// Numbas version: finer_feedback_settings
{"name": "current value of a share with a constant growth dividend", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "current value of a share with a constant growth dividend", "tags": [], "metadata": {"description": "Find the present value of a share which returns a constant growth dividend.", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "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>", "advice": "<p>We are asked to find the current value of a share which returns a dividend with constant growth, therefore, we will use the formula</p>\n<p>$\\displaystyle P_0=\\frac{D_0(1+g)}{r_s-g}$</p>\n<p>In our situation, we have,&nbsp;</p>\n<p>$D_0=\\var{D}$,&nbsp;</p>\n<p>$g=\\var{g}\\%=\\var{gdec}$,</p>\n<p>$r_s=\\var{rr}\\%=\\var{rrdec}$,</p>\n<p>and therefore we have</p>\n<p>$\\displaystyle P_0=\\frac{\\var{D}(1+\\var{gdec})}{\\var{rrdec}-\\var{gdec}}$</p>\n<p>which upon calculation gives&nbsp;</p>\n<p>$\\begin{align}P_0&amp;=\\$\\var{Prounded}\\quad \\text{(to the nearest cent)}\\end{align}$</p>\n<p></p>\n<p>Note: We could have written this formula as $\\displaystyle P_0=\\frac{D_1}{r_s-g}$ where $D_1=D_0(1+g)$ is the first dividend in the future.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Prounded": {"name": "Prounded", "group": "Ungrouped variables", "definition": "precround(P,2)", "description": "", "templateType": "anything", "can_override": false}, "P": {"name": "P", "group": "Ungrouped variables", "definition": "D*(1+gdec)/(rrdec-gdec)", "description": "<p>P_0=\\frac{D_0(1+g)}{r_s-g}</p>", "templateType": "anything", "can_override": false}, "D": {"name": "D", "group": "Ungrouped variables", "definition": "Dcents/100", "description": "", "templateType": "anything", "can_override": false}, "rrdec": {"name": "rrdec", "group": "Ungrouped variables", "definition": "rr/100", "description": "", "templateType": "anything", "can_override": false}, "gdec": {"name": "gdec", "group": "Ungrouped variables", "definition": "g/100", "description": "", "templateType": "anything", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1..4)", "description": "", "templateType": "anything", "can_override": false}, "rr": {"name": "rr", "group": "Ungrouped variables", "definition": "random(5..10)", "description": "", "templateType": "anything", "can_override": false}, "Dcents": {"name": "Dcents", "group": "Ungrouped variables", "definition": "random(5..199)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["Dcents", "D", "rr", "rrdec", "g", "gdec", "P", "Prounded"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>What is the current value of&nbsp;a single share if the required rate of return is $\\var{rr}\\%$&nbsp;per annum, the share has just paid a dividend of $\\$\\var{D}$&nbsp;and the dividend&nbsp;is expected to&nbsp;increase at a constant rate of $\\var{g}\\%$&nbsp;per annum.</p>\n<p></p>\n<p>$\\$$ [[0]] (to the nearest cent)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P", "maxValue": "P", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the&nbsp;nearest cent.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}