NAME_______________________________
FIN 203
Signature______________________________
FRANK G. ZARB SCHOOL OF BUSINESS
MID-TERM EXAM SAMPLE
OUTLAW
This is a 3-hour exam so please pace your answers appropriately. Show all work for full credit. If
your answer is wrong, you will not receive full credit if no work is shown. Please circle your
numeric answers so I can easily identify your answer. Good luck.
1.
You deposit $4,000 today in a bank that promises to pay an annual interest of 8%?
a. What is future value of this sum at the end of 12 years?
b. What if the bank pays 8% interest compounded monthly? What if the bank pays
8% interest compounded quarterly?
c. What interest will the bank have to pay if the future value has to be $12,000 at the
end of 12 years?
d. Using information from (1a) only, what quarterly compounded interest rate
should the bank quote in order to provide the same interest as the 10% annual
rate? What should be the quoted continuously compounded rate if it is to be the
same as the 10% annual rate? Provide the rates per annum.
e. What is the APR? Do we use APR or EAR when we are calculating the present
value of an investment?
2.
You receive a credit card application offering an introductory rate of 0.5%
compounded monthly for the first six months, increasing thereafter to 17%
compounded monthly.
a. What is the period rate for the first six months? What is the period rate after six
months?
b. Assuming you transfer $6,000 from your existing credit card balance and make no
subsequent payments, how much interest will you owe at the end of the first year?
c. You decide to go with a different credit card that quotes a rate of 1% compounded
monthly. You are making equal payments of $400 to pay down the balance. Is this
an annuity of perpetuity? Why? What is the difference between an annuity and
perpetuity?
d. In addition, to paying down your credit card balance, you consider saving for
retirement. If you want to be a millionaire when you retire in 25 years, how much
should you save each month if you can earn an annual 11% return?
e. How much more will you have to deposit each month if you wait 10 years to start
saving? Why do you have to deposit more?
3.
Evaluate the following bonds:
a. An 8 ½%, 25-year, $1,000 bond is presently selling at a yield-to-maturity (YTM)
of 9 ¾%. Assuming annual interest payments, what should you pay for the bond?
b. What should you pay if interest is paid semiannually?
c. Instead of a 25-year bond, they decide to issue 15-year bonds with annual
payments. What should you pay for this bond if the YTM is 9 ¾%? Explain the
differences in prices changes for (3a) and (3c) in terms of maturity.
d. You buy an 8%, 15-year, $1,000 bond that pays interest annually when it is
selling with a YTM of 7%. Immediately after you buy the bond, the YTM
increases to 9%. What was the percentage change in the price of the bond?
e. A bond has a market price that exceeds its face value. What type of bond is this?
Describe the relationship between the coupon rate and the YTM.
4.
A local wine equipment manufacturer is planning to issue stocks. The company just
paid a dividend of $3.40. Analysts expect the dividends to grow at an annual rate of
4.5% for the foreseeable future.
a. If investors are expected to demand a rate of return of 11%, what should be the
price of the share if the dividend growth model is used?
b. After examining company statements, the analysts have revised their forecasts.
They now expect no dividends to be paid for the next three years. Instead, the first
dividend of $3.40 is expected to be paid at the end of year 4 and will remain at
$3.40 for years 5 and 6. Thereafter the dividends are expected to grow at an
annual rate of 6%. What is the new price of the shares given these revised
forecasts? Assume a rate of return of 11%.
c. Instead, the manufacturer announces that they will pay a constant dividend of
$3.40 indefinitely. How much is this stock worth?
d. Analysts don’t think the wine manufacturer will pay the constant dividend
forever. They expect the firm to pay $3.40 dividend for nine years and then cease
dividend payments forever. What should be the share price?
e. Evaluate the following statement: Managers should not focus on maximizing
shareholders’ wealth because doing so will cause them to neglect meeting other
obligations such as payroll and interest expenses.
5.
Assume the returns of a stock for the previous five years are as follows: 8%, 12%, 4%, 9% and 14%.
a. What is the arithmetic average? What is the geometric average?
b. What is the historical standard deviation of the returns of this stock?
c. Another stock in the same industry has had the following year end prices and
dividends:
Year
1
2
3
4
5
6
Price
$60.18
73.66
94.18
89.35
78.49
95.05
Dividend
$.60
.64
.72
.80
1.20
What are the arithmetic and geometric returns for the stock?
d. You buy a stock for $62.50 per share and hold it for one year. During the year, the
stock paid a dividend of $1.50 and the year-end stock price was $71.25. What was your
holding period return on the stock? Also, divide the return of the stock into its two
components: the dividend yield and the capital gains component.
e. Explain the three forms of market efficiency and its significance as it relates to
trading strategies.
Equations for Midterm
1.
FV = PV x (1+r)n
2.
PV = FV / [(1+r)n]
3.
r = [FV/PV]1/n – 1
4.
n = ln[FV/PV] / ln(1+r)
5.
FV of Annuity = C x [(1+r)n + 1]/r
6.
PV of Annuity = C x {1-[1/(1+r)n]}/r
7.
EAR = [1 + APR / m]m - 1 or EAR = e^APR – 1 for continuous compounding
8.
APR = m[(1 + EAR)1/ m - 1]
9.
1 - 1/(1+r)n
1
B0 = C ¾¾¾¾¾¾ + F ¾¾¾
r
(1+r)n
10.
Current Yield = annual coupon payment / current price
11.
% price change = [(end price - beg. price) / beg. price] x 100
12.
¥
P0 = å
t=1
Dt
D1
D2
D3
D4
¾¾¾ = ¾¾¾ + ¾¾¾ + ¾¾¾ + ¾¾¾ + ………….>
(1+r)t
(1+r)1
(1+r)2
(1+r)3
(1+r)4
13.
D0(1+g)
P0 = ¾¾¾
(r-g)
14.
r = (D1/P0) + g
15.
P0 = D / r for preferred stock, therefore, r = D / P0
16.
Total Return = ending price – beginning price + cash flow during period
beginning price
17.
Dividend yield = (dividend payments during period)/(beg. price of stock)
18.
Capital gains yield = (end price - beg. price) / beg. price
19.
Arithmetic mean = [ S Ri]/N
20.
Geometric mean = [(1+R1)(1+R2)(1+R3)…(1+Rn)]1/n - 1
21.
s2 =[ S {Ri – E(R)}2]/(N-1) for individual assets over N years
22.
Risk premium = Expected return – Risk free rate
=
D1
¾¾¾
(r-g)
Solutions:
1a.
FV=$10,072.68
1b.
FV=$10,413.56; $10,348.28
1c.
I/Y=9.59%
1d.
APR=9.65%; 9.53%
========================================
2a.
0.042%; 1.418%
2b.
$544.76
2c.
Annuity
2d.
PMT=$634.46
2e.
$1564.48
========================================
3a.
PV=$884.32
3b.
PV=883.66
3c.
PV=903.55
3d.
-15.74%
========================================
4a.
$54.66
4b.
$44.61
4c.
$30.91
4d.
$18.82
========================================
5a.
7.8%; 7.61%
5b.
7.01%
5c.
11.82%; 10.58%
5d.
Dividend yield=2.4%; Capital gains yield=14%; Return=16.4%