American University of Beirut
Suliman S. Olayan School of Business
Quiz 1
Spring 2009-2010
Student's Name:
ID #:
Date:
Please be sure that you read and understand the following points:
Time Duration is 25 minutes.
Non Programmable Calculators are allowed.
All documents and notes are NOT allowed
There are 6 questions
Last question is a bonus question (5 points) requiring no explanation
Remaining questions have 20 pts each, any answer without some reasonable
amount of computations or explanation will be considered incorrect
Answer on the exam paper
Q1. Ebersoll Manufacturing Company sells all its merchandise on credit. It has a profit
margin of 4 percent, days sales in receivables equal to 60 days, receivables of $150,000,
total assets of $3 million, and a debt ratio of 0.64. What is the firm’s return on equity
(ROE)? (Assume a 365-day year)
ROE= PM * TAT * EM
= 0.04 * Sales/3,000,000 * EM
1) Sales
Days Sales in Receivables = 365 / Receivables Turnover
Receivable Turnover = 365/ Days Sales in Receivables
Receivable Turnover = 365/60 = 6.08
Receivable Turnover = 6.08
Receivable Turnover = Sales/ Accounts Receivables
Sales = Receivable Turnover * Accounts Receivables
Sales = 6.08 * 150,000
Sales = 912,000
2) EM
Debt Ratio = Debt/Asset
EM = 1 / (1-Debt Ratio)
EM = (1/ (1 – 0.64)
EM= 2.78
3) ROE
ROE = PM * TAT * EM
= 0.04 * Sales/3,000,000 * EM
= 0.04 * 912,000/3,000,000 * 2.78
ROE = 0.0338 = 3.38%
Q2. A client has $202,971.39 in an account that earns 8% per year, compounded
monthly. The client’s 35th birthday was yesterday and she will retire when the account
reaches $1 million.
a- At what age should she retire if she puts no more money into the account.
b- At what age can she retire if she puts $250/month into the account every month
beginning one month from today?
a- I/Y = 8/12
PV = - 202,971.39
FV = 1,000,000
CPT N
N= 240 months
N= 240/12 = 20 years
She should retire at the age of 55
b- I/Y = 8/12
PV = - 202,971.39
FV = 1,000,000
PMT = -250
CPT N
N= 220 months
N= 220/12 = 18.33
She should retire at the age of 53
Q3. Assume that Company X and Company Y have similar $1,000 par value bond
issues outstanding. The bonds are equally risky.
Company X’s bond has a 9% annual coupon, matures in 4 years and is currently priced at
$829.
Company Y’s bond has a 12% annual coupon and matures in 4 years
How much are you willing to pay for Company Y’s bond today?
Company X:
N= 4
PV = -829
PMT = 0.09 * 1000 = 90
FV = 1,000
CPT I/Y
I/Y = 14.99
Equally risky I/Y for both bonds is the same
Company Y:
N= 4
I/Y = 14.99
PMT = 0.12 * 1,000 = 120
FV = 1, 000
CPT PV
PV = - 914.62
Q4. Mitts Cosmetics Co.’s stock recently paid $2 dividend. This dividend is expected
to grow by 25% for the next three years and then grow forever at a constant rate of 5
percent. If the required rate of return is 12%, what is the price of the stock today?
D0 = 2
D1 =2 * (1.25) = 2.5
D2 = 2.5 * (1.25) = 3.125
D3 = 3.125 * (1.25) = 3.906
D4 = 3.906 * (1.05) = 4.1
Solve for P3
P3 = D4/ R-g
= 4.1 / 0.12- 0.05
= 4.1/ 0.07
P3 = 58.57
Solve for P0
P0 = D1/ (1 + R) + D2/ (1 + R)2 + D3/ (1 + R) 3 + P3/ (1 + R) 3
P0= 2.5/1.12 + 3.125/ (1.12)2 + 3.906/ (1.12)3 + 58.58/(1.12)3
P0 = 2.23 + 2.49 + 2.78 + 41.70
P0 = 49.2
Q5. You are serving on a jury and the plaintiff is suing the city for injuries sustained
after falling down an uncovered manhole. In the trial, the doctors testified that it will be 3
years before the plaintiff is able to return to work. The jury has already decided in favor
of the plaintiff and decided to grant him the following:
The present value of three years’ future salaries. You assume the salaries will be for the
following three years $40,000, $43,000 and $45,000, respectively.
Assume that the salary payments are equal amounts paid at the end of each month. If the
interest rate you choose is 9% EAR, what is the size of the settlement today?
a) Get APR
Calculator:
2nd ICONV
EFF = 9
C/Y =12
CPT NOM
APR = 8.65%
Formula:
1
[
APR = m (1 + EAR ) m - 1 ]
APR = 12 (1+0.09)1/12 -1
APR = 8.65%
b) PV of first year monthly salaries
N= 12
I/Y = 8.65 /12
PMT = 40,000/12 =3,333.33
CPT PV
PV0 = -38,187.17
c)PV of second year monthly salaries
N = 12
I/Y = 8.65/12
PMT = 43,000/12 = 3583.33
CPT PV
PV1= -41,051.22
Discount back to today at the EAR
PV0 = 41,051.22 / 1.09
PV0 = 37,661.67
d) PV of third year monthly salaries
N = 12
I/Y = 8.65/12
PMT = 45,000/12 = 3,750
CPT PV
PV1= -42,960.61
Discount back to today at the EAR
PV0 = 42,960.61/ (1.09)2
PV0 = 36,159.09
e) The size of the settlement today:
38,187.17 + 37,661.67 + 36,159.09= 112,007.93
Q6. Consider the following statements:
I. A 20 year, 10 percent coupon bond has more price risk than a 20 year, 20
percent coupon bond.
II. A 20 year, 10 percent coupon bond has more reinvestment risk than a 20 year, 20
percent coupon bond.
III. A 20 year, 10 percent coupon bond has more price risk than a 30 year, 10 percent
coupon bond.
IV. A 20 year, 10 percent coupon bond has more reinvestment risk than a 30 year,
10 percent coupon bond.
Of the preceding statements, the following are most accurate:
A- I only
B- I and IV
C- II and III
D- III and IV
E- None of the above
