✔ 最佳答案
嗯，當 perpetuity 咁計，即係 dividend/yield = D/i 。
原理是
P = D/(1+i) + D/(1+i)² + D/(1+i)³ + ...
= [D/(1+i)]/[1 - 1/(1+i)] {Sum of GP to infinity}
= [D/(1+i)]/[i/(1+i)]
= D/i
這類題型寫得不夠清楚，其實一般 corporate finance 的題目都寫得不清楚，只有專讀 financial mathematics 的才會清楚地分辨出 nominal interest rate 同埋 effective interest rate 及佢地的 effective period 種種的 details。
你題目講的 10% 係指 APR （嚴格來說即是 annual nominal interest rate），還是 EAR?
如果把 10% 看作 APR，effective interest rate （小心 EAR 只應指 effective ANNUAL interest rate）是：
(a) i = 10%/12 (per month)
(b) i = 10%/4 (per quarter)
(c) i = 10%/2 (per half year)
(d) i = 10%/0.5 (per two years)
所以 Present value today (price) 是
(a) $1/(10%/12) = $120
(b) $3/(10%/4) = $120
(c) $6/(10%/2) = $120
(d) $24/(10%/0.5) = $120
〔以下的make sense一點，required return亦應是effectively compounded的。但以上都並非無意思，也有訊息可以帶出。〕
如果把 10% 看作 EAR，那麼每個case的effective interest rate i (per period)是：
(a) (1+i)¹² = 1+10%, i = 0.00797414 (per month)
(b) (1+i)⁴ = 1+10%, i = 0.024113689 (per quarter)
(c) (1+i)² = 1+10%, i = 0.048808848 (per half year)
(d) (1+i)^0.5 = 1+10%, i = 0.21 (per two years)
所以 Present value today (price) 是
(a) $1/i = $125.4053661
(b) $3/i = $124.4106611
(c) $6/i = $122.9285309
(d) $24/i = $114.2857143
這是合理的結果，因為 compounding frequency 愈高，如配合相對scaling的payment pattern，由於 compound effect，所得的回報是最高的。
這也是要學 limiting case 是 force of interest 的原因：
(1 + r/n)^n → e^r as n → ∞
r 就係 force of interest, continuously compounded interest rate, log-return, etc.
2013-11-26 23:02:21 補充：
你這麼晚還可以問到老師，你的老師都很盡責～
你也要做個好學生～
(◕‿◕✿)
