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{"name": "MATH1510 Financial Mathematics 1 Practical 3", "extensions": [], "custom_part_types": [], "resources": [["question-resources/NPV_Graph.crtx", "/srv/numbas/media/question-resources/NPV_Graph.crtx"], ["question-resources/NPV_Graph.png", "/srv/numbas/media/question-resources/NPV_Graph.png"], ["question-resources/NPV_Graph_Qqcucrw.png", "/srv/numbas/media/question-resources/NPV_Graph_Qqcucrw.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"": {"definition": "", "type": "number", "parameters": [], "language": "jme"}}, "ungrouped_variables": ["c0", "c1", "c2", "roundc2", "irra", "investa", "roundinvesta", "cash1", "cash2", "irrd", "cf1", "cf2", "roundcf2", "irrb", "investb", "roundinvestb", "cflow1", "roundcflow1", "cflow2", "roundcflow2", "irrc1", "irrc2", "investc1", "investc2", "roundinvestc1", "roundinvestc2", "int1", "int2", "int3", "int4", "int5", "qa", "npva", "irr"], "name": "MATH1510 Financial Mathematics 1 Practical 3", "tags": [], "advice": "<p style=\"padding-left: 30px;\">1. In order to obtain the net present value of any investment, you must discount each cash flow back to time $t=0$ (see&nbsp;<a href=\"/numbas-previews/question-8456-net-present-value/index.html\">Numbas- Net Present Value</a>) with respect to the interest rate. After discounting each cash flow to time 0, add them up to get the sum of the net present values of each investment.</p>\n<p>In the above question, the interest rates are: {int1*100}%, {int2*100}%, {int3*100}%, {int4*100}% and {int5*100}%.</p>\n<p style=\"padding-left: 30px;\">2. The internal rate of return is the interest rate at which the net present value is equal to 0 (i.e. $NPV(i)=0$) It is possible to have a negative IRR, zero IRR or more than one IRR. In order to have a unique solution to $NPV(i)=0$, there must only be one sign change in the cash flows of the investement. If there is more than one change in sign, it may mean that there is more than one solution. If the sum of the cash flows is equal to zero, then the IRR=0%.</p>\n<p>In the above question, investment a) and b) only have one sign change meaning that these two investments have one IRR. Investment c) has two sign changes indicating two IRR's. The sum of the cash flows of investment d) is equal to zero, so the IRR is 0%.</p>\n<p style=\"padding-left: 30px;\">3. In Excel, using the IRR function returns the IRR of the investment. If there is more than one IRR, using this function in Excel will return the rate that is closest to the guess. For this reason, &nbsp;Excel does not provide the full answer (both rates) for investment c).</p>", "rulesets": {}, "parts": [{"prompt": "<p><span>What is the sum of the NPV's (to two decimal places) of each&nbsp;investment when the interest rates are: {int1*100}%, {int2*100}%, {int3*100}%, {int4*100}% and {int5*100}%?</span></p>\n<p><span></span>Investment a: [[0]]</p>\n<p><span>Investment b: [[1]]</span></p>\n<p><span>Investment c: [[2]]</span></p>\n<p><span>Investment d: [[3]]</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[0][3]", "minValue": "qa[0][3]", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[1][3]", "minValue": "qa[1][3]", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[2][3]", "minValue": "qa[2][3]", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[3][3]", "minValue": "qa[3][3]", "variableReplacementStrategy": "originalfirst", "strictPrecision": true, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "5", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Using the graphs and/or computed values, which project should have more than one internal rate of return?</p>", "matrix": ["qa[0][6]", "qa[1][6]", "qa[2][6]", "qa[3][6]"], "shuffleChoices": false, "marks": 0, "variableReplacements": [], "choices": ["<p>Investment a</p>", "<p>Investment b</p>", "<p>Investment c</p>", "<p>Investment d</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": "1", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p><span>Compute all the IRR (%) of each investment to the nearest 1%, using the Excel function <strong>=IRR</strong>.