// Numbas version: exam_results_page_options {"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": [{"preamble": {"js": "", "css": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"Prounded": {"templateType": "anything", "definition": "precround(P,2)", "description": "", "group": "Ungrouped variables", "name": "Prounded"}, "P": {"templateType": "anything", "definition": "D*(1+gdec)/(rrdec-gdec)", "description": "
P_0=\\frac{D_0(1+g)}{r_s-g}
", "group": "Ungrouped variables", "name": "P"}, "D": {"templateType": "anything", "definition": "Dcents/100", "description": "", "group": "Ungrouped variables", "name": "D"}, "rrdec": {"templateType": "anything", "definition": "rr/100", "description": "", "group": "Ungrouped variables", "name": "rrdec"}, "gdec": {"templateType": "anything", "definition": "g/100", "description": "", "group": "Ungrouped variables", "name": "gdec"}, "g": {"templateType": "anything", "definition": "random(1..4)", "description": "", "group": "Ungrouped variables", "name": "g"}, "rr": {"templateType": "anything", "definition": "random(5..10)", "description": "", "group": "Ungrouped variables", "name": "rr"}, "Dcents": {"templateType": "anything", "definition": "random(5..199)", "description": "", "group": "Ungrouped variables", "name": "Dcents"}}, "functions": {}, "name": "current value of a share with a constant growth dividend", "rulesets": {}, "parts": [{"useCustomName": false, "marks": 0, "showFeedbackIcon": true, "showCorrectAnswer": true, "sortAnswers": false, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": "", "customName": "", "unitTests": [], "gaps": [{"useCustomName": false, "variableReplacements": [], "mustBeReduced": false, "marks": 1, "allowFractions": false, "mustBeReducedPC": 0, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "extendBaseMarkingAlgorithm": true, "showPrecisionHint": false, "showCorrectAnswer": true, "type": "numberentry", "scripts": {}, "minValue": "P", "customMarkingAlgorithm": "", "precision": "2", "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "customName": "", "precisionMessage": "You have not given your answer to the nearest cent.", "precisionPartialCredit": 0, "maxValue": "P", "variableReplacementStrategy": "originalfirst", "precisionType": "dp", "strictPrecision": false, "unitTests": []}], "prompt": "What is the current value of a single share if the required rate of return is $\\var{rr}\\%$ per annum, the share has just paid a dividend of $\\$\\var{D}$ and the dividend is expected to increase at a constant rate of $\\var{g}\\%$ per annum.
\n\n$\\$$ [[0]] (to the nearest cent)
"}], "extensions": [], "ungrouped_variables": ["Dcents", "D", "rr", "rrdec", "g", "gdec", "P", "Prounded"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International", "description": "Find the present value of a share which returns a constant growth dividend."}, "tags": [], "advice": "We are asked to find the current value of a share which returns a dividend with constant growth, therefore we will use the formula
\n$\\displaystyle P_0=\\frac{D_0(1+g)}{r_s-g}$
\nIn our situation we have,
\n$D_0=\\var{D}$,
\n$g=\\var{g}\\%=\\var{gdec}$,
\n$r_s=\\var{rr}\\%=\\var{rrdec}$,
\nand therefore we have
\n$\\displaystyle P_0=\\frac{\\var{D}(1+\\var{gdec})}{\\var{rrdec}-\\var{gdec}}$
\nwhich upon calculation gives
\n$\\begin{align}P_0&=\\$\\var{Prounded}\\quad \\text{(to the nearest cent)}\\end{align}$
", "statement": "If you are unsure of how to do a question, click on Reveal answers to see the full working. Then, once you understand how to do the question, click on Try another question like this one to start again. Do each question repeatedly to ensure you have mastered it.
", "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/"}]}