$4,347.86$34,447.275$34,447.27$7,451.47$2,755.78$4,695.69$29,751.586$29,751.58$7,451.47$2,380.13$5,071.35$24,680.237$24,680.23$7,451.47$1,974.42$5,477.06$19,203.178$19,203.17$7,451.47$1,536.25$5,915.22$13,287.959$13,287.95$7,451.47$1,063.04$6,388.44$6,899.5110$6,899.51$7,451.47$551.96$6,899.51$0.00Extensions:i. Create a graph that shows how the payments are divided between interest andprincipal repayment over time.Go back to cells D184 and D185, and change the interest rate and the term to maturity tosee how the payments would change.ii. Suppose the loan called for 10 years of monthly payments, with the same originalamount and the same nominal interest rate. What would the amortization schedule shownow?Now we would have a 12*10 = 120 payment loan at a monthly rate of .08/12 = 0.666667%.The monthly payment would be:($606.64)MonthBeg. Amt.PmtInterestPrincipalEnd. Bal.1$50,000.00$606.64$333.33$273.30$49,726.702$49,726.70$606.64$331.51$275.13$49,451.573$49,451.57$606.64$329.68$276.96$49,174.614$49,174.61$606.64$327.83$278.81$48,895.805$48,895.80$606.64$325.97$280.67$48,615.136$48,615.13$606.64$324.10$282.54$48,332.607$48,332.60$606.64$322.22$284.42$48,048.188$48,048.18$606.64$320.32$286.32$47,761.869$47,761.86$606.64$318.41$288.23$47,473.6310$47,473.63$606.64$316.49$290.15$47,183.4911$47,183.49$606.64$314.56$292.08$46,891.4112$46,891.41$606.64$312.61$294.03$46,597.3813$46,597.38$606.64$310.65$295.99$46,301.3914$46,301.39$606.64$308.68$297.96$46,003.4315$46,003.43$606.64$306.69$299.95$45,703.4816$45,703.48$606.64$304.69$301.95$45,401.5317$45,401.53$606.64$302.68$303.96$45,097.5718$45,097.57$606.64$300.65$305.99$44,791.5819$44,791.58$606.64$298.61$308.03$44,483.5520$44,483.55$606.64$296.56$310.08$44,173.4721$44,173.47$606.64$294.49$312.15$43,861.3222$43,861.32$606.64$292.41$314.23$43,547.1023$43,547.10$606.64$290.31$316.32$43,230.7724$43,230.77$606.64$288.21$318.43$42,912.3425$42,912.34$606.64$286.08$320.56$42,591.7826$42,591.78$606.64$283.95$322.69$42,269.0927$42,269.09$606.64$281.79$324.84$41,944.2528$41,944.25$606.64$279.63$327.01$41,617.2429$41,617.24$606.64$277.45$329.19$41,288.0530$41,288.05$606.64$275.25$331.38$40,956.6631$40,956.66$606.64$273.04$333.59$40,623.0732$40,623.07$606.64$270.82$335.82$40,287.2533$40,287.25$606.64$268.58$338.06$39,949.2034$39,949.20$606.64$266.33$340.31$39,608.8935$39,608.89$606.64$264.06$342.58$39,266.3136$39,266.31$606.64$261.78$344.86$38,921.4437$38,921.44$606.64$259.48$347.16$38,574.2838$38,574.28$606.64$257.16$349.48$38,224.8139$38,224.81$606.64$254.83$351.81$37,873.0040$37,873.00$606.64$252.49$354.15$37,518.8541$37,518.85$606.64$250.13$356.51$37,162.3442$37,162.34$606.64$247.75$358.89$36,803.4543$36,803.45$606.64$245.36$361.28$36,442.1744$36,442.17$606.64$242.95$363.69$36,078.4845$36,078.48$606.64$240.52$366.11$35,712.3646$35,712.36$606.64$238.08$368.56$35,343.8147$35,343.81$606.64$235.63$371.01$34,972.7948$34,972.79$606.64$233.15$373.49$34,599.3149$34,599.31$606.64$230.66$375.98$34,223.3350$34,223.33$606.64$228.16$378.48$33,844