《20點》求教高等財務題目....(解超久還是不會)請高手指

Question

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!!

Answer 1

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