Prelim1 2012 Solutions

8/9/2019 Prelim1 2012 Solutions

1/6

Name:

NetID:

HADM

2250

Prelim I

Prof.

Andrey

D.

Ukhov

In

Class.

Name

(please

print):

Cornell

ID:

NetID:

Ct

{*G-}-*

ro

,*;

Instructions:

-

Print

your

name

and ID

on all

pages.

- Close book,

close notes.

-

One

or

multiple

financial

calculators

and

non-financial

calculators

are

allowed.

- You

have exactly

75

minutes

for the exam.

Total

16

questions,

32

points,

and 7

pages

(including

the cover

and

formula

pages).

- Make

sure that no

page

is

missing in

your

exam.

- When

working

on

questions,

o For

problem

solving: show

your

work to earn

partial

credits; write

your

final

answers in the

box below each

question.

o

For

multiple choice

questions:

no

partial

credit is available;

copy

your

choices

(A/BlClDlE)

to

the

table

in

page

2.

o

For

short answer

questions:

do not exceed the number

of words specified.

-

The questions

are

NOT

presented

in

the order

of

difficulty.

-

Allocate

your

time

wisely.

By signing below

you

agree

to the University rules on exams.

Any violation

of

academic

integrity

will

result

in

serious

penalty.

(Signature)

Tests

without a signature

will be discarded.

Good

Luck

1/8

rof, Andrey

D.

Ukhov, HADM 2250

Fall

2012, PreIim

I


2/6

:

::1,11.i

.F.,.1

q{:.':,.r.3 4ttrt i4rr,,+

Name:

NetID:

Multiple Choice

Questions

(Total

6

Questions,2

points

each)

Please

legibly

write

your

answers

(AlBlClDlE)

within

the

boxes

below.

::i:li

:it:i

i -rr r a i-rr\ i aa(l/i

i

ir-r ,A iB :l[oft

i

Hi

t

Lt

i

i+

i i

i i

:

iiiiii

itilrl

iiiiii

ii'iii

:ii:ii

:ii:ii

Please

double-check

your

answers before submitting the

exam.

No

partial

credit is

possible

in

multiple-cho

ice

questions.

For

instructor's

use only

Score

Q0

I

-6

Q7-16

Total

Prof.

Andrey

D.

Ukhov,

HADM 2250

Fall 2012,

Prelim

I

218


3/6

Name:

NetID:

1.

Which of the following cash flowpatterns is an

"annuity

due"?

A. A stream of cash flows occurring for less than two

years

B. An annuity stream

of

payments

that are

disbursed rather

than

received

C.

An

annuity stream of

payments

that are received rather

than

disbursed

D.

A

set

of

equal

cash

flows

occurring

at

the

end

of

each

period

t

il, A

uet

af equal c*sh

flslss

occui"ring in the

beginniarg

of

each

period

2.

A loan where the borrower

pays

interest

each

period,

and

repays some

principal

of the

loan

over

time

until

the

final

payment

is

called a(n)

_

loan.

kA.

amortized

B. continuous

C.

balloon

D.

pure

discount

E. interest-only

3. The interest rate

charged

per

period

multiplied by the number of

periods

per

year

is

called

the

_

rate.

A. effective annual

fs

A,

annual

percentage

C.

periodic

interest

D. compound interest

E.

daily

interest

4. Compute the

yield

to maturity

(YTM)

for a 4

year

zero-coupon bond that

you

bought for

$6s8.731

658 .73r

-

1000 I

(T

+

YTM)^4

(

1+yTM)n4

-

1000

I 659.731

-

1.51

80703 5

(1+YTM)^2

-

t.2320ggg

I+YTM

-

1.10gggg

YTM: lI%

Prof. Andrey D. Ukhov, FIADM 225A Fall 2012, Prelim I 3t8


4/6

Name: NetID:

5.

You are

starting abar.

A reasonable rate

of return for this business

is

I5%o

(per

year).

