Masters Program Business Informatics. 2006/2007.
MBI-4
Financial Management.
Submodule Finance.
Sample examination.
MIDTERM EXAMINATION.
Time allowed: 3 hours.
December 20th 2006, 14.00 – 17.00
During the exam, students are allowed to make use of:
1. A formula sheet, handed out separately.
2. A – financial – scientific calculator without programming facilities.
3. Scrap paper.
Passing on calculators, formula sheets or scrap paper is NOT allowed.
Please don’t detach the pages ( except the formula-sheet ).
Students name: standard solution.
Exam number:………………………..
MBI-4 Course Financial Management, part Finance. Midterm examination.
1
Problem 1. On qualitative issues. ( 20 points ) Each correct answer 1 point.
Read this before you answer the questions.
Below follow 20 statements. Indicate by encircling the proper answer whether, according to
the materials studied, that statement is correct (TRUE) or incorrect (FALSE). When the right
answer has been indicated, 1 point will be rewarded. However, if the given answer is not
right, 1 point will be deducted. When you are too uncertain about the answer and are reluctant
to gamble, encircle NA ( no answer ). Such an answer scores zero.
a. When performing financial analysis, Accounting focuses on market
values and future events, whereas Finance emphasizes bookvalues
and accountability regarding past events.
b. Many firms have devised defences that make it much more costly
or difficult for other firms to take them over. This poses an important
agency problem to the shareholders, because it is likely that the
management of such a firm will not pursue the maximization of
shareholder’s wealth.
c. Changing a firm’s working capital policy by additionally investing
in inventories and accounts receivable will influence that firm’s cash
flow in a negative way.
d. A firm’s equity capital consists generally of accounts payable, bank
loans, bonds and mortgage loans on the firm’s property. The main
characteristic of equity is, that an annual interest is to be paid.
e. Assume an APR ( annual percentage rate ) of a car loan is 12 %. If
payments on this loan are made quarterly, the effective annual interest
rate will be lower than 12 %.
f. The accounting department of a firm makes financial forecasts on
behalf of a 5-years investment plan using future costs and revenues
measured in prices of constant dollars. In other words: in prices of
today! When such estimations have to be discounted, a real interest
rate MUST be used.
g. A couple of years ago an investor bought a 3 % 10 years euro
denominated treasury bond with a face value of € 1,000. On
December 30 2006 Mr Trichet, President of the European Central
Bank, announces a one percent increase of the Euro interest rate to
4 %. All bond prices fall. When no further interest increases occur
during 2007, the yield-to-maturity on the investor’s bond in 2007 will
be lower than 4 %.
h. A zero-coupon bond doesn’t pay interest during its lifetime. It is
simply paying out the face value at maturity date. This implies that
the yield-to-maturity of such a bond is zero until the year that the
bond will mature.
i. According to the discounted dividend model of stock valuation, the
price-earnings ratio of a so-called growth stock will be equal to that of
a so-called income stock if the net income per share of both types of
stock is equal, as well as the risk involved.
j. Economists often refer to the stock market as an efficient market.
The semi-strong form efficiency assumes that stock prices reflect all
available public information. This implies that it is impossible to earn
consistently superior returns by analysing annual reports.
FALSE
TRUE
TRUE
FALSE
FALSE
TRUE
FALSE
FALSE
FALSE
TRUE
MBI-4 Course Financial Management, part Finance. Midterm examination.
2
k. A share of stock paying no dividends at all should be priced lower
than a comparable stock – regarding earnings and risk – that always
applies a pay-out ratio of 40 %
l. In answering the question whether an investment project is
profitable, the Net Present Value Rule is consistent with the Internal
Rate of Return rule. In other words: when the Net Present Value of a
project is negative, its Internal Rate of Return is negative as well.
m. The Profitability Index is an investment criterion that determines
in an unambiguous way which project should be chosen by ranking
mutual exclusive projects in a capital rationing context.
n. A project has a life of 5 years and a pay-back period of 5 years.
