Cash flows
REAL vs. NOMINAL
Lecture for Corporate Finance
Ing. Tomáš Heryán, Ph.D.
Corporate Finance
FIU/BAFIK
Outline of the lecture
• Cash flows
• Real cash flows
• Real vs. nominal interest rate
• All these examples are from Seminar 02/03
Cash flows
Cash flow is the net amount of cash
and cash equivalents being
transferred into and out of a
business.
At the most fundamental level, a
company’s ability to create value for
shareholders is determined by its
ability to generate positive cash
flows, or more specifically,
maximize long-term free cash flow.
Cash flows for all periods are measured
in time 0 dollars and discounted using
the real discount rate i.e. a discount rate
which doesn't contain the effect of any
expected inflation.
If there is more than one cash flow
within some time period, future and
present value is calculated as a sum of its
particular compounded or discounted
values using next equation.
Saving the same amount 1/2
2. How much will you dispose if you deposit CZK 50,000 each year for 3 years? Your
account bears 4% p.a.
• A case with many years will solve an annuity.
Saving the same amount 2/2
6. Consider that you will deposit 7 thousand CZK and you intend to withdraw savings
after 6 years. What amount will you save if the interest rate is 3% p.a.
• A case with many years will solve an annuity.
Periods (n) can vary
3. What will your savings be if you save $ 100,000 next year and then in the third and
the fourth year if your interest is 3% p.a., but the interest is on a monthly basis?
• Always be careful of small n! ☺ 2020-2040?
Do not forget what You have already learned
4. Consider continuous compounding. What will be the value of CZK 20,000 that you
deposit into this savings account in following two years? The interest is 2% p.a.
• The Euler number 2.718 ☺
Example of nominal cash flows
8. You intend to travel to Canada for a whole year and assume that you will be able to
save 30,000 next year to cover the costs. CZK, following year 45 thousand CZK and at
the end of the third year it will be 60 thousand CZK. What will be your pre-flight
savings if the account bears 5% p.a.
• Just combination of future values compounding, however, the last
year is NOT compounded.
Typical case of cash flows (bonds)
5. How would you pay for the bond? The nominal value is CZK 2,000; the expected
yield is 9%; coupon payment 8%; and the bond is payable in 3 years.
• Fixed coupon.
Coupon do not have to be always fixed
7. You are offered to purchase a bond with a nominal value of CZK 1,500 with a
maturity of three years, with the yields in individual years being: CZK 250, CZK 320
and after the third year CZK 410. Will you be willing to buy the bond for 2000 CZK
when the alternative investment cost is 8%?
• Variable coupons within bonds.
• Please, be careful of buying or selling this particular bond.
Real cash flows
Real value is defined only within
conditions in which inflation exists.
If there is not any inflation, then
nominal interest rate will be the
same as real one.
Rate of inflation is the rate at which
the general level of prices for goods
and services is rising, and
subsequently, purchasing power of
money is falling.
It means that for the same money kept at
home it is not possible to buy the same
amount of goods and services in future
in case of positive inflation rate.
Prices could decrease too. In this case we
speak about deflation. In connection
with the inflation real value of cash flow
(Cr) is defined under inflation (π),
equation below. Rate of inflation is
measured and reported on the webpage
of the Czech Statistical Office.
Inflation – CPI
Various numbers are often given
to express the inflation rate using a
consumer price index, which,
though different is correct. The
period for which the inflation rate is
indicated (the reference period) and
the base period, which the reference
period is compared with, should be
mentioned unambiguously.
* Inflation rate as an increase
in CPI compared with the
corresponding month of the
preceding year characterizes the
percentage change comparing the
price level in the reference month
of a given year with the
corresponding month of the
preceding year.
Inflation – PPI
The prices of industrial producers
are surveyed monthly on the basis
of data provided by the selected
organizations (about 1200) for the
selected representatives (about
4800). The reported prices are those
agreed upon between the supplier
and the customer inland. They
exclude VAT, excise tax, costs of
transport to the customer and costs
incidental to the transport, and are
invoiced for the more important
trade cases.
