1
MIDTERM EXAM SOLUTION
MSci 261 Engineering Economics
Fall 2011
Department of Management Sciences,
Faculty of Engineering
Problem 1.
For each multiple choice question below, select the one correct response by circling the
letter.
1.1
[2 marks]
A present amount
P
is equivalent to an annuity series of
N
payments each of size
A
(with the first
payment one period after
P
), and both are equivalent to a future amount
F
at the same time as the
N
th payment in
the annuity series.
The interest rate is
i
, and
i
>0.
(a)
F
=
N
N
N
i
i
i
A
)
1
(
1
)
1
(
lim
.
(b)
F
<
NA .
(c)
A = P/N
+
iP .
(d)
P
>
NA .
(e) none of the above.
1.2
[2 marks]
A company has two mutually exclusive proposed investments, labelled A and B.
Proposal A has
the larger first cost.
Each proposal has a present worth greater than zero.
Proposal B has a greater present worth.
Internal rates of return have been calculated for each proposal, and for the incremental investment in A compared
to B.
(a)
The present worth of the incremental investment in A over B is positive.
(b)
The IRR of the incremental investment in A over B is less than the MARR of the company.
(c)
The annual worth of A is greater than the annual worth of B.
(d)
The IRR of A is less than the MARR.
(e)
none of the above
1.3
[2 marks]
Three proposed investments, labeled A, B, C are independent
except that
A and B cannot both be
done, and C can be done only if B is also done.
Doing nothing is possible.
How many mutually exclusive,
feasible alternatives are there?
(a)
8
(b)
6
(c)
5
(d)
4
(e)
3 .
1.4
[2 marks]
A company uses a MARR estimated as the weighted cost of capital, i.e., MARR=w
d
i
d
+w
e
i
e
.
Joe
mistakenly calculates three present worths for a proposed investment, using the three interest rates MARR, i
d
and
i
e
, denoted PW(MARR), PW(i
d
) and PW(i
e
). The proposed investment has a large first cost, followed by several
years of positive net revenues.
(a)
PW(MARR) < PW(i
d
) < PW(i
e
) .
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(b)
PW(i
d
) < PW(MARR) < PW(i
e
) .
(c)
PW(i
e
) < PW(MARR) < PW(i
d
) .
(d)
PW(i
d
) < PW(i
e
) <
PW(MARR) .
(e)
none of the above.
Problem 2.
a)
[4 marks]
Bank A offers interest on savings accounts of 3% per year, compounded daily, and Bank B offers
3.1%, compounded monthly.
If you want to deposit $1000 now in a bank account, to earn interest for one year,
which bank has the better interest rate for you?
Show relevant calculations.
i
A
= (1+3%/365)
365
1 = 3.045%
1 mark
i
B
= (1+3.1%/12)
12
1 = 3.144%
1 mark
Therefore, bank B is preferable with greater interest rate. 2 marks
b)
[4 marks]
Joe is saving to buy a car in 2.5 years (30 months).
He needs to have $18,000 in 2.5 years.
He
plans to deposit $500 per month into a savings account, for the next 2.5 years.
The interest on the savings account
is at 12% per year, compounded monthly.
He will either have too little money, or too much money saved to buy
the car. Calculate either how much more money he will need in 2.5 years, or how much extra money he will have
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 Winter '09
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 Net Present Value, Bob’s MARR

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