E120
Homework 9 Solutions
1. Note: The original solution is incorrect, as the covariance between these two assets is
0.005, not 0.05.
With that, we get:
2
(a) M = rM = 0.1476923, and M = 0.0559882.
2
(b) M = rM = 0.1557252, and M = 0.0644036.
Below is the

E120
Homework 3
Due 02/20/2013
1. Suppose your bank account pays interest monthly with an annual interest rate of 6%.
(a) Assume that the rate is being compounded monthly
i. What amount of interest will you earn each month (i.e. the eective monthly
rate)?

E120
Homework 9
Due 04/24/2013
1. Suppose that there are 2 assets with r1 = 0.20, 1 = 0.40, r2 = 0.10, 2 = 0.25, 12 =
0.05, where 12 is the correlation of returns between asset 1 and asset 2.
(a) If r0 = 0.02, what are the market portfolio return and vari

E120
Homework 10 Solutions
1. Fall 2011, problem 1.
(a) The cash ow for periods 0, 1, . . . , 239 is (C, C, . . . , C). We want
C+
C
C
0.05 + . . . +
1 + 12
1 + 0.05
12
239
= 150000
Solving for C gives 150K/152.1566685455 = 985.826.
(b)
i. The loan balanc

E 120: Principles of Engineering Economics
Midterm Exam
Oct 19, 2011
Instructor: Nguyen Truong
(please print)
Name:
SID:
Any communication with other students during the exam (including showing, viewing or sharing any writing) is strictly prohibited. Any

E 120: Principles of Engineering Economics
Final Exam
May 10, 2011
Instructor: Nguyen Truong
Name:
(please print)
SID:
Any communication with other students during the exam (including showing,
viewing or sharing any writing) is strictly prohibited. Any v

E120
Homework 4
Due 02/27/2013
1. Compute the internal rate of return on projects with the following cash ows.
Year Project A Project B
0
3000
6000
1
2500
5000
2
1000
2000
2. CPC, Inc., has a project with the following cash ows.
Year Cash Flows ($)
0
8000

E 120: Principles of Engineering Economics
Final Exam
August 12, 2011
Instructor: Ilan Adler
Name:
(please print)
SID:
Any communication with other students during the exam (including showing,
viewing or sharing any writing) is strictly prohibited. Any v

E 120: Principles of Engineering Economics
Final Exam
December 12, 2011
Instructor: Nguyen Truong
Name:
(please print)
SID:
Any communication with other students during the exam (including showing,
viewing or sharing any writing) is strictly prohibited.

E 120 Discussion 2&3
Yang Wang
Feb. 15, 2013
[email protected]
( ) =
1. EAR / APR / Discount rate / Perpetuity / Annuity
() =
1
[1 (
) ]
1 +
e.g.1
Bank has APR 4% compounded quarterly. If you receive $400 at the end of each month forever,
what i

E 120 Discussion 1
Yang Wang
Feb. 1, 2013
[email protected]
1. Concepts
Annual percentage rate (APR): Amount of interest earned in one year without the effect of
compounding. APR itself cannot be used for moving cash flows because APR does not ref

E 120 Discussion 7
Yang Wang
[email protected]
March 15, 2013
Spot rate
Invest $1 now, will receive (1 + ) at the end of ith period.
Short rate
Invest $1 at the end of ( 1) period, will receive (1 + ) at the end of ith period.
Forward rate
Inve

E 120 Discussion 5
Yang Wang
[email protected]
March 1, 2013
1 - Bond
Bond cash flow
(, , , , , + )
P: Bond price
FV: Face value
C: Coupon payment
k: # periods per year = # compoundings per year (only for bond)
n: # periods in total
y: Yield to ma

E 120 Discussion 8
Yang Wang
April 5, 2013
[email protected]
1. Expectation
Suppose X is a discrete random variable takes on value x with probability Pcfw_X=x, then the
expectation of X is defined as
[ ] = cfw_ =
e.g.1 Let X denotes the value of

E120
Homework 5 Solutions
1. (a) We rst compute the eective 6 month yield (since we are given semi-annual
coupons of $40 for 20 periods).
$1034.74 =
40
1+r
+ . +
40
(1+r)20
+
1000
.
(1+r)20
Simplify the right hand side using the geometric series formula.