The industrial producer price
index is calculated from the
reported prices using constant
weights. The index measures the
average trend in prices of all
industrial products produced and
sold in the domestic, Czech market.
Real values
1. Calculate the real interest rate on deposits under the following conditions:
a) the interest rate shall be 2,5%, the inflation rate shall be 1,7%.
b) the interest rate is 2.3%, the inflation rate is 2.9%.
• Be careful whether or not the inflation is higher than nominal interest rate.
Using a real FV
3. What is the real value of a deposit of CZK 42,000 over 3 years at an interest rate of
4.5% and an inflation rate of 1.3%?
• It is always necessary to thing about the inflation in the real world ☺
The basic questions remains PV/FV?
5. In 15 years, you want to dispose of CZK 1 million. The nominal interest rate is
5.8% p.a. and the inflation rate is 3.4%.
a) How much do you have to deposit?
b) What will be the fair value of CZK 1 million after 15 years if you have them at
home?
• Use the right formulae even if the money are left below a pillow ☺
Discount rates
In economics and finance, the term
"discount rate" could mean one of
two things, depending on context.
On the one hand, it is the interest
rate at which an agent discounts
future events in preferences in a
multi-period model, which can be
contrasted with the phrase discount
factor.
On the other, it means the rate at
which commercial banks can
borrow from the central bank.
In the United States, the U.S. Federal
Reserve controls the discount rate, which
is the interest rate for the Federal
Reserve charges commercial banks on
loans they receive. The Federal Reserve's
discount rate is broken into three
discount window programs: primary
credit, secondary credit, and season
credit, each with its own interest rate.
Primary credit programs are reserved for
commercial banks in high standings with
the Reserve as these loans are typically
only given for a very short time
(typically overnight).
Czech National Bank interest rates
Czech National Bank rates
The main monetary policy instrument takes the
form of repo tenders. The CNB accepts surplus
liquidity from banks and in return transfers
eligible securities to them as collateral.
The two parties agree to reverse the transaction
at a future point in time, when the CNB as
borrower repays the principal of the loan plus
interest and the creditor bank returns the
collateral to the CNB.
The basic duration of these operations is 14 days;
the two-week repo rate (2W repo rate) is
therefore considered to be of key importance in
terms of monetary policy.
Better to discount 10Y bond yields
PRIBOR
The PRIBOR benchmark is defined as the
average interest rate at which unsecured CZK
funds are offered by Panel Banks in the interbank
market, just prior to 11:00am local time.
PRIBOR has been deemed an 'Interest Rate
Benchmark' by the CFBF (Czech Financial
Benchmark Facility), as it is determined on the
basis of the rate at which banks may lend to other
banks in the money market.
Real case within a Czech bank
6. We want to dispose of a real amount of CZK 550,000 over 25 years. The nominal
interest rate is 2.3% p.a. and the inflation rate is 3.1%. How much do you have to
deposit today?
• Rather use the money for a business or an investment.
Inflation over a long-term period
7. How much will be a purchasing power of CZK 1 million in 30 years be expected if
inflation is expected to be 5% per year?
• Further, there is even not any insurance for such a deposit at home.
Differentiate between types of interest rates
8. Calculate the nominal interest rate if the inflation rate is 2.8% and the real interest
rate is 0.8%.
• If You know the real interest rate You cannot calculate a real one again ☺
From the business world
9. Calculate the real interest rate if you get CZK 1,115 at the end of the year for CZK
1,000 received for the sale of goods and the price of the goods has risen to CZK 1,095.
• Try to use Your logic to solve this example
Literature
1) Seminar 02/03 Examples
2) ROSS, S. A., R. W. WESTERFIELD, J. JAFFE & B. D. JORDAN, 2019. Valuation
and Capital Budgeting. In: Corporate Finance, PART II, pp. 85-298. ISBN 978-1-
260-09187-8.
3) BERK, J. & P. DeMARZO, 2017. The Time Value of Money. In: Corporate
Finance, Chap. 4, pp. 130-174. ISBN 978-1-292-16016-0.
• Have You already bought Your own calculator ?? ☺
Thank you for
your attention!
☺