</span></p>\n<p><span>Investment a: [[0]] </span></p>\n<p><span>Investment b: [[1]]</span></p>\n<p><span>Investment c: [[2]]&nbsp;</span></p>\n<p><span>Investment d:&nbsp;[[3]]&nbsp;</span></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[0][4]", "minValue": "qa[0][4]", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[1][4]", "minValue": "qa[1][4]", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "1", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[2][4]", "minValue": "qa[2][4]", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "qa[3][4]", "minValue": "qa[3][4]", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": "50", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}, {"prompt": "<p>Based on your answer in c), for which project&nbsp;did the<strong> =IRR</strong> function not provide the full answer?</p>", "matrix": ["qa[0][6]", "qa[1][6]", "qa[2][6]", "qa[3][6]"], "shuffleChoices": false, "marks": 0, "variableReplacements": [], "choices": ["<p>Investment a</p>", "<p>Investment b</p>", "<p>Investment c</p>", "<p>Investment d</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": "1", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "<p>Consider four investments generating the following cashflows against the interest rate:</p>\n<p style=\"padding-left: 30px;\">a) <strong>{qa[0][0]}</strong> at $t=0$, <strong>{qa[0][1]}</strong> at $t=1$, <strong>{qa[0][2]}</strong> at $t=2$</p>\n<p style=\"padding-left: 30px;\">b) <strong>{qa[1][0]}</strong> at $t=0$, <strong>{qa[1][1]}</strong> at $t=1$, <strong>{qa[1][2]}</strong> at $t=2$</p>\n<p style=\"padding-left: 30px;\">c) <strong>{qa[2][0]}</strong> at $t=0$, <strong>{qa[2][1]}</strong> at $t=1$, <strong>{qa[2][2]}</strong> at $t=2$</p>\n<p style=\"padding-left: 30px;\">d) <strong>{qa[3][0]}</strong> at $t=0$,<strong> {qa[3][1]}</strong> at $t=1$, <strong>{qa[3][2]}</strong> at $t=2$</p>\n<p>Create an Excel spreadsheet to compute the NPV of the above&nbsp;cash flows for the interest rate for values 0, 5%, 10%, 15%, . . . ,&nbsp;200%. Use these values to construct a plot similar to the one below:</p>\n<p><img src=\"/question/8585/practical-3-q1-2-3/resources/question-resources/NPV_Graph_Qqcucrw.png\" style=\"display: block; margin-left: auto; margin-right: auto;\"/></p>\n<p></p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"roundcflow2": {"definition": "precround(cflow2,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundcflow2", "description": ""}, "roundcflow1": {"definition": "precround(cflow1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundcflow1", "description": ""}, "investc2": {"definition": "(((-{roundcflow1}-(({roundcflow1}^2)-(4*{c0}*{roundcflow2}))^(0.5))/(2*{c0}))-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "investc2", "description": ""}, "c0": {"definition": "random(-8..-6#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c0", "description": ""}, "irr": {"definition": "[\n  [roundinvesta, roundinvesta],\n  [roundinvestb, roundinvestb],\n  [roundinvestc1, roundinvestc2],\n  [irrd, irrd]\n]", "templateType": "anything", "group": "Ungrouped variables", "name": "irr", "description": ""}, "cflow2": {"definition": "((-{c0}*(1+{irrc1})^2)-({cflow1}*(1+{irrc1})))", "templateType": "anything", "group": "Ungrouped variables", "name": "cflow2", "description": ""}, "cflow1": {"definition": "((-{c0}*(1+{irrc2})^2)-(-{c0}*(1+{irrc1})^2))/({irrc2}-{irrc1})", "templateType": "anything", "group": "Ungrouped variables", "name": "cflow1", "description": ""}, "irrb": {"definition": "random(-0.21..-0.1#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "irrb", "description": ""}, "irra": {"definition": "random(0.05..0.5#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "irra", "description": ""}, "irrc1": {"definition": "random(0.2..0.25#0.01)", "templateType": "randrange", "group": "Ungrouped variables", "name": "irrc1", "description": ""}, "irrc2": {"definition": "random(0.6..0.66#0.01)", "templateType": "randrange", "group": "Ungrouped variables", "name": "irrc2", "description": ""}, "cash2": {"definition": "-({c0}+{cash1})", "templateType": "anything", "group": "Ungrouped