Introduction to Management Science 5th Edition, 课后习题答案 Chapter 13

CHAPTER 13 COMPUTER SIMULATION WITH RISK SOLVER PLATFORM

SOLUTION TO SOLVED PROBLEMS

13.S1 Saving for Retirement

Patrick G ordon i s t en y ears a way f rom r etirement. H e h as a ccumulated a $100,000 n est e gg that h e w ould l ike t o i nvest f or h is g olden y ears. F urthermore, h e i s c onfident t hat h e c an invest $10,000 m ore e ach y ear u ntil r etirement. H e i s c urious a bout w hat k ind o f n est e gg h e

can e xpect t o h ave a ccumulated a t r etirement t en y ears f rom n ow.

Patrick p lans t o s plit h is i nvestments e venly a mong f our i nvestments: a M oney M arket F und, a Domestic S tock F und, a G lobal S tock F und, a nd a n A ggressive G rowth F und. B ased o n p ast performance, P atrick e xpects e ach o f t hese f unds t o e arn a r eturn i n e ach o f t he u pcoming t en years a ccording t o t he d istributions s hown i n t he f ollowing t able.

Money M arket Uniform (Minimum = 2%, M aximum = 5%)

Domestic S tock Normal (Mean = 6%, S tandard D eviation = 5%)

Global S tock Normal (Mean = 8%, S tandard D eviation = 10%)

Aggressive G rowth Normal (Mean = 11%, S tandard D eviation = 16%)

Assume t hat t he i nitial n est e gg ($100,000) a nd t he f irst y ear’s i nvestment ($10,000) a re made r ight n ow (year 0) a nd a re s plit e venly a mong t he f our f unds (i.e., $27,500 i n e ach f und). The r eturns o f e ach f und a re a llowed t o a ccumulate (i.e., a re r e--‐invested) i n t he s ame f und

and n o r edistribution w ill b e d one b efore r etirement. F urthermore, n ine a dditional investments o f $10,000 w ill b e m ade a nd s plit e venly a mong t he f our f unds ($2,500 e ach) a t year 1, y ear 2, ..., y ear 9.

A f inancial a dvisor h as t old P atrick t hat h e c an r etire c omfortably i f h e c an a ccumulate $300,000 b y y ear 10 t o s upplement h is o ther s ources o f r etirement i ncome. U se a 1000--‐trial RSPE s imulation t o e stimate e ach o f t he f ollowing.

The u ncertain e lements i n t his p roblem a re t he a nnual r eturn o f e ach i nvestment o ver t he next 10 y ears (Year 0 t hrough Y ear 9). T o s imulate t his, w e d efine a n u ncertain v ariable c ell for t he a nnual r eturn o f e ach i nvestment i n e ach y ear. T hese c ells a re d efined i n r ows 12, 17, 22, a nd 27 o f t he s preadsheet b elow.

To t rack t he i nvestments, w e c alculate t heir b alances i n e ach y ear. R ow 10, 15, 20, a nd 25 show t he i nvestment m ade b y P atrick i n e ach y ear.

Rows 11, 16, 21, a nd 26 c alculate t he b alance i n e ach f und a t t he s tart o f t he y ear. F or Y ear 0 i n e ach f und, t his w ill s imply b e t he i nitial i nvestment ($25,000) p lus t he a nnual investment ($2,500). F or e ach f uture y ear, i t w ill b e t he b alance a t t he e nd o f t he p receding year p lus t he a nnual i nvestment. F or e xample, f or Y ear 1 o f t he m oney m arket f und, t he starting b alance i s D11 = C13 + D10.

Rows 13, 18, 23, a nd 28 c alculate t he y ear--‐end b alance f or e ach f und. T his w ill b e t he starting b alance t imes t he n et r eturn. F or e xample, f or t he m oney m arket f und i n Y ear 0 this w ill b e C13 = C11*(1+C12).

Finally, t he Y ear 10 t otals a re a dded u p i n M30 t o c alculate P atrick’s f inal n est e gg. T his c ell is d efined a s a r esults c ell i n R SPE. T wo s tatistic c ells a re d efined i n M31 a nd M32 t o estimate t he m ean a nd s tandard d eviation o f t he f inal n est e gg.

The r esults o f a 1000--‐trial s imulation r un a re s hown b elow.

a. What w ill b e t he e xpected v alue (mean) o f P atrick’s n est e gg a t y ear 10?

The m ean o f t he n est e gg a t y ear 10 i s n early $356 t housand.

b. What w ill b e t he s tandard d eviation o f P atrick’s n est e gg a t y ear 10?

The s tandard d eviation o f P atrick’s n est e gg a t y ear 10 i s n early $54 t housand.

c. What i s t he p robability t hat t he t otal n est e gg a t y ear 10 w ill b e a t l east $300,000?

There i s n early a n 88% c hance t hat t he t otal n est e gg a t y ear 10 w ill b e a t l east $300,000.