BU537 Lecture Notes - Anton Chekhov, Financial Planner, Mutual Fund
BUSI 3361 (01 15 19) ASSIGNMENT #1
Due$January$30,$2017$at$9:00$a.m.
TOTAL VALUE (54 Marks)
$
$
For$all$problems,$ignore$any$tax$considerations.$Use$at$least$6$decimal$places$when$expressing$
percentages$as$a$decimal$number$(e.g.$.123456$=$12.3456%)$
!
1. In!30!years,!you!would!like!to!retire!with!$1,000,000!in!savings.!Assuming!that!you!had!$90,000!to!
invest,!today,!what!annual!interest!rate!would!you!require!to!reach!your!goal?!!(4!Marks)!
PV!=!$90,000!
FV!=!$1,000,000!
t!=!30!years!
r!=!?!
!
FV = PV (1 + r)t!
∴!FV/PV = (1 + r)t
∴!(FV/PV)1/t = 1 + r
∴!r =!(FV/PV)1/t – 1
!
r!=!($1,000,000/$90,000)1/30!–!1!
r!=!.083574!or!8.3574%!
!
2. Fish,!a!remake!of!the!successful!Broadway!musical,!Cats!(for!fish-lovers),!will!take!one!year!to!
produce!and!will!require!that!the!production!company!make!an!immediate!investment!of!
$3,000,000.!Beginning!at!the!end!of!that!first!year!and!continuing!in!perpetuity,!the!production!
company!will!receive!a!single!lump!sum!payment!of!$500,000!a!year.!The!company’s!cost!of!capital!
is!18%.!Should!Fish!be!produced?!(4!Marks)!
C!=!$500,000!
R!=!0.18!
PV!=!?!
!
!
!
PV!=!$500,000!/!.18!=!$2,777,777!<!$3,000,000!∴!Fish!should!not!be!produced!
!
3. Anton!Chekhov,!a!playwright,!invests!$80,000!in!a!new!theatre!that!is!expected!to!increase!in!value!
by!9%!per!year!for!the!next!five!years.!At!that!time,!he!will!sell!the!theatre!and!use!the!proceeds!to!
purchase!an!annuity!to!receive!an!annual!income!for!10!years.!Anton’s!financial!planner!advises!that!
interest!rates!at!the!time!he!will!purchase!the!annuity!will!likely!be!12%.!Assuming!that!Anton!
receives!his!income!in!a!single!payment!each!year;!how!much!will!Anton!receive!each!year!if:!
!
a. He!receives!his!income!at!the!start!of!each!year?!(7!Marks)!
!
PV!=!$80,000!
r!=!.09!
t!=!5!years!
FV!=!?!
!
FV = PV (1 + r)t
!
FV!=!$80,000!(1!+!.09)5!
FV!=!$123,089.92!!!(3!Marks)!
!
!
!
€
PV0=C
1−1
1+r
( )
t
r
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
(1+r)
€
123,089.92 =C
1−1
1+.12
( )
10
.12
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
(1+.12)
C=$19,450.86
(4!Marks)!
!
!
!
!
b. He!receives!his!income!at!the!end!of!each!year?!(2!Marks)!
€
123,089.92 =C
1−1
1+.12
( )
10
.12
⎡
⎣
⎢
⎢
⎢
⎢
⎤
⎦
⎥
⎥
⎥
⎥
C=$21,784.97
!
4. Working!as!a!grip!in!a!TV!production!remake!of!The!Little!Rascals;!you!suffered!a!workplace!
accident,!which!has!left!you!unable!to!work!for!the!next!five!years.!Your!employer’s!insurer!has!
offered!you!a!choice!of!accepting!either!of!two!5-year!cash!flow!streams!or!lump!sum!amounts.!You!
may!accept!settlement!A!or!settlement!B!either!as!a!cash!flow!stream!or!as!a!lump!sum.!Given!the!
cash!flow!stream!and!lump-sum!amounts!associated!with!each,!and!assuming!that!you!can!earn!an!
8%!rate!of!return,!which!alternative!(A!or!B)!and!in!which!form!(cash!flow!stream!or!lump-sum!
amount)!would!you!prefer?!(7!Marks)!
! !
!!
Cash!flow!stream!
Document Summary
Use at least 6 decimal places when expressing percentages as a decimal number (e. g. 123456 = 12. 3456%) In 30 years, you would like to retire with ,000,000 in savings. Assuming that you had ,000 to invest, today, what annual interest rate would you require to reach your goal? (4 marks) Beginning at the end of that first year and continuing in perpetuity, the production company will receive a single lump sum payment of ,000 a year. At that time, he will sell the theatre and use the proceeds to purchase an annuity to receive an annual income for 10 years. Anton"s financial planner advises that interest rates at the time he will purchase the annuity will likely be 12%. Assuming that anton receives his income in a single payment each year; how much will anton receive each year if: he receives his income at the start of each year? (7 marks)