This implies that – given a positive discount rate – this project will be
rejected if the Net Present Value rule is applied.
o. When determining the incremental cash flow of an investment
proposal, sunk cost should be disregarded, but indirect effects and
opportunity costs will be accounted for.
p. It is likely that the economic break-even point of a newly
introduced product is larger than the accounting break-even point,
assuming all other data being equal.
q. The total risk of a stock’s return can be broken down in market risk
and unique risk. When added to a portfolio it is likely that the unique
risk will be eliminated, at least partially. This diversification effect
will depend on mutual correlation of the returns of the stock in that
portfolio.
r. The beta of a stock can be negative, zero or positive. It can be
smaller than –1 and larger than + 1. When the correlation of the return
of that stock with the return of the Market Portfolio falls, the beta will
drop as well.
s. Some firms are using the WACC – weighted average cost of capital
– as the discount rate when assessing the acceptability of investment
proposals. This is a correct procedure on the condition that the risk of
the project equals that of the total firm, regardless the way that project
will be financed.
t. The Modigliani-Miller Theorems state, that in a world without taxes
the value of a company rises when additional debt is taken on, but in a
world with taxation that company value will drop with more debt
because of the interest payments.
FALSE
FALSE
FALSE
TRUE
TRUE
TRUE
TRUE
TRUE
MBI-4 Course Financial Management, part Finance. Midterm examination.
FALSE
FALSE
3
Problem 2. On time-value-of-money. ( 8 points )
A young couple, well aware of finance, are planning their retirement early. All amounts are
forecasted in current purchasing power. The appropriate discount rate to be used is 5 percent
per year.
They are planning to retire in 40 years from now. At the day of retirement, they plan to sell
their own house, that will generate € 1,500,000. From that revenue they have to redeem a
mortgage of € 350,000. Then they intend to move to Spain and rent a comfortable apartment.
They expect that the total annual cost of living – including rent – will be € 125,000.
However, in order to sell their house for the foreseen revenue, a major overhaul has to be
executed after 20 years from now at an expected cost of € 250,000.
They expect to live in Spain another 20 years.
a. How much money do they need to have available in a pension savings fund in order to
cope with the cost of living after 40 years from now? Consider the net revenue from
the sale of their house as the final payment into that fund. Assume that the couple will
have no other sources of income from the moment of retirement onwards and that the
annual cost of living must be available at the beginning of each year.
Determine cost of living at t40 using PVA due:
125,000 * (1 – 1.05-20 )/0.05 * 1.05 =
minus net revenue house sale 1,500,000 – 350,000 =
to be saved prior to retiring
1,635,665
1,150,000
485,665
4 points
The couple plans to save a fixed amount of money at the end of each of the following 40
years, covering the fund determined in question a) as well as the cost of overhaul of their
house.
b. Determine the amount of the annual savings needed.
Determine present value of future expenses using PV
Pension fund 485,665 * (1.05)-40
=
68,987
Overhaul 250,000 * (1.05)-20
=
94,222
total
163,209
Determine the associated annual savings deposit using PVA:
163,209 / [ ( 1 – 1.05-40 )/ 0.05 ] = 9,511.52
Of course equivalent amounts could have computed at t40, using FVA to find the annual
savings deposit amount.
4 points
MBI-4 Course Financial Management, part Finance. Midterm examination.
4
Problem 3. On bonds. ( 8 points).
Three years ago an investor bought a bond with a face value of € 10,000 and an annual
coupon rate of 6 % with a maturity of 10 years.
Last year the required market interest rate on this kind of bonds fell to 5 % per year.
At the first of January 2007, the most recent coupon just being paid out, a lifetime of 7 years
is remaining. During the whole year 2007 a yield-to-maturity of 5 % could be expected.
a. Determine the market value of this bond on 01-01-2007.
