IE 343 Fall 209
Final Exam
Name: _______________________
Student ID: ___________________
IE 343 Practice Final Exam
Closed Book, Closed Notes
Show all of your work. Your work and answers must be shown on the pages provided.
Write your name on all pages in the space provided.
For some problems note that no interest tables are required; you are to carry the answer
to the point where the equation for the problem is specified –e.g.,
“1,000(A/P,10%,5)+1,500+200(A/F,10%,5)”
and stop here. Your grade on these problems will be based on the correctness of the
equations and the clarity of your work leading up to the equations.
For the remaining problems, interest tables may be required and will be provided for
you to perform your calculations.
1
1) a) What is the annual uniform amount that must be deposited into a savings account
that pays 10% compounded annually for the next 20 years in order to accumulate $150,000
at the end of 20 years? The first deposit is made at the end of year 1 and the last deposit is
made at the end of year 20.
Use the attached table to obtain the exact numerical value.
5 points
b) What is the future equivalent worth of 10 end of year payments of $1,000
invested at 10% compounded annually? The first deposit is made at the end of
year 1 and the last deposit is made at the end of year 10.
Use the attached table to obtain the exact numerical value.
5 points
c) What is the present equivalent worth of 10 end of year payments of $4,000
invested at 10% compounded annually? First deposit is made at the end of year
1 and the last deposit is made at the end of year 10.
Use the attached table to obtain the exact numerical value.
5 points
2) A company wants to accumulate $10,000,000 by the end of six years. The company
will set aside $1,000,000 two years from today and another uniformly increasing
cash flow thereafter. The cash flow is summarized below,
2
End of Year
0
1
2
3
4
5
6
Cash flow
0
0
1,000,000
1,000,000+X
1,000,000+2X
1,000,000+3X
1,000,000+4X
What should X be, in order to accumulate the $10,000,000 at the end of year six?
Interest rate is 10%.
Use the gradient formulation and the factors available in the interest rate table
provided. Compute the answer, expression alone will not be sufficient.
13 points
3
3) Write an expression for each of the following; do not solve.
a) Suppose you make weekly deposits of $500 into a bank account that pays a
nominal interest rate of 10% compounded daily. Write the expression to
determine the balance at the end of year 1.
4 points
b) Suppose you make quarterly deposits of $500 into a bank account that pays a
nominal interest rate of 10% compounded quarterly. Write the expression to
determine the balance at the end of year 4.
4 points
c) Suppose you make annual deposits of $500 into a bank account that pays a
nominal interest rate of 10% compounded semiannually. Write the expression to
determine the balance at the end of year 4.
4 points
4
4) A company is considering one of two different pieces of equipment for its
manufacturing plant. The first piece of equipment costs $30,000 and requires
$9,000 annually in O&M cost. It will have $12,000 salvage value at the end of its 4year useful life. The second piece of equipment costs $40,000 and it requires
$10,000 in O&M expenses. It is expected to a have 6-year useful life and the
salvage value at the end of its useful life will be $15,000. The MARR is 10% per
year. Assume repeatability.
a) Draw the cash flow diagrams for each piece
5 points
b) Determine which of the projects is preferred economically. (Please be consistent
with the cash flow diagrams in part a.)
10 points
Write the expressions only; do not solve for the final answer.
5
5) Your company has purchased equipment (for $60,000) that will reduce materials
and labor costs by $15,000 each year for 7 years. The equipment is in the 5-year
GDS property class. The effective income tax rate is 34%.
Show all work! Solve for exact numerical values.
a) What is the depreciation deduction in year three?
3 point
b) What is the book value at the end of year four?
3 point
c) Assuming that the machine will be sold for $12,000 at the end of year three, what is
the ATCF at the end of year three?
9 point
d) Assuming that the machine will be sold for $12,000 at the end of its useful live
(year 7), what is the ATCF at the end of year three?
6 point
6
6) A proposed project that requires an investment of $25,000 now is expected to
generate a series of four revenues in today’s dollars (year zero dollars). The first
cash flow is 7,000 real dollars and occurs at the end of the first year and increases
by 1,000 real dollars per year thereafter. Assume that the annual general price
inflation rate is 5% and the combined (market) interest rate is 10% per year during
this inflationary period. What is the equivalent present worth of this investment?
Solve for exact numerical value.
10 points
7
7) A company has determined that the price and the monthly demand of one of its
products are related by the equation D=Sqrt(400-P) where p is the price per unit in
dollars and D is the monthly demand. The associated fixed costs are $2,000 per
month and the variable costs are $100 per unit.
a) How many units should be produced and sold each month to maximize profit?
9 points
b) How do you know that the answer to part (a) maximizes profit?
2 points
c) Write the expression to determine the breakeven point(s). Do not solve write
expression only.
3 points
8
Rough sheet:
9
Do not write on this page.
Grade sheet.
Question
Points
1 (15)
2 (13)
3 (12)
4 (15)
5 (21)
6 (10)
7 (14)
E (20)
Total:
10
Formulas:
⎧1 ⎡ (1+ i) N −1
N ⎤⎫
Find P given G: P = G⎨ ⎢
−
⎥⎬
N
(1+ i) N ⎦⎭
⎩ i ⎣ i(1+ i)
⎧1
⎫
N
⎬
Find A given G: A = G⎨ −
N
i
(1+
i)
−1
⎩
⎭
€
⎧1 ⎡ (1+ i) N −1
⎤⎫
Find F given G: F = G⎨ ⎢
− N ⎥⎬
i
⎦⎭
⎩ i ⎣
€
k
⎛
r ⎞
Effective/nominal interest rate: i = ⎜1+ ⎟
⎝ M ⎠
€
Price of a bond: VN = C(P /F,i%,N) +rZ(P / A,i%,N)
€
Capitalized worth method:
€
Depreciation using SL method:
Depreciation using DB method:
⎛ 1 ⎞ k −b
R$ and A$: (R$) k = (A$) k ⎜
⎟
⎝ 1+ f ⎠
i −f
im, ir, and f: ir = m
1+ f
€
⎡ k
⎤
EUAC: EUACk = ⎢⎣∑ TC j (P /F,i%, j) ⎥⎦( A /P,i%,k )
j =1
€
k
PW for challenger: PW k (i%) = I − MV (P /F,i%,k) + ∑ E j (P /F,i%, j)
j =1
€
€
11