Present Value of Future Gold Production<\/p>\n\n\n\n
Suppose the current price of gold is $1,200 per ounce. Hans Consultants forecasts that:<\/p>\n\n\n\n
For the next two years, gold prices will grow at an average rate of 12% per year.
After two years, the growth rate will decline to a long-run trend of 3% per year.
You expect to produce 1 million ounces of gold in eight year<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To calculate the present value (PV)<\/strong> of the future gold production, we need to forecast the price of gold 8 years from now<\/strong>, then discount that value back to the present.<\/p>\n\n\n\n We grow the gold price in two stages:<\/p>\n\n\n\n $$ $$ So, the forecasted price per ounce in year 8 is approximately \\$1,797.79<\/strong>.<\/p>\n\n\n\n $$ Using the discount factor for 8 years at 10%:<\/p>\n\n\n\n $$ The present value (PV) of a future cash flow tells us what that amount is worth today, considering the time value of money. Money loses value over time due to inflation, opportunity cost, and risk, so future revenues must be discounted back to today’s terms.<\/p>\n\n\n\n In this case, a mining project will produce 1 million ounces of gold eight years<\/strong> from now. To determine its PV, we must estimate the price per ounce in year 8<\/strong>, then apply a discount rate<\/strong> to bring that value to present terms.<\/p>\n\n\n\n We\u2019re told gold prices are expected to grow at 12% annually for two years<\/strong>, then at 3% annually for six more years<\/strong>. Starting at \\$1,200, we calculate the price after two years by applying compound growth:<\/p>\n\n\n\n $$ This becomes the base for the next phase:<\/p>\n\n\n\n $$ Thus, the projected gold price in year 8 is \\$1,797.79<\/strong>. At 1 million ounces, this means the revenue in year 8 will be \\$1.798 billion<\/strong>.<\/p>\n\n\n\n To find the present value<\/strong>, we apply the discount formula:<\/p>\n\n\n\n $$ Using a 10% discount rate over 8 years:<\/p>\n\n\n\n $$ This value reflects how much the future revenue is worth today<\/strong>, assuming a 10% return requirement.<\/p>\n","protected":false},"excerpt":{"rendered":" Present Value of Future Gold Production Suppose the current price of gold is $1,200 per ounce. Hans Consultants forecasts that: For the next two years, gold prices will grow at an average rate of 12% per year.After two years, the growth rate will decline to a long-run trend of 3% per year.You expect to produce […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-213875","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213875","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=213875"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/213875\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=213875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=213875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=213875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep-by-Step Solution<\/strong><\/h3>\n\n\n\n
\n
\u27a4 We’ll assume a discount rate of 10%<\/strong>, a typical industry rate for mining project evaluations.<\/li>\n<\/ol>\n\n\n\n
\n\n\n\nStep 1: Forecast Gold Price in Year 8<\/strong><\/h3>\n\n\n\n
Years 1\u20132 (12% annual growth)<\/strong><\/h4>\n\n\n\n
P_2 = 1200 \\times (1.12)^2 = 1200 \\times 1.2544 = 1505.28
$$<\/p>\n\n\n\nYears 3\u20138 (3% annual growth for 6 years)<\/strong><\/h4>\n\n\n\n
P_8 = 1505.28 \\times (1.03)^6 = 1505.28 \\times 1.19405 \\approx 1797.79
$$<\/p>\n\n\n\n
\n\n\n\nStep 2: Calculate Future Revenue<\/strong><\/h3>\n\n\n\n
\\text{Revenue in Year 8} = 1,000,000 \\times 1797.79 = 1,797,790,000
$$<\/p>\n\n\n\n
\n\n\n\nStep 3: Discount Revenue to Present Value<\/strong><\/h3>\n\n\n\n
\\text{PV} = \\frac{1,797,790,000}{(1.10)^8} = \\frac{1,797,790,000}{2.1436} \\approx 838,547,200
$$<\/p>\n\n\n\n
\n\n\n\n\u2705 Final Answer: \\$838,547,200 (approx.)<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300 Words)<\/strong><\/h3>\n\n\n\n
P_2 = 1200 \\times (1.12)^2 = 1505.28
$$<\/p>\n\n\n\n
P_8 = 1505.28 \\times (1.03)^6 = 1797.79
$$<\/p>\n\n\n\n
PV = \\frac{\\text{Future Value}}{(1 + r)^n}
$$<\/p>\n\n\n\n
PV = \\frac{1,797,790,000}{(1.10)^8} \\approx 838,547,200
$$<\/p>\n\n\n\n