E120
Homework 1
Due 02/06/2013
1. Calculate the future value of $2000 in
(a) 5 years at an interest rate of 5% per year.
(b) 10 years at an interest rate of 5% per year.
(c) 5 years at an interest rate of 10% per year.
(d) Why is the amount of interest ea

E120
Homework 2
Due 02/13/2013
1. What is the present value of $1000 paid at the end of each of the next 100 years if the
interest rate is 7% per year?
2. You are the head of the Schwartz Family Endowment for the Arts. You have decided
to fund an arts sch

E120
Homework 6
Due 03/18/2013
1. Consider four bonds having annual payments as shown in the table below. They are
traded to produced a 15% yield.
(a) Determine the price of each bond.
(b) Determine the duration of each bond.
(c) Which bond is most sensit

E120
Homework 5
Due 03/06/2012
1. Suppose a ten-year, $1000 bond with an 8% coupon rate and semiannual coupons is
trading for a price of $1034.74.
(a) What is the bonds yield to maturity (expressed as an APR with semiannual
compounding)?
(b) If the bonds

E120
Homework 10
Due 05/01/2013
From Fall 2011 final exam, do:
1
2(a)
2(b)
3
4(b)
4(c)
From Spring 2011 final exam, do:
1
2
4(b)
4(d)
For 4(b), 'efficient' means 'optimal'.

E120
Homework 7
Due 04/10/2013
1. The probability that the economy will experience moderate growth next year is 0.6.
The probability of a recession is 0.2, and the probability of a rapid expansion is also
0.2. If the economy falls into a recession, you ca

E120
Homework 8
Due 04/17/2013
1. The expected returns and variances (of returns) for three assets are:
ASSET RETURN VARIANCE
1
0.10
0.04
2
0.15
0.09
3
0.17
0.25
The correlations between the returns are 12 = 0.20, 13 = 0.50, 23 = 0.30. Note that
AB = Cov(

E120
Homework 2 Solutions
1. P V =
1000
1.07
+
1000
1.072
+ . +
1000
1.07100
= 14269.25.
Again, make sure you know how to apply the geometric series formula to obtain the
above number.
2. P V =
1M
1.085
+
1M
1.0810
+
1M
1.0815
+ . . . = 2.1307057M .
Note

E120
Homework 3 Solutions
0.06 12
12
equivalent to 6%
12
1. (a) The EAR is 1 +
1 = 0.0617 = 6.17%.
= 0.5% per month (note that this is only true when we
This is
have monthly compounding).
We wish to determine the amount of cash C to put into the bank for

E120
Homework 4 Solutions
1. We solve for r, where 3000 +
2500
1+r
+
1000
(1+r)2
= 0. This gives r = 0.128667.
The other cash ow should also have the same IRR.
2. (a) 8000 +
4000
1+r
+
3000
(1+r)2
+
2000
(1+r)3
= 0 = r = 0.0693244.
(b) Since this is an in

E120
Homework 6 Solutions
1. (a) You can crank out the prices of these bonds, and nd
PA = $885.8387, PB = $771.6775, PC = $657.5162, PD = $869.5652
(b) Similar to what we did in previous problems, we nd the durations
DA = 2.718315, DB = 2.8383214, DC = 3,

E 120 Discussion 4
Yang Wang
Feb. 22, 2013
[email protected]
1 Mortgage / Loan
e.g. You borrowed $1,000,000 from bank to buy an apartment in San Francisco. You need to make
monthly payment to the bank for 30 years. Suppose the bank has APR 4% comp

determined by trial. Further, the same value of k must be given when
rx = re as when rx = 60 ft (18.3 m). In this procedure, only the correct
assumed value of re is shownto save space. Assume that re = 350 ft
(106.7 m). Then, 1/350 = 0.00286 and, from Fig

Controlling means keeping to plan in spite of the many problems that
may get in the way. The aim is to coordinate planning and control of
each process so that the needs of the end-customer are met correctly. The
definition of supply chain management used

equation for Q above, to solve some problems in gravity wells by
measuring two or more rates of flow and corresponding drawdowns in
the well to be studied. Observations in nearby test holes or boreholes
are unnecessary. The steps are outlined in this proc

the typical limits for certain impurities in water supplies. The daily
water flow rate for this city is, from step 1, (20,900 gal/min)(24 h/day)
(60 min/h) = 30,096,000 gal/day (1318.6 L/s). If a slow sand filter were
used, the required area would be (30.