// Numbas version: exam_results_page_options
{"name": "Theoretical ex-rights price", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>If you are unsure of how to do&nbsp;a question, click on&nbsp;<em>Reveal answers</em>&nbsp;to see the full working. Then, once you understand how to do the question, click on&nbsp;<em>Try another question like this one</em>&nbsp;to start again. Do each question repeatedly to ensure you have mastered it.</p>", "parts": [{"marks": 0, "customName": "", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "showFeedbackIcon": true, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "prompt": "<p>The current market price of shares in a certain company is&nbsp;$\\$\\var{CMP}$. The company issues a $\\var{bonusnumber}$ for $\\var{oldnumber}$&nbsp;rights offer {phrase} $\\$\\var{SP}$.&nbsp;Calculate the theoretical ex-rights price of a share.</p>\n<p>$\\$$ [[0]] (to the nearest cent)</p>", "scripts": {}, "unitTests": [], "variableReplacements": [], "gaps": [{"marks": 1, "correctAnswerFraction": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "precisionPartialCredit": 0, "extendBaseMarkingAlgorithm": true, "minValue": "X", "customName": "", "showCorrectAnswer": true, "customMarkingAlgorithm": "", "precision": "2", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "precisionMessage": "You have not given your answer to the&nbsp;nearest cent.", "maxValue": "X", "precisionType": "dp", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "useCustomName": false, "strictPrecision": false, "scripts": {}, "unitTests": [], "showFeedbackIcon": true, "allowFractions": false, "mustBeReduced": false}]}], "extensions": [], "ungrouped_variables": ["oldnumberseed", "bonusnumberseed", "cf", "oldnumber", "bonusnumber", "CMP", "SP", "X", "Xrounded", "phrase"], "name": "Theoretical ex-rights price", "variable_groups": [], "tags": [], "advice": "<p>We are asked to find the ex-rights share price, therefore we will use the formula</p>\n<p>$\\displaystyle X=\\frac{N\\times \\text{Cum Rights Market Price } +&nbsp;\\text{ Subscription Price})}{N+1}$</p>\n<p>where $N$ is the number of rights need to buy one&nbsp;share, that is,&nbsp;$N=\\frac{\\text{number you need to have for the bonus}}{\\text{bonus number}}$.</p>\n<p>In our situation we have,&nbsp;</p>\n<p>$N=\\frac{\\var{oldnumber}}{\\var{bonusnumber}}$,</p>\n<p>$\\text{Cum Rights Price}=\\var{CMP}$,</p>\n<p>$\\text{Subscription Price}=\\var{SP}$</p>\n<p>and therefore we have</p>\n<p>$\\displaystyle X=\\frac{\\frac{\\var{oldnumber}}{\\var{bonusnumber}}\\times\\var{CMP} +&nbsp;\\var{SP}}{\\frac{\\var{oldnumber}}{\\var{bonusnumber}}+1}$</p>\n<p>which upon calculation gives&nbsp;</p>\n<p>$\\begin{align}X&amp;\\approx\\var{X}\\\\&amp;=\\$\\var{Xrounded}\\quad \\text{(to the nearest cent)}\\end{align}$</p>\n<p></p>", "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Financial maths. Shares."}, "rulesets": {}, "variables": {"SP": {"group": "Ungrouped variables", "name": "SP", "templateType": "anything", "definition": "random(precround(CMP/2,2)..precround(CMP-1,2))", "description": "<p>with CMP&gt;=2, this means SP will be &gt;=1 and &lt;CMP</p>"}, "Xrounded": {"group": "Ungrouped variables", "name": "Xrounded", "templateType": "anything", "definition": "precround(X,2)", "description": ""}, "X": {"group": "Ungrouped variables", "name": "X", "templateType": "anything", "definition": "((oldnumber/bonusnumber)*CMP+SP)/((oldnumber/bonusnumber)+1)", "description": ""}, "cf": {"group": "Ungrouped variables", "name": "cf", "templateType": "anything", "definition": "gcf(oldnumberseed,bonusnumberseed)", "description": ""}, "oldnumber": {"group": "Ungrouped variables", "name": "oldnumber", "templateType": "anything", "definition": "precround(oldnumberseed/cf,0)", "description": ""}, "bonusnumber": {"group": "Ungrouped variables", "name": "bonusnumber", "templateType": "anything", "definition": "precround(bonusnumberseed/cf,0)", "description": ""}, "bonusnumberseed": {"group": "Ungrouped variables", "name": "bonusnumberseed", "templateType": "anything", "definition": "random(1..oldnumberseed-1)", "description": ""}, "CMP": {"group": "Ungrouped variables", "name": "CMP", "templateType": "anything", "definition": "random(2..25#0.01)", "description": ""}, "oldnumberseed": {"group": "Ungrouped variables", "name": "oldnumberseed", "templateType": "anything", "definition": "random(2..10)", "description": ""}, "phrase": {"group": "Ungrouped variables", "name": "phrase", "templateType": "anything", "definition": "random('with a subscription price of', 'priced at', 'with an exercise price of')", "description": ""}}, "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}