The bar

will

bring

profits

of

$

100,000

at

the

end of first

year.

The

profits

will

grow

at

3o/o

per

year.

You

expect

the bar to operate

forever.

You expect

to

run the bar for 6

years,

collect 6

years

of

profits,

and

sell

the bar immediately after

you

receive

6th

year

of

profits. How

much

will

you

sell the bar for?

R:

15%:0.15, g:3%:

0.03.

The

buyer of

the

bar

is

buying

a

perpetuity.

The first

payment

the buyer receives after buying at t:

6,

equals

C7

which is:

C7:

C*(1+g)^6:

$100,000

*

(1

+

0.03)

"

6:

$119,405.23

Value(attimet:6): C7

l(r

-g):

$119,405.23

/(0.15

-

0.03):

$995,043.58

6.

You

own

two bonds in

your portfolio.

One

is

a 5

year

zero

coupon bond, the other

one

is

a3-year zero coupon bond. You bought them when interest rate was 10olo

(annual).

The interest rate increased to

12o/o

immediately

after

you

bought the two

bonds. What

was the

percent gain (or

loss) on

your

portfolio

(on your

total holdings).

Price

paid

for 5-year bond: P5

:

1000

/

(1+0.10)^5:5620.9213

Price

paid

for

3-year bond: P3

:

1000 /

(1+0.10)^3

:

$751.3148

TOTAL PAID

:

$T,372.236

Values after

rates increase:

P5

:

1000

/

(1+0.

l2)^5

:

5567.4269

P3

:

1000

/

(1+0.12)^3

:

$71

1.7802

TOTAL PAID

:51,279.207

Percent change in

portfolio

value

(loss):

($r,27

9.207

-

st,37

2.23 6

)

I

sT,37

2.23 6

:

-

0.067 7

9

Prof. Andrey

D.

Ukhov,

HADM

2250

Fall 2012, Prelim I 4t8


5/6

Name:

NetID:

Problems

(10 questions.

2

points

each)

7.

Five

Guys Co.

is

considering

taking

loans

from

two

banks.

First National Bank

charges

13.1%

compounded monthly

on

its loans. First

United

Bank

charges

13.4%o

compounded semiannually.

Which

bank

would Five

Guys choose?

Solution:

EAR

and

APR

question.

FNB has EAR:(1+13.1%112)^12-l:13.916%; FLIB

has EAR:(1+13.4%12\^2-I:13.849%.

Therefore FUB charges lower effective interest rate.

Partial credit if both EARs

are

correctly calculated.

8. Suppose a mutual fund firm offers to

quadruple your

money in 36 months. What rate of return

per

quarter

are

you

being

offered?

::

i 12.2s%

i

::

i . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . .

. . . . . . . -

. .

.

:

Solution: Timeline and cash flows for the

quadruple part.

We have T:3613:12

quarters,

PV:l and

FV=4, we need R.

R:

(4l|)^(1112)-l

:12.246oh

or

12.25o/o.

Partial credit

if

all timeline/cash

flow

information

is correct

or all

basic

known information

is

correctly

recognized.

9.

You

put

up

$32,000

today in

made in

two

years.

What will

:

i

3282.44

S

olution

:

Annuity with

PV= 3 2000

*(

1

+.

0

8)

=3

4 5 60, R:8

0%,

T

:24

w

e

need

C.

C:jiiii^44

Partial credit if all known

info

is correctly identified. esp. the

PV

of the annuity is 34560.

10. You are buying a bar in Detroit. You will

pay

for the bar now

(January

1')

and receive the

frst

cash

flow

(profits) from

the

bar

of

$25,000

exactly

one

year

from now.

From that

time

onward,

you

will receive

quarterly profits,

and the

profits

will

decay

at l%o

per quarter,

forever. APR

:

2)%o.How much would

you pay

for this bar?

?$socl

*.1,o:,3,-.

