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CAPITAL MARKETS
TRUE OR FALSE STATEMENTS
1. The higher the interest rate is, the larger the present value of a future yield is.
2. The present value of perpetuity cannot be calculated.
3. The price of the land is an external factor.
4. A future investment’s present value is determined by the market price.
5. It is worth to invest, if the expected gross yield exceeds the investment cost.
PROBLEMS
1. The Alumni of Miskolc Club decided to establish a foundation, to support the 5 best graduates
with 100 thousand forint each. The interest rate is 8 percent.
a.)
What deposit before one year of graduation does enable to pay a one time support?
b.)
What deposit before one year of graduation does enable to pay continually?
c.)
What equal deposits will be needed if the first payment is only after 5 years?
2. The Human Bank wants to establish a foundation in order to support well educated economics
students. The foundation plans to give the first subsidies, 100-100 thousand forints for 6
students, after 3 years. The interest rate is 6,5 percent.
a.)
What deposit from today does enable to pay the support continually after three
years?
b.)
What a sum of money is needed to a one time support?
3. An investment provides 1400 thousand forints per year for each of the next 4 years. The initial
cost of the investment is 4000 thousand. From this the owner’s own resource is 1000
thousand, the rest is bank loan for 4 years with 13 percent lending rate. The bank rate is 9
percent.
a.)
Can the owner pay back the loan?
b.)
What is the present value of the future profits?
c.)
What is the real cost of the investment?
4. You have to decide about a plant’s rent. The rent is 2 million forints. To pay, you have to
borrow the money for 4 years with 15 percent lending rate. The plant’s gross yield can reach
2,6 million forints in the next five years, 75 percent from it is cost.
a.)
What is the cost of the investment?
b.)
Is it worth to rent, if the bank rate is 10 percent?
5. An entrepreneur wants to buy his previous workplace (a newsagent’s). The cost is 3 million
forints. He wants to finance it from bank loan. He can choose a 3-year loan with 16 percent
interest rate or he can pay back 1 million in every year (three times). In this case the lending
rate is 20 percent. The expected yield is 1,5 million per year. Interest rate is 10 percent.
a.)
Which loan would you choose?
b.)
Is it worth to start the business?
6. An entrepreneur buys a mine and starts his mushroom growing business. The price of the
mine is 10 million forint, the entrepreneur has the money. The starting cost is 2 million, which
will be a bank loan with 40 percent interest rate for 2 years. He has to pay back the money and
the interest rate at the end of the second year. The revenue is 1,6 million in the first year, 2
million in the second, and 2,5 million after that. From the third year the entrepreneur has to
spend 7 hundred forint per year.
a) Can the entrepreneur pay back the bank loan, if the interest rate is 25 percent?
b) Is it worth to invest?
7. The expected yield of an investment is 1,1 million forint in the first year, 1,2 in the second. In
the third and after that 1,25 million forint, but from the fourth year 20 percent of the gross
yield has to be spent on modernisation of the machines. The price is 6 million forint. Twothird of the sum is missing, but available through a loan with 15 percent interest rate for 4
years.
a.)
Can the entrepreneur pay back, if the bank loan is 10 percent?
b.)
What is the present value of the future profits?
c.)
Which yield from the fourth year makes the interest rate equal to internal rate of
return?
8. An entrepreneur would like to rent a restaurant. The leasehold for 5 years is 5 million forint
(he has to pay in advance). The entrepreneur has half of the money. The other part would be a
bank loan. He can choose from two conditions: he can pay back in two equal terms in the end
of the 2nd and the 3rd years with 15 percent interest rate, or he can pay back in one sum in the
end of the 3rd year with 12 percent interest rate. The yield of the restaurant is expected to
reach the one million per year in the next 7 years. Interest rate is 8 percent.
a.)
Which loan would you choose?
b.)
Is it worth to rent the restaurant?
9. The grandparents of a freshman give 600 thousand forints on condition that he is allowed to
spend it only after graduating. He can deposit the money in a savings account with 7,5 percent
interest rate. He can choose other investments, for example government securities with 6,5
percent interest rate, where 20 percent of the deposit will be tax allowance in the first year. An
investment counsellor’s would pay back the loan in 160 thousand forint instalments in the
next four years.
a) Which solutions would you choose?
SOLUTIONS
1. a) One time support: 462,9 thousand Ft. b) Continual support: 6250 thousand Ft. c)
1065,6/year.
2. a) Continual support 8138,4 thousand Ft. b) One time support 496,7 thousand Ft.
3. a) He can pay back. b) PVyield: 4,536 million Ft. c) It is worth to invest (NPV=0,074).
4. a) 2,389 million forint. b) No (PVyield=2,06 million Ft).
5. a) The first loan is cheaper (PVloan1=3,51; PVloan2=3,8) b) It is worth to start (PVyield= 3,73 is
larger than the costs of the business).
6. a) He can pay back (PVloan=2,5, PVyield1-2=2,56). b) No (PVyield= 7,168, NPV=-5,3408).
7. a) He cannot pay back (PVloan=4,778, PVyield1-4=3,614). b) 10,44. c) Required yield:
0,512/year.
8. The 2nd loan is cheaper (PVloan1=2,9; PVloan2=2,78). It is not worth to rent (the present value of
the yields is 5,17, the costs 5,28.
9. The second. (PVA=600; PVB=684,24; PVC=535,89).