10,000 / (1.05)7
= 7,106.81
600 * [ 1 – (1.05)-7 ]/0.05 = 3,471,82
value is
10,578.63
2.5 points
b. Determine the market value of this bond on 12-31-2007, the last coupon just being
paid out.
10,000 / (1.05)6
= 7,462,15
-6
600 * [ 1 – (1.05) ]/0.05 = 3,045.42
value is
10,507.57
2.5 points
c. Show by computation that the total annual return of this bond in 2007 equals the
market required yield-to-maturity.
Interest return plus/minus capital gain/loss:
{ 600 + (10,507.57 – 10,578.63 )} / 10,578.63 * 100 % = 5 %
3 points
MBI-4 Course Financial Management, part Finance. Midterm examination.
5
Problem 4. On cash flow determination. ( 8 points ).
Complete the schedule below according to the following data. Prepare firstly on scrap paper
and then fill in the schedule. No additional schedules can be handed out!
A firm considers to replace its packaging machine currently in use. That old machine has a
fiscal book value of € 30, to be depreciated straight-line over its remaining life time of 3
years, no salvage value expected. It can be sold now on the second hand market for € 25.
A new machine costs € 70 with an expected salvage value of € 10. This machine will have a
lifetime of 3 years and be depreciated straight-line to its salvage value. Then the machine will
be sold.
If the new machine is introduced, the old machine is redundant. Because of the quality of the
new machine, revenues can be increased from € 120 with € 40 up to € 160 each of the next 3
years. However, annual operating cost will rise as well, expectedly with € 10.
A change of net working capital is expected as well. The net working capital is 30 % of sales,
which will also be the case concerning the additional revenues. The net working capital must
be available at the beginning of the year. All of this working capital will be recovered at the
end of the lifetime of the machine. The income of this company is taxed at a rate of 20 %.
The cost of capital of this firm is 10 % per year. All amounts above are in € 1,000.
Notice: the computation of the Net Present Value is NOT required in this problem.
Cash flow schedule investment in a new packaging machine.
Points in red
Revenue increase 1
Cost increase 1
Depreciation increase 1
EBIT increase
Tax increase 1
Net income change
Add back depreciation 1
Sale old machine 0.5
Tax refund on loss 0.5
Investment 0.5
salvage value 0.5
Increase NWC 0.5
Recovery NWC 0.5
CASH FLOW
T0
T1
T2
40
-10
-10
20
-4
16
10
T3
40
-10
-10
20
-4
16
10
40
-10
-10
20
-4
16
10
25
1
- 70
10
- 12
12
- 56
26
26
48
If finance costs are included: - 1
point
T0 is the moment of investment at the start of the first year. T1,2,3 are the end of the first,
second and third year of operations.
Notice: Perhaps you don’t need all the lines of the schedule!
MBI-4 Course Financial Management, part Finance. Midterm examination.
6
Problem 5. On capital budgeting. ( 8 points )
A company considers to invest in a project A, generating following cash flows:
Investment cash flow start of year 1
- 56
Cash flow end of year 1
+ 26
Cash flow end of year 2
+ 26
Cash flow end of year 3
+ 48
The opportunity costs of this firm, the cost of capital, are 15 % per year
.
a) Determine the Net Present Value of this project A and conclude whether this project
would be accepted or not.
- 56 + 26/1.15 + 26 / (1.15)2 + 48 / (1.15)3 = 17.83
3 points
The accountant of this company states, that the Internal Rate of Return of project A is about
31.4 %.
b) Is that correct? Could you prove your answer?
yes, correct:
2 points
- 56 + 26 / 1.314 + 26 / (1.314)2 + 48 / (1.314)3 approaches 0
The company could invest in a Project B as well, which also requires an investment of 56 but
only generates a cash flow of + 76 at the end of year 1 and nothing afterwards.
c) Determine the Net Present Value and the Internal Rate of Return of project B.
