// Numbas version: exam_results_page_options
{"name": "Theoretical value of one right", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "ungrouped_variables": ["oldnumberseed", "bonusnumberseed", "cf", "oldnumber", "bonusnumber", "CMP", "SP", "V", "Vrounded", "phrase"], "tags": [], "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>", "variablesTest": {"maxRuns": 100, "condition": ""}, "extensions": [], "advice": "<p>We are asked to find the value of a right, therefore we will use the formula</p>\n<p>$\\displaystyle V=\\frac{N(\\text{Cum Rights Price } - \\text{ Subscription Price})}{N+1}$</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>$\\displaystyle V=\\frac{\\frac{\\var{oldnumber}}{\\var{bonusnumber}}(\\var{CMP} - \\var{SP})}{\\frac{\\var{oldnumber}}{\\var{bonusnumber}}+1}$</p>\n<p>which upon calculation gives&nbsp;</p>\n<p>$\\begin{align}V&amp;\\approx\\var{V}\\\\&amp;=\\$\\var{Vrounded}\\quad \\text{(to the nearest cent)}\\end{align}$</p>\n<p></p>", "name": "Theoretical value of one right", "functions": {}, "parts": [{"prompt": "<p>The current market price of shares in a certain company is&nbsp;$\\$\\var{CMP}$. The company issues a $\\var{bonusnumber}$ for $\\var{oldnumber}$&nbsp;rights offer {phrase} $\\$\\var{SP}$.&nbsp;Calculate the theoretical value of one right.</p>\n<p>$\\$$ [[0]] (to the nearest cent)</p>", "unitTests": [], "customName": "", "showCorrectAnswer": true, "useCustomName": false, "marks": 0, "variableReplacements": [], "sortAnswers": false, "scripts": {}, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "gaps": [{"showPrecisionHint": false, "minValue": "V", "maxValue": "V", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the&nbsp;nearest cent.", "strictPrecision": false, "precision": "2", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customName": "", "correctAnswerFraction": false, "correctAnswerStyle": "plain", "unitTests": [], "mustBeReducedPC": 0, "mustBeReduced": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "useCustomName": false, "marks": 1, "scripts": {}, "allowFractions": false, "customMarkingAlgorithm": "", "precisionType": "dp", "showFeedbackIcon": true}], "type": "gapfill", "customMarkingAlgorithm": "", "showFeedbackIcon": true}], "variables": {"bonusnumber": {"description": "", "templateType": "anything", "name": "bonusnumber", "definition": "precround(bonusnumberseed/cf,0)", "group": "Ungrouped variables"}, "oldnumber": {"description": "", "templateType": "anything", "name": "oldnumber", "definition": "precround(oldnumberseed/cf,0)", "group": "Ungrouped variables"}, "bonusnumberseed": {"description": "", "templateType": "anything", "name": "bonusnumberseed", "definition": "random(1..oldnumberseed-1)", "group": "Ungrouped variables"}, "V": {"description": "", "templateType": "anything", "name": "V", "definition": "(oldnumber/bonusnumber)*(CMP-SP)/((oldnumber/bonusnumber)+1)", "group": "Ungrouped variables"}, "phrase": {"description": "", "templateType": "anything", "name": "phrase", "definition": "random('with a subscription price of', 'priced at', 'with an exercise price of')", "group": "Ungrouped variables"}, "oldnumberseed": {"description": "", "templateType": "anything", "name": "oldnumberseed", "definition": "random(2..10)", "group": "Ungrouped variables"}, "SP": {"description": "<p>with CMP&gt;=2, this means SP will be &gt;=1 and &lt;CMP</p>", "templateType": "anything", "name": "SP", "definition": "random(precround(CMP/2,2)..precround(CMP-1,2))", "group": "Ungrouped variables"}, "cf": {"description": "", "templateType": "anything", "name": "cf", "definition": "gcf(oldnumberseed,bonusnumberseed)", "group": "Ungrouped variables"}, "Vrounded": {"description": "", "templateType": "anything", "name": "Vrounded", "definition": "precround(V,2)", "group": "Ungrouped variables"}, "CMP": {"description": "", "templateType": "anything", "name": "CMP", "definition": "random(2..25#0.01)", "group": "Ungrouped variables"}}, "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Financial maths. Shares."}, "rulesets": {}, "preamble": {"js": "", "css": ""}, "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/"}]}