// Numbas version: exam_results_page_options
{"name": "NPV test", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"test": {"templateType": "anything", "definition": "map([cashflows[x][0],separateThousands(cashflows[x][1],\",\")],x,0..holding_time)", "description": "", "group": "Ungrouped variables", "name": "test"}, "summation_str": {"templateType": "anything", "definition": "latex(join(map(dpformat(Cashflow_X_PV[x],0,\"en\"),x,0..holding_time),\" + \")+\" = \"+dpformat(sum(cashflow_X_PV),2,'en'))", "description": "", "group": "Ungrouped variables", "name": "summation_str"}, "cashflows_table_PV_CPV": {"templateType": "anything", "definition": "table(map([cashflows[x][0],dpformat(cashflows[x][1],0,\"en\"),'$'+latex('\\\\frac{ 1 }{ {(1 +' + sigformat(req_return_rate,2,\"en\")  +')}\\^{'+x+'}}')+'$',precround(PV_facts[x],3),dpformat(Cashflow_X_PV[x],0,\"en\")],x,0..holding_time),[\"Year\",\"Projected Cashflow in \u00a3\",\"PV Calculation\",\"PV Factor\",\"Cashflow * PV factor\"])", "description": "", "group": "Ungrouped variables", "name": "cashflows_table_PV_CPV"}, "req_return_rate": {"templateType": "anything", "definition": "random(0.04..0.1#0.005)", "description": "", "group": "Ungrouped variables", "name": "req_return_rate"}, "answer": {"templateType": "anything", "definition": "sum(map(cashflows[x][1]/((1+req_return_rate)^cashflows[x][0]),x,0..holding_time))", "description": "<p>Main formula code</p>", "group": "Ungrouped variables", "name": "answer"}, "cashflows_table_PV_f": {"templateType": "anything", "definition": "table(map([cashflows[x][0],dpformat(cashflows[x][1],0,\"en\"),'$'+latex('\\\\frac{ 1 }{ {(1 +' + sigformat(req_return_rate,2,\"en\")  +')}\\^{'+x+'}}')+'$',precround(PV_facts[x],3)],x,0..holding_time),[\"Year\",\"Projected Cashflow in \u00a3\",\"PV Calculation\",\"PV Factor\"])", "description": "<p>cashflow_table with present value factors and calculations in latex</p>", "group": "Ungrouped variables", "name": "cashflows_table_PV_f"}, "cashflows_table": {"templateType": "anything", "definition": "table(map([cashflows[x][0],dpformat(cashflows[x][1],0,\"en\")],x,0..holding_time),[\"Year\",\"Projected Cashflow in \u00a3\"])", "description": "", "group": "Ungrouped variables", "name": "cashflows_table"}, "req_return_rate_perc": {"templateType": "anything", "definition": "100*req_return_rate", "description": "", "group": "Ungrouped variables", "name": "req_return_rate_perc"}, "Cashflow_X_PV": {"templateType": "anything", "definition": "map(PV_facts[x]*cashflows[x][1],x,0..holding_time)", "description": "", "group": "Ungrouped variables", "name": "Cashflow_X_PV"}, "holding_time": {"templateType": "anything", "definition": "random(3..5#1)", "description": "<p>Holding time for asset in years</p>", "group": "Ungrouped variables", "name": "holding_time"}, "asset_price": {"templateType": "anything", "definition": "random(1000000..30000000#1000000)", "description": "", "group": "Ungrouped variables", "name": "asset_price"}, "cashflows": {"templateType": "anything", "definition": "let(cflows,[[0,-1*asset_price]]+zip(list(1..holding_time#1), repeat(siground(asset_price*random((req_return_rate * (1-r_cashflow_const))..(req_return_rate * (1+r_cashflow_const))#0.01),2),holding_time)), cflows[0..holding_time]+[[cflows[holding_time][0],cflows[holding_time][1]+asset_price]])", "description": "", "group": "Ungrouped variables", "name": "cashflows"}, "r_cashflow_const": {"templateType": "anything", "definition": "random(0.1..0.3#0.01)", "description": "<p>Determines how variable the randomly generated <g class=\"gr_ gr_41 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling\" id=\"41\" data-gr-id=\"41\">cashflows</g> are.