(Solution) IEOR 221 - Spring 2016 Assignment 3 Due 02/12/2016 1. Suppose Two Competing Projects Have Cash Ows Of The Form (A1 , B1 , B1 , ., B1 ) And (A2 , B2 ,... | Snapessays.com


(Solution) IEOR 221 - Spring 2016 Assignment 3 Due 02/12/2016 1. Suppose two competing projects have cash ows of the form (A1 , B1 , B1 , ., B1 ) and (A2 , B2 ,...


can someone help me to do the problem 3? thanks a lot ....IEOR 221 - Spring 2016

 

Assignment 3

 

Due 02/12/2016

 

1. Suppose two competing projects have cash ?ows of the form (

 

-

 

A

 

1

 

,B

 

1

 

,B

 

1

 

,...,B

 

1

 

) and

 

(

 

-

 

A

 

2

 

,B

 

2

 

,B

 

2

 

,...,B

 

2

 

), both with the same length and

 

A

 

1

 

,A

 

2

 

,B

 

1

 

,B

 

2

 

all positive. Sup-

 

pose

 

B

 

1

 

/A

 

1

 

> B

 

2

 

/A

 

2

 

. Show that project 1 will have a higher IRR than project 2.

 

2. There are two cash ?ows of the form

 

A

 

= (5

 

,

 

14

 

,

 

-

 

15

 

,

 

-

 

7

 

,

 

10

 

,

 

2) and

 

B

 

= (1

 

,

 

14

 

,

 

3

 

,

 

-

 

7

 

,

 

-

 

8

 

,

 

2).

 

You can choose at most one cash ?ow. Find a range of

 

r

 

satisfying

 

A > B

 

. Find a

 

range of

 

r

 

which you will not take anything.

 

3. A loan company is o?ering a loan of $

 

L

 

for 20 years on the Internet with the following

 

characteristics:

 

 

A quote rate of 7

 

.

 

256% (which is used to calculate $

 

p

 

, the monthly payments).

 

 

3 points (that is, you have to pay 3%. of

 

L

 

when you get the loan) and initiation

 

fee of $1000.

 

 

An actual APR of 7

 

.

 

53% (compounded monthly).

 

 

No closing cost.

 

Find

 

L

 

and

 

p

 

.

 

4. Suppose that your aunt and uncle each separately o?er you a bond. Both bonds have

 

the same maturity

 

T

 

years and face value

 

F

 

. However, the coupon of your aunt’s

 

bond are

 

a

 

1

 

,a

 

2

 

,...,a

 

T

 

, where

 

a

 

i

 

=

 

a

 

i

 

-

 

1

 

-

 

d

 

(

 

d

 

is positive constant and

 

i

 

= 2

 

,

 

3

 

,...,T

 

);

 

the coupon of your uncle’s bond is

 

c

 

every year, where

 

c

 

is the average of the

 

a

 

i

 

’s,

 

i.e.

 

c

 

=

 

1

 

T

 

?

 

T

 

i

 

=1

 

a

 

i

 

. It turns out that both your aunt and uncle ask for $100 for the

 

bond. Given that you have only $100 to use, which one would you choose? Assume

 

the interest rate is strictly positive and less than 1.

 

5. Determine whether it is true or false. Justify your answer providing either a short

 

proof or a (counter) example as appropriate.

 

Given two bonds with the same price, face value, expiration date and yield means that

 

their coupons payments are identical.

 


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