NPV:
IRR ;
76 / 1.15 – 56 = 10.09
76/56 – 1 = 0.357 = 35.7 %
2 points
d) If investment funds are limited and both projects are mutual exclusive, yet this
year being the only possibility to take them on, what project would be preferred ? Why?
Actually it depends on the NPV of projects that can be taken on at t1 and/or t2 by the cash
flow differences of the projects. Ignoring that consideration, use Profitability Index of A
being 17.83/56 compared to PI of B that is 10.09/ 56 , deciding on A.
1 point
MBI-4 Course Financial Management, part Finance. Midterm examination.
7
Problem 6. On different lifetimes. ( 4 points ).
In order to perform some special operations a firm could rent a machine for a period of three
years for an annual payment of € 20,000 at the end of each year. The contract cannot be
dissolved during its life. At this moment it is not certain at all if the rent can be extended
afterwards. But if that would be the case, it will certainly be more expensive. Spare parts and
maintenance will be provided by the owner of this machine.
There is however an alternative available: a similar machine can be purchased. The
investment will cost € 50,000 and the machine has a lifetime of 5 years after which its
residual value is zero. The operating costs ( spare parts and maintenance ) have to be paid by
the firm itself and are estimated at € 10,000 per year at the end of each of the first 4 years of
usage.
The cost of capital of this firm are 12 % per year and enough funds for investment are
available.
Determine what – from a financial point of view – would be the decision: buy or rent ? As the
firm has a contract to deliver products that require these operations, either of the alternatives
above have to be chosen.
Recognize the element of different lifetimes and use the model available for solving this
type of problems.
Use the Equivalent Annual Cost method:
Renting option:
20,000 per year
Buying option:
PV operating costs 10,000 * [ 1 – ( 1.12 )-4 ] / 0.12 = 30,373
Investment
50,000
80,737
EAC is 80,737 / { [1 – ( 1.12 )-5 ] / 0.12 } = 22,296
Rent is cheaper, and when that rises in three years above the amount of EAC with buying,
decide for purchase.
4 points
MBI-4 Course Financial Management, part Finance. Midterm examination.
8
Problem 7. On valuation of common stock. ( 5 points )
Use when answering following questions the discounted dividend model.
Alpha Supermarket Ltd. is expected to earn a constant Earnings per Share of € 25 per year.
Its pay-out ratio has been, and will be in the future 100 %.
The stock market requires an annual return of 20 % on stocks with the risk characteristics of
Alpha.
No change in the operations and policies of Alpha is expected.
a) Determine the market price of one share of common stock of Alpha.
25 / 0.2 = 125
1 point
Zeta Supermarket Ltd. has exactly the same characteristics as Alpha concerning sales, costs,
profitability, investments and risk . It also earned € 25 per share during the last year.
However there is one difference: Zeta retains 40 % of its earnings and is able to reinvest it at a
rate of return of 25 % per year. This is expected to last forever.
b) Compute the next year’s expected dividend per share of Zeta.
Determine growth rate: 0.4 * 0.25 = 0.1
1 point
Next year’s dividend: (1 – 0.4)* 25 * (1.1) = 16.50 1 point
c) Now determine the current market price of one share of common stock of Zeta.
16.50 / ( 0.2 – 0.1 ) = 165
1 point
d) Compute the price-earnings ratio for both companies and explain the reason of the
( possible ) difference of the ratios.
Alpha 125/ 25 = 5
Zeta 165/25 = 6.6
caused by the PV of growth opportunities realized by Zeta through retaining earnings.
1 point
MBI-4 Course Financial Management, part Finance. Midterm examination.
9
Problem 8. On portfolios and the CAPM. ( 5 points )
In the textbook ( as well as in class ) an empirical study has been discussed, that shows that
when more different stocks are added to a portfolio of risky assets, the risk of the portfolio is
expected to decrease.
Answer following questions briefly; up to five words will be sufficient.
a. What investor’s strategy is this study describing? And what kind of risk can be reduced ?