</p>", "group": "Ungrouped variables", "name": "r_cashflow_const"}, "PV_facts": {"templateType": "anything", "definition": "map(1/((1+req_return_rate)^x),x,0..holding_time)", "description": "", "group": "Ungrouped variables", "name": "PV_facts"}}, "statement": "<p>Calculate the NPV (net present value) for the following property asset to <strong>3 significant figures</strong>:</p>", "parts": [{"notationStyles": ["plain", "en", "si-en"], "minValue": "answer", "strictPrecision": true, "type": "numberentry", "precisionPartialCredit": "50", "correctAnswerFraction": false, "prompt": "<p><strong>Asset price:</strong> &pound;{formatnumber(asset_price,\"en\")}</p>\n<p><strong>Required Rate of Return:</strong> {req_return_rate*100}%</p>\n<p><strong>Holding time:</strong> {holding_time} years</p>\n<p></p>\n<div width=\"300px;\" float=\"left\">\n<p style=\"text-align: left;\">{cashflows_table}</p>\n</div>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "showCorrectAnswer": true, "precisionType": "sigfig", "precisionMessage": "You have not given your answer to the correct precision.", "mustBeReducedPC": 0, "maxValue": "answer", "precision": "3", "mustBeReduced": false, "correctAnswerStyle": "plain", "marks": 1, "showPrecisionHint": true, "allowFractions": false}], "metadata": {"licence": "All rights reserved", "description": "<p>Calculate the net present value for the following property assets:</p>"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "tags": [], "extensions": [], "functions": {}, "preamble": {"css": "table {\n  border: 1px solid black;\n\n}\ntr:hover {background-color: rgb(218, 232, 241)}\ntd {border-left: 1px solid black;}\nth{border: 1px solid black;}", "js": ""}, "variable_groups": [], "advice": "<p>The complete formula for calculating NPV is:</p>\n<p>\\[\\textrm{Net Present Value} =&nbsp;\\sum _{ n=0 }^{ N }{ \\frac {{C}_{n}}{{(1+r)}^{n}} } \\]</p>\n<p>Where $C_n$ is the cashflow for the current year, $r$ is the required rate of return in decimal form, $n$ is the current year and $N$ is the number of years the asset is to be held for.</p>\n<p></p>\n<p><strong>Let's break it down...</strong></p>\n<p>Convert the required rate of return to a decimal:</p>\n<p>\\[\\textrm{Required Return Rate} = \\frac{\\var{req_return_rate_perc}\\%}{100\\%}\\]</p>\n<p>\\[=\\var{req_return_rate}\\]</p>\n<p></p>\n<p>Then, calculate&nbsp;the present value factor for each year:</p>\n<p><em>At the start of the first year, the asset is bought so the <g class=\"gr_ gr_18 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling\" id=\"18\" data-gr-id=\"18\">cashflow</g> is minus the asset price. In the last year, the asset is sold, resulting in a large increase in <g class=\"gr_ gr_19 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling\" id=\"19\" data-gr-id=\"19\">cashflow</g>.</em></p>\n<p>\\[{\\textrm{PV factor} = \\frac { 1 }{ { (1+r) }^{ n } }&nbsp;}\\]</p>\n<p></p>\n<p>{cashflows_table_PV_f}</p>\n<p></p>\n<p>Next, we must multiply the cashflow for each year by the corresponding PV factor:</p>\n<p></p>\n<p>\\[\\textrm{Cashflow} \\cdot \\textrm{PV Factor} ={C}_{n} \\cdot \\frac{1}{{(1+r)}^{n}}\\]</p>\n<p></p>\n<p>{cashflows_table_PV_CPV}</p>\n<p></p>\n<p>Finally, to finish using the formula, we need to add up all of the $(\\textrm{Cashflow} \\cdot \\textrm{PV Factor})$ values to get the net present value (NPV):</p>\n<p></p>\n<p>\\[\\textrm{Net Present Value} =&nbsp;\\sum _{ n=0 }^{ N }{ {(\\textrm{Cashflow} \\cdot \\textrm{PV Factor})}_{n} } \\]</p>\n<p></p>\n<p>\\[\\var{summation_str}\\]</p>\n<p></p>\n<p>Which is &pound;{sigformat(sum(Cashflow_X_PV),3,\"en\")} to 3 significant figures.&nbsp;</p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>\n<p></p>", "rulesets": {"": []}, "name": "NPV test", "ungrouped_variables": ["asset_price", "req_return_rate", "holding_time", "cashflows", "r_cashflow_const", "answer", "cashflows_table", "test", "cashflows_table_PV_f", "PV_facts", "req_return_rate_perc", "cashflows_table_PV_CPV", "summation_str", "Cashflow_X_PV"], "type": "question", "contributors": [{"name": "Rory Shanahan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1513/"}]}]}], "contributors": [{"name": "Rory Shanahan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1513/"}]}