:

O.OS

t?c.ol

\

tE

66(.\

{=

Gb.og)3

=3

loans

to

his friends. That is, he lends

six dollars

today and

is the annual rate his friends

are

effectively

paying

him

:

i

302,7 53.8204

Solution: Timeline and cash flows.

Weekly

rate rs

716-1:1 6.6667%.

EAI{

-

or 302,753.8zoh.

Partial credit if

the

weeklv rate is

correct

exchange for an

8

percent,

24-year annuity. The first

payment

is

the annual

cash flow

be?

o\

ql6.t[6]

,

)

Qr

oh

?

v

Vo

Uot

11.

Michael

Coreleone

offers six-for-seven

gets

seven

dollars back

in a week.

What

for the

loans?

(1

.

1

6667)"52-1:3 027 .5382

and the EAR formula

is

set

.**-

--"-"\-+._

sl8rof. Andrey

D.

Ukhov,

FIADM 2250 Fall 2012,

Prelim

I

correctl


6/6

Name: NetID:

12. Given an

interest rate

of

10%

compounded

quarterly,

what

is the value

in

year

seven

of

a

perpetual

annual cash

flow

stream

of

$110

each

year

that begins in

year

eleven?

__________________

Solution:

Timeline and cash flows.

i

787'88

i

First calculate

EAR:(l+.114)^4-l:10.381o/o.

As of

year

ten

the PV:110/.10381:1059.5987.

In

year

seven

PV:

I

059.

5

987

I

(1.1038

I

)^3:787.88.

Partial credit

if EAI{- 1 0.3 8106. PV as

of

year

ten- I 05 9

.5981 and

PV

of

CAT SCVCN 15 PV

1o)/(1.10381)"3.

13.

You

have

just

made

your

first

$2,000

contribution

to

your

individual retirement account.

Assuming

you

earn a

12%o

rate of return and make no additional contributions, what

will

your

account be worth when

you

retire in 40

years?

186,10 r.94

Solution:

Timeline

and cash

flows.

PV:2000, r:I2Yo, T:40, then FV:2000*

(

1

+.

12)^40

:

186, L01.94.

Partial

credit

if

all known

info

(PV"

r.

T)

is

correctly identified.

14. Sunstone Resorts has identified an investment

project

that

pays

$1,200

in

one

year,

$1,400

in two

years,

$1,600

in three

years,

and

$1,800

in four

years.

If the discount rate is 6.75

percent,

what

is

the maximum

price

Sunstone

should

pay

for

the

project?

i--_------------------

i

5054.06

i

i......................................................................................................i

Solution: Timeline and cash flows.

pv:1

200/1.0675^

1+1

4001

1.067 5^2+t6001 t.0675^3+1 800 r.067 5^4

:

5054.06.

Partial credit

if PV:1200I|.0675 1+1400/1.0675^2+160011.0675^3+1800II.0675"4.

1

5. You are starting a club

in New York

City.

The

club

will

bring

profits

of

$50,000

every

six months,

growing

at 3Yo

per

six-month

period,

forever. You will keep the club for 3

years,

and sell

it

immediately after receiving the 6th

payment.

How much is the business worth today? Assume

APR:20%.

V"=.ffi.o'=?lY,}85.}i

16. Assume the total cost of a college education

will

be

$500,000

when

your

child

enters college

in

16

years.

You

presently have $100,000

to

invest.

What

annual rate

of

interest must

you

earn

on

your

investment to cover the cost of

your

child's college

education?

(You

invest all money

now

and

make no additional investments into the account.)

i---*-*-

i

10:587-0-

Solution: Timeline

and cash

flows.

T:16, PV:100,000

and

FV:500,000

we need

r. R:(500,000/100,000)"(ll16)

-

|

:10.58oh.

Partial

credit

if

all known info

(T.

PV. FV)

is

correctly

identified.

Prof. Andrey D. Ukhov, IIADM

2250 Fall 2012,

Prelim I

618

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