{"id":202746,"date":"2025-03-18T05:20:08","date_gmt":"2025-03-18T05:20:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=202746"},"modified":"2025-03-18T05:20:10","modified_gmt":"2025-03-18T05:20:10","slug":"present-value-of-future-gold-production","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/18\/present-value-of-future-gold-production\/","title":{"rendered":"Present Value of Future Gold Production"},"content":{"rendered":"\n

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 years.<\/p>\n\n\n\n

Assumptions:
Gold prices have a beta of 0, meaning there is no market risk premium.
The risk-free rate is 5.5% per year.
Discounting is done continuously or annually (specify the approach if needed).
Required:
Calculate the present value of the 1 million ounces of gold produced in eight years, assuming the given growth and discount rates.<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

To calculate the Present Value (PV) of Future Gold Production<\/strong>, we follow these steps:<\/p>\n\n\n\n

Step 1: Forecast Future Gold Price in Year 8<\/strong><\/h3>\n\n\n\n

The gold price grows in two phases:<\/p>\n\n\n\n

    \n
  1. First 2 Years<\/strong>: Growth at 12% per year<\/strong>.<\/li>\n\n\n\n
  2. After Year 2<\/strong>: Growth at 3% per year<\/strong>.<\/li>\n<\/ol>\n\n\n\n

    Step 1.1: Price at Year 2<\/strong><\/h4>\n\n\n\n

    Using the compound growth formula<\/strong>:
    [
    P_2 = P_0 \\times (1 + g_1)^2
    ]
    [
    P_2 = 1200 \\times (1.12)^2 = 1200 \\times 1.2544 = 1505.28
    ]<\/p>\n\n\n\n

    Step 1.2: Price at Year 8<\/strong><\/h4>\n\n\n\n

    From Year 2 to Year 8, price grows at 3% per year<\/strong>:
    [
    P_8 = P_2 \\times (1 + g_2)^6
    ]
    [
    P_8 = 1505.28 \\times (1.03)^6 = 1505.28 \\times 1.19405 = 1796.63
    ]<\/p>\n\n\n\n

    Step 2: Compute Future Revenue<\/strong><\/h3>\n\n\n\n

    [
    \\text{Revenue at Year 8} = \\text{Gold Price in Year 8} \\times \\text{Production}
    ]
    [
    = 1796.63 \\times 1,000,000 = 1,796,630,000
    ]<\/p>\n\n\n\n

    Step 3: Discount to Present Value<\/strong><\/h3>\n\n\n\n

    Using continuous discounting<\/strong>:
    [
    PV = FV \\times e^{-rt}
    ]
    [
    PV = 1,796,630,000 \\times e^{- (0.055 \\times 8)}
    ]
    [
    PV = 1,796,630,000 \\times e^{-0.44}
    ]
    [
    PV = 1,796,630,000 \\times 0.643
    ]
    [
    PV = 1,155,254,090
    ]<\/p>\n\n\n\n

    Conclusion<\/strong><\/h3>\n\n\n\n

    The present value of producing 1 million ounces of gold in 8 years<\/strong> is $1.155 billion<\/strong>. This accounts for expected gold price growth and risk-free discounting.<\/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-202746","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202746","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=202746"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/202746\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=202746"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=202746"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=202746"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}