no nickname 發問時間: 教育與參考考試 · 1 0 年前

《20點》求教高等財務題目....(解超久還是不會)請高手指

求大大解這題:

Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance?

題目我看的懂就是要求遺產的現值.....

切勿只翻譯,因為我看的懂英文,只是不知道怎麼算!!

1 個解答

評分
  • Amber
    Lv 4
    1 0 年前
    最佳解答

    T=0 5,000

    T=1 5,000*(1+5%) ÷(1+12%)

    T=2 5,000*(1+5%)^2÷(1+12%)^2

    T=3 5,000*(1+5%)^3÷(1+12%)^3

    T=4 5,000*(1+5%)^4÷(1+12%)^4

    T=5 5,000*(1+5%)^5÷(1+12%)^5

    T=6 5,000*(1+5%)^6÷(1+12%)^6

    以此類推到無窮期數,再將所有的計算結果加總,就是遺產的現值,

    你可以發現這種計算方式,就是Gordon Model的固定成長模式,

    Current Price = Expected dividend ÷ (Required rate - Growth rate)

    Current price = 5,000*(1+5%) ÷(12%-5%)=$75,000

    但是請注意$75,000是T=1到T=無窮期數的現值,

    還漏掉了T=0的$5,000,

    所以總遺產的正確現值=75,000+5,000=$80,000

    參考資料: 自己
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