variables", "name": "cash2", "description": ""}, "cash1": {"definition": "random(1..5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "cash1", "description": ""}, "int5": {"definition": "random(1.6..2#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int5", "description": ""}, "int4": {"definition": "random(1.2..1.59#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int4", "description": ""}, "int1": {"definition": "random(0..0.39#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int1", "description": ""}, "int3": {"definition": "random(0.8..1.19#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int3", "description": ""}, "int2": {"definition": "random(0.4..0.79#0.05)", "templateType": "randrange", "group": "Ungrouped variables", "name": "int2", "description": ""}, "c2": {"definition": "((-{c0}*(1+{irra})^2)-({c1}*(1+{irra})))\n", "templateType": "anything", "group": "Ungrouped variables", "name": "c2", "description": ""}, "c1": {"definition": "random(1..5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c1", "description": ""}, "irrd": {"definition": "0", "templateType": "number", "group": "Ungrouped variables", "name": "irrd", "description": ""}, "cf2": {"definition": "((-{c0}*(1+{irrb})^2)-({cf1}*(1+{irrb})))\n\n", "templateType": "anything", "group": "Ungrouped variables", "name": "cf2", "description": ""}, "roundinvestc2": {"definition": "precround(investc2,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundinvestc2", "description": ""}, "roundinvestc1": {"definition": "precround(investc1,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundinvestc1", "description": ""}, "cf1": {"definition": "random(1..5#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "cf1", "description": ""}, "investb": {"definition": "(((-{cf1}-(({cf1}^2)-(4*{c0}*{roundcf2}))^(0.5))/(2*{c0}))-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "investb", "description": ""}, "investa": {"definition": "(((-{c1}-((({c1}^2)-(4*{c0}*{roundc2}))^(0.5)))/(2*{c0}))-1)*100\n ", "templateType": "anything", "group": "Ungrouped variables", "name": "investa", "description": ""}, "npva": {"definition": "[\n  (5*c0+(c1/(1+int1))+(roundc2*((1+int1)^(-2)))+(c1/(1+int2))+(roundc2*((1+int2)^(-2)))+(c1/(1+int3))+(roundc2*((1+int3)^(-2)))+(c1/(1+int4))+(roundc2*((1+int4)^(-2)))+(c1/(1+int5))+(roundc2*((1+int5)^(-2)))),\n  (5*c0+(cf1/(1+int1))+(roundcf2*((1+int1)^(-2)))+(cf1/(1+int2))+(roundcf2*((1+int2)^(-2)))+(cf1/(1+int3))+(roundcf2*((1+int3)^(-2)))+(cf1/(1+int4))+(roundcf2*((1+int4)^(-2)))+(cf1/(1+int5))+(roundcf2*((1+int5)^(-2)))),\n  (5*c0+(roundcflow1/(1+int1))+(roundcflow2*((1+int1)^(-2)))+(roundcflow1/(1+int2))+(roundcflow2*((1+int2)^(-2)))+(roundcflow1/(1+int3))+(roundcflow2*((1+int3)^(-2)))+(roundcflow1/(1+int4))+(roundcflow2*((1+int4)^(-2)))+(roundcflow1/(1+int5))+(roundcflow2*((1+int5)^(-2)))),\n  (5*c0+(cash1/(1+int1))+(cash2*((1+int1)^(-2)))+(cash1/(1+int2))+(cash2*((1+int2)^(-2)))+(cash1/(1+int3))+(cash2*((1+int3)^(-2)))+(cash1/(1+int4))+(cash2*((1+int4)^(-2)))+(cash1/(1+int5))+(cash2*((1+int5)^(-2))))\n]", "templateType": "anything", "group": "Ungrouped variables", "name": "npva", "description": ""}, "roundcf2": {"definition": "precround(cf2,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundcf2", "description": ""}, "qa": {"definition": "shuffle([\n  [c0, c1, roundc2, npva[0], irr[0][0],irr[0][1], 0],\n  [c0, cf1, roundcf2, npva[1], irr[1][0], irr[1][1], 0],\n  [c0, roundcflow1, roundcflow2, npva[2], irr[2][0], irr[2][1], 2],\n  [c0, cash1, cash2, npva[3], irr[3][0], irr[3][1], 0]\n])", "templateType": "anything", "group": "Ungrouped variables", "name": "qa", "description": ""}, "investc1": {"definition": "(((-{roundcflow1}+(({roundcflow1}^2)-(4*{c0}*{roundcflow2}))^(0.5))/(2*{c0}))-1)*100", "templateType": "anything", "group": "Ungrouped variables", "name": "investc1", "description": ""}, "roundinvesta": {"definition": "precround(investa,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundinvesta", "description": ""}, "roundc2": {"definition": "precround(c2,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundc2", "description": ""}, "roundinvestb": {"definition": "precround(investb,0)", "templateType": "anything", "group": "Ungrouped variables", "name": "roundinvestb", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}]}], "contributors": [{"name": "James Fung", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/699/"}]}