Tutorial Sheet 1.1 Time Value of Money Flashcards
interest rates (r) can be thought of as:
▪ the … or the … an investor must receive to accept the investment;
▪ the discount rate of a cashflow in order to…;
▪ the … or the value an investor forgoes by …
required rate of return; minimum rate
compute the present value of an investment
opportunity cost; choosing a particular investment.
Interest rates are set in the market by …
From an investors’ perspective, the interest rate can be decomposed as follows:
𝒓 = … (sum of 5 items)
supply and demand of funds from investors and borrowers
𝑹𝒆𝒂𝒍 𝒓𝒊𝒔𝒌 𝒇𝒓𝒆𝒆 𝒊𝒏𝒕𝒆𝒓𝒆𝒔𝒕 𝒓𝒂𝒕𝒆 + 𝑰𝒏𝒇𝒍𝒂𝒕𝒊𝒐𝒏 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 +𝑫𝒆𝒇𝒂𝒖𝒍𝒕 𝒓𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 + 𝑳𝒊𝒒𝒖𝒊𝒅𝒊𝒕𝒚 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 + 𝑴𝒂𝒕𝒖𝒓𝒊𝒕𝒚 𝒑𝒓𝒆𝒎𝒊𝒖𝒎
The real risk-free interest rate captures the …
▪ The inflation premium captures the… the purchasing power of a unit of currency.
For example, spending €1 today is as attractive as spending € (1 + Rreal) in one year with no inflation.
However, you need €(1 + I) in one year to get € 1 of today’s spending power.
The nominal risk-free interest rate (Rnominal) combines the …. It holds:
** (= Fisher Equation)
▪ The … captures the possibility that the borrower will fail to fulfil a promised payment.
▪ The liquidity premium captures the risk of …
▪ The … captures the compensation for investing in securities with different maturity dates.
investor’s time preference of current versus future real consumption
expected inflation which reduces; real risk-free rate and the inflation premium
Fisher equation: 1 + nominal rate = (1 + inflation premium) * (1 + real rate)
default risk premium
loss due to the impossibility of converting an investment quickly into cash.
maturity premium
▪ Discounting and Compounding build the foundation for the time value of money concept and make…
▪ For a single cash flow, it describes the relationship between an initial investment or present value (PV), which earns a rate of return (r), and …
Going forward in time: *(1+r)
Going backwards in time: /(1+r)
cash flows occurring at different points in time comparable for investment decisions
its future value (FV), which will be received n periods from today.
Note: the … must be defined in the same time units (e.g., months, quarters, years, etc.)
Compounding factor:
Discounting factor:
stated interest rate and the number of compounding periods
(1+r)^n
1/(1+r)^n
FV = CF * (1+ (r/m))^(m*n)
PV = ….
As m -> infinity, i.e. continuous compounding,
FV =
PV =
Therefore, the stated (annual) rate “r” can deviate significantly from the effective annual rate (EAR):
EAR = …
With continuous compounding, EAR = e^r -1
CFt / (1+(r/m))^(m*n)
m frequency of compounding
n compounding period
FV = CF * e^rn
PV = CF / e^rn
(1+(r/m))^m -1
Other types of Cash Flows: Perpetuity and Annuity
A perpetuity is a … starting in one year and continuing forever
Perpetuity valuation formula:
promised series of constant payments (x)
PVp = x/r = Cash payment/ r
An annuity is a promised series of …
▪ The PV of an annuity could be simply computed by …
▪ Since an annuity is equivalent to receiving a perpetuity in t=0 and paying a perpetuity in t=n
&
▪ the value of a perpetuity starting in t=n is the value of a perpetuity starting in t=0 discounted for n years, we can use…
constant payments (x) starting in one year and continuing for n years
summing the present values of each payment
𝑷𝑽𝑨=(x/r) - ((x/r)*(1+r)^-n)
A perpetuity with geometric progression is a promised series of constant payments (x) starting in one year and continuing forever where each …(e.g. growth rate or inflation rate).
preceding payment is increased by a fixed number
Check slide 20 for formulae and maybe write them down in a formula sheet