Diversification: reduction of unsystematic ( company-specific, unique ) risk. 1 point
b. What property of the portfolio’s assets are causing the decrease of the portfolio’s risk ?
mutual correlation of the returns of the assets. 1 point
c. In what specific situation could the risk of a portfolio, consisting of two risky assets,
completely be eliminated?
when the correlation coefficient of the returns of these assets are – 1.
1 point
d. Regression analysis shows, that in a stock market, where CAPM-equilibrium is assumed,
the risk-free rate being 5 %, an increase of the Market Portfolio’s return from 11 % to
13 % is associated with an increase of the return of a stock X from 8 % to 9 %.
What is the size of the Beta ( β ) of stock X ?
( 9 – 8 ) / ( 13 – 11 ) = 0.5
1 point
e. Draw in the graph below precisely the Security Market Line, when the risk-free rate is 5 %
and the Market Portfolio has a return of 11 %.
11%
5%
0
1
2
risk
1 point
MBI-4 Course Financial Management, part Finance. Midterm examination.
10
Problem 9. On the Weighted Average Cost of Capital. ( 4 points )
The capital structure of a firm only consists of Equity and Perpetual Bonds. The recently
published balance sheet shows ( at book-value of course ! )
Equity: Paid-in capital, 1 million shares @ € 20
Retained earnings
8 % Perpetual bonds, 500,000 at € 100 par value
20,000,000
30,000,000
50,000,000
The current market price of one share of stock of this company is € 60. The beta of this stock
is 0.8. The Stock Market Portfolio index shows a risk premium of 10 %. The risk-free rate of
return is currently 4 %. The bond market is now requiring a yield-to-maturity of 5 % for
perpetual bonds with the risk profile similar to this company’s. The income of this company is
taxed at a rate of 30 %.
a. Compute the current market value of the firm’s equity capital.
1,000,000 * 60 = 60,000,000
1 point
b. Compute the current market value of the firm’s bonds.
( 0.08 * 50,000,000 )/ 0.05 = 80,000,000
1 point
c. Determine the firm’s cost of equity ( expressed in a percentage ! )
4 % + 10 % * 0.8 = 12 %
1 point
d. Compute the firm’s Weighted Average Cost of Capital ( expressed in a percentage ! )
(1 – 0.3)* 0.05 * (80/140) + 0.12* (60/140) = 0.0714= 7.14 %
1 point
end of examination
MBI-4 Course Financial Management, part Finance. Midterm examination.
11
Formula-sheet. It is allowed to detach this page from the exam form.
FV = CF0 * ( 1 + r )t
single payment CF
CFt
PV = (1  r ) t
single payment CF
PV perpetuity = CF1 / r
PV growth perpetuity = CF1 / ( r – g ) if g < r
1
r
PV A  C  
1
r (1  r )t



annuity C ,present value
Or: PV A = C1 * [ 1 – ( 1 + r )-t ] / r
FV A = C1*[ ( 1 + r )t – 1 ] / r
annuity C ,future value
[ When annuity due: multiply factors with ( 1 + r ). ]
Annual effective rate: ( 1 + APR/n )n - 1
Required return asset i = rf + ( rm - rf ) * βi from CAPM
re = Dt / Pt-1 + [ Pt – Pt-1] / Pt-1 return on ( stock ) investment
g = re * plowback ratio
pay-out ratio = 1 – plow-back ratio
re = ra + ( ra – rd )* (D/E)
from leverage
WACC = re* [E/(D + E )] + (1 – T)*rd* [D/(D + E)]
Tax shield of debt = T*D
portfolio = Wa*a + Wb*b composite portfolio risk
E ( rp ) = Wa * E ( ra ) + ( 1 – Wa ) * E ( rb ) 2-asset portfolio return
P0 = D1 / re
value income stock
P0 = D1 / ( re - g ) value growth stock
MBI-4 Course Financial Management, part Finance. Midterm examination.
12