.8551$33,844.85$606.64$225.63$381.01$33,463.8452$33,463.84$606.64$223.09$383.55$33,080.3053$33,080.30$606.64$220.54$386.10$32,694.1954$32,694.19$606.64$217.96$388.68$32,305.5255$32,305.52$606.64$215.37$391.27$31,914.2556$31,914.25$606.64$212.76$393.88$31,520.3757$31,520.37$606.64$210.14$396.50$31,123.8758$31,123.87$606.64$207.49$399.15$30,724.7359$30,724.73$606.64$204.83$401.81$30,322.9260$30,322.92$606.64$202.15$404.49$29,918.4361$29,918.43$606.64$199.46$407.18$29,511.2562$29,511.25$606.64$196.74$409.90$29,101.3663$29,101.36$606.64$194.01$412.63$28,688.7364$28,688.73$606.64$191.26$415.38$28,273.3565$28,273.35$606.64$188.49$418.15$27,855.2066$27,855.20$606.64$185.70$420.94$27,434.2667$27,434.26$606.64$182.90$423.74$27,010.5268$27,010.52$606.64$180.07$426.57$26,583.9569$26,583.95$606.64$177.23$429.41$26,154.5470$26,154.54$606.64$174.36$432.27$25,722.2771$25,722.27$606.64$171.48$435.16$25,287.1172$25,287.11$606.64$168.58$438.06$24,849.0573$24,849.05$606.64$165.66$440.98$24,408.0774$24,408.07$606.64$162.72$443.92$23,964.1675$23,964.16$606.64$159.76$446.88$23,517.2876$23,517.28$606.64$156.78$449.86$23,067.4277$23,067.42$606.64$153.78$452.86$22,614.5778$22,614.57$606.64$150.76$455.87$22,158.6979$22,158.69$606.64$147.72$458.91$21,699.7880$21,699.78$606.64$144.67$461.97$21,237.8181$21,237.81$606.64$141.59$465.05$20,772.7682$20,772.76$606.64$138.49$468.15$20,304.6083$20,304.60$606.64$135.36$471.27$19,833.3384$19,833.33$606.64$132.22$474.42$19,358.9185$19,358.91$606.64$129.06$477.58$18,881.3386$18,881.33$606.64$125.88$480.76$18,400.5787$18,400.57$606.64$122.67$483.97$17,916.6088$17,916.60$606.64$119.44$487.19$17,429.4189$17,429.41$606.64$116.20$490.44$16,938.9790$16,938.97$606.64$112.93$493.71$16,445.2691$16,445.26$606.64$109.64$497.00$15,948.2592$15,948.25$606.64$106.32$500.32$15,447.9493$15,447.94$606.64$102.99$503.65$14,944.2994$14,944.29$606.64$99.63$507.01$14,437.2895$14,437.28$606.64$96.25$510.39$13,926.8996$13,926.89$606.64$92.85$513.79$13,413.1097$13,413.10$606.64$89.42$517.22$12,895.8898$12,895.88$606.64$85.97$520.67$12,375.2199$12,375.21$606.64$82.50$524.14$11,851.08100$11,851.08$606.64$79.01$527.63$11,323.45101$11,323.45$606.64$75.49$531.15$10,792.30102$10,792.30$606.64$71.95$534.69$10,257.61103$10,257.61$606.64$68.38$538.25$9,719.35104$9,719.35$606.64$64.80$541.84$9,177.51105$9,177.51$606.64$61.18$545.45$8,632.06106$8,632.06$606.64$57.55$549.09$8,082.97107$8,082.97$606.64$53.89$552.75$7,530.21108$7,530.21$606.64$50.20$556.44$6,973.78109$6,973.78$606.64$46.49$560.15$6,413.63110$6,413.63$606.64$42.76$563.88$5,849.75111$5,849.75$606.64$39.00$567.64$5,282.11112$5,282.11$606.64$35.21$571.42$4,710.69113$4,710.69$606.64$31.40$575.23$4,135.45114$4,135.45$606.64$27.57$579.07$3,556.39115$3,556.39$606.64$23.71$582.93$2,973.46116$2,973.46$606.64$19.82$586.81$2,386.64117$2,386.64$606.64$15.91$590.73$1,795.92118$1,795.92$606.64$11.97$594.67$1,201.25119$1,201.25$606.64$8.01$598.63$602.62120$602.62$606.64$4.02$602.62$0.00
Problem
0%5%60%
Sheet2
InterestPrincipal
Sheet3
