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## Present value

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**Character**The rice is so soft ~ 1 ) Nicholas Tse Assume that he is a wealth maximizer , he will choose a girlfriend that can generate the highest future income .**2) Faye Wong**A divorced woman with a 6-year-old daughter ,Tong Tong. Her annual income will be 2 million per year**3) Cecilia Cheung**Famous Single- singer, as she is less famous now , her annual income will be 1 million per year .**I will choose the one who can earn more $$**Relationship**Assume that Nicholas will choose the one who will generate**more future income ,and he will be with the girl for 10 years . Now ,we discount the future income of Cecilia and Faye into present value first .Interest rate :10% /year**Present value of receiving a constant amount at the end of**each year for finite number of years . Y Y Y Y ————+ ——— + ——— + ……… ——— (1+r)¹ (1+r)² (1+r)³ (1+r)ⁿ Y 1 = ———[ 1 ― ————] r(1+r)ⁿ * n = time (number of year)**Cecilia will earn**1 million per year , and she will work for 10 years. So the present value of her future income is : 1 million 1 ——————[ 1 ─ ——————] = $6144567 10% (1+10 %)¹º**Faye Wong will**earn 2 million per year ,and she will work for 10 years. So the present value of her future income is : 2 million 1 ───── [ 1 −——————] = $12289134 10% (1+10 %)¹º**Mum , We have a happy family**again ~**But there is a point that Faye has a daughter, Tong Tong and**she will spend Faye’s income. • Tong Tong will spend $ 1200000 per year , and she will spend Faye’s income for 10 years.**So , as Tong Tong will spend $1200000 /year ,the present**value of Faye´s future income will decrease 2 million 1 ───── [ 1 ─ ───── ] - Tong Tong’s expenditure 10% (1+10 %)¹º 2 million 1 $1200 000 1 = ───── [ 1 − ────── ] − ────── [ 1 − ───── ] 10% (1+10 %)¹º 10% (1+10 %)¹º =$12289134 −$7373480 =$ 4915654**And Cecilia’s future income ( in terms of present value)**remains constant = $6144567 But Faye’s future income( in terms of present value ) decreases =$ 4915654 So Nicholas will choose Cecilia now ~**I win ~**Fung Fung I love You!! I love You too , Cecilia ~because you got more money …HaHa**We will**go back to Beijing ~ Sorry , Mum**The End**By Irene (10) & Cecilia (17)