Institute of Health Management and Health Economics
Faculty of Medicine
University of Oslo
English
Institute of Health Management and Health Economics
University of Oslo
Written exam Monday12 June 2006
09.00-13.00
HME4303 Project evaluation and analysis of investment
decisions
Results will be available three weeks after the deadline, see the list on the
board outside the Institute of Health Management and Health Economics,
Forskningsveien 3. The results will also be posted on Studentweb.
The receiving day of the results is the day the results are posted on the board
outside the Institute. Appeals must be submitted within three weeks of this
date.
The written exam consists of 6 pages including this page. You will find the
formulas on the last 2 pages.
Exam resources:
Calculators are allowed at the written school exam.
Remember to write down your candidate number so that you have when the
results are made available.
1
PROBLEM 1
Bond A matures in three years from now, while Bond B matures in five years from now.
The annual coupon rate is 8% for Bond A and 4% for Bond B. The yield-to-maturity on
the two bonds is 6.0% for Bond A and 5.6% for Bond B.
a)
Find the price of each bond (as a percentage relative to face value).
Briefly explain why one of the bonds is priced above par while the other is priced
below par.
PROBLEM 2
As winner of a TV-talk show competition, you may choose one of the following prizes:
a. $ 100,000 now
b. $ 180,000 at the end of five years
c. $ 11,400 a year for ever (first pay out next year)
d. $ 19,000 for each of 10 years (first pay out next year)
e. $ 6,500 next year and increasing thereafter by 5 percent a year forever
Assuming an interest rate of 12 percent, which is the most valuable prize?
PROBLEM 3
You own an oil pipeline which will generate a $2 million cash return over the coming
year. The pipeline's operating costs are negligible, and the pipeline is expected to last for
a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows
are expected to decline by 4 percent per year. The discount rate is 10 percent.
a. What is the present value (PV) of the pipeline's cash flows if its cash flows are
assumed to last forever (although declining by 4 percent per year)?
b. What is the PV of the cash flows if the pipeline has to be scrapped after 20 years?
PROBLEM 4
The Pfizer stock is priced according to the dividend model with a perpetual constant
growth.
Dividend payments take place once a year, and the latest dividend payment has just been
made. One year ahead, the dividend is expected to be NOK 8, the required rate of return
on the stock is 13%, and the constant growth is 9%. The payout ratio is 0.4.
a)
Calculate the price of the stock, its P/E-ratio (P0/EPS1), and the company’s return
on equity.
b)
Calculate the present value of growth opportunities inherent in the stock price.
Explain your answer.
2
PROBLEM 5
The Gullit stock will either increase by 40% or decrease by 20% during the next period.
The Sølvgrå stock will either decrease by 10% or increase by 20%, and it goes up when
the Gullit stock goes down. Both outcomes have the same probability. The covariance
between stock returns is -0.045. You consider to invest a proportion a in the Gullit stock
and a proportion
1-a in the Sølvgrå stock.
a)
Calculate the correlation coefficient between stock returns.
Show in a diagram the relationship between expected return and standard
deviation of return for values of a in the interval 0 - 1.
Estimate the risk-minimizing position in the two stocks.
The information above is valid only for a given period. Based on several observations, it
turns
out that the beta-value of the Gullit stock is 0.8, while it is 0.2 for the Sølvgrå stock. The
risk-free rate of return is 6%, while the expected return on the market portfolio is 10%.
b)
Given that the expected return on each stock is as calculated under Question a),
and you base your answer on the Capital Asset Pricing Model (CAPM), which
stock would you recommend?
Explain your answer by making relevant calculations.
c) What is the security market line, (SML)?
PROBLEM 6
The Borstal Company has to choose between two machines (A and B) which do the same
job but have different life expectancies. A is expected to last three years, whereas B will
be worn out after 4 years. The two machines have the following expected costs:
Year
2000
2001
2002
2003
2004
Machine A
$40,000
10,000
10,000
10,000 + Replacement costs
Machine B
$50,000
8,000
8,000
8,000
8,000 + Replacement costs
The costs are expressed in real terms (2000-prices). The machines have no salvage
(scrapping) values.
a. Suppose you are Borstal's financial manager. If you had to buy one or the other
machine and rent it to your production manager for that machine's economic life
(3 or 4 years, respectively), what annual rental payment would you have to
charge? Assume a 6 percent real discount rate and ignore taxes.
3
b. Which machine should Borstal buy? Assume that the production will go on
indefinitely, and that Borstal has to stick to the machine type it chooses in the first
place)
c. The rents calculated in part (a) above are in real terms (2000-prices). If you
assume that inflation will be 8 percent annually, how much would you have to
charge each year in current prices?
PROBLEM 7
The board of Rikshospitalet University Hospital is discussing whether or not to invest in
a new Lasik Eye Surgery clinic. Some of their ophthalmologists specializing in eye
surgery have extra capacity, and a Lasik Eye Surgery clinic will potentially make some
extra money both for the surgeons and for the hospital.
The board has hired you as a financial consultant. Your task is to conduct a complete
project analysis on the project. The main question from the board is whether the project
will be profitable or not
Briefly explain how you will conduct such a task. What sort of information do you need ?
What sort of calculations will you perform ? What is important when defining cash flows
?
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Formulas
1

1
PV  C   
t 
 r r 1  r  
Annuity to year t:
Constant growth to year t:
Perpetuity with growth:
Perpetuity
:
Future Value:
From real to nominal interest:
rNom
1  g 
1 

1 r 
PV  C 
rg
C
PV 
rg
C
PV 
r
FV  PV  (1  r) t
= r Real (1+inf) + inf
t
Bond valuation:
100  rk
100

t
(1  r ) n
t 1 (1  r )
n
Price:
P0  
(given that 100 is the face
value)
Stock Valuation:
Price:
P0 
DIV1
rg

DIV1 
  ROE
g  1 
EPS
1


Growth in dividend:
P/E:
Growth opportunities:
P / E  P0 / EPS1 
DIV1 / EPS1
rg
EPS1
 PVGO
r
NPV1
PVGO 
rg
P0 
NPV1  ( EPS1  DIV1 ) 
( EPS1  DIV1 )  ROE
r
b
5
Other:
 12   1   2  12
Covariance or correlation:
Beta:
i 
 im
 m2
, or:  i   im 
CAPM :
ri  rf  (rm  rf )  i
WACC:
rA 
i
m
D
E
 rD   rE
V
V
Portfolio:
Expected return: rp  w  r1  (1  w)  r2
Variance:  2p  a 2  12  (1  a) 2   22  2  a  (1  a)  12
a=share of stock 1
1.
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