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Samenvatting - Ondernemingsfinanciering (CHAPTER 2 - Financiële algebra)
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KU Leuven Campus Brussel - Schakelprogramma Handelswetenschappen - Ondernemingsfinanciering - CHAPTER 2: Financiële algebra
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Inhoudsopgave1 Enkelvoudige versus samengestelde interest ........................................................................ 2
2 Meerdere verdisconteringsperioden..................................................................................... 2
3 Huidige waarde van een stroom van kasstromen .................................................................. 3
4 Net present value rule.......................................................................................................... 3
5 Rate of return rule ............................................................................................................... 3
6 Moeten we rekening houden met veranderende rentetarieven ............................................ 4
7 Special cash flow streams: annuities and perpetuities ........................................................... 4
7.1 Annuïteit ................................................................................................................................ 4
7.2 Perpetuïteit............................................................................................................................ 5
7.3 Tweestappenmodellen: Combinatie annuïteit + groeiende perpetuïteit ............................. 6
CHAPTER 2: FINANCIAL ALGEBRA 1 van 6
, CHAPTER 2: Financiële algebra
1 Enkelvoudige versus samengestelde interest
- Simple interest: FV = PV × (1 + r × t) discount factor = present
Lineaire functie value van 1 euro in jaar 𝑡
1 aan rate 𝑟
- Compound interest: FV = PV × (1 + r)𝑡 ⟺ 𝑃𝑉 = 𝐹𝑉 × (1+r)𝑡
Exponentiële functie
bv. What is the future value of 100 euro if interest is compounded annually at a rate of 7% for 2 years?
100 × (1 + 0,07)2 = 114,49
bv. What is the present value of 300 euro you get in 6 years when the annual interest rate is 4%?
1
300 × 1,04 6 = 237,09
2 Meerdere verdisconteringsperioden
𝒓 𝒓 𝒓𝒆𝒇𝒇
𝒎 𝑭𝑽 (real = effective =
(nominal interest rate
(aantal periodes per jaar) 𝒎 (waarde van € 1 in één jaar) annually compounded
= APR) (periodieke interest rate)
rate)
6% 1 6% 1,06 6%
6% 2 3% 1,032 = 1,0609 6,090 %
6% 4 1,5 % 1,0154 = 1,0609 6,136 %
6% 12 0,5 % 1,00512 = 1,06168 6,168 %
6% 52 0,1154 % 1,0115452 = 1,06180 6,180 %
6% 365 0,0164 % 1,000164365 = 1,06183 6,183 %
= periodieke interest rate
𝐴𝑃𝑅 𝑚
- Multiple discounting periods: 𝑟𝑒𝑓𝑓 = (1 + 𝑚
) −1
bv. The interest you earn is 6% yearly compounded monthly. What is the real/effective interest rate?
12
(1 + 0,06
12
) − 1 = 0,06167
bv. The annually compounded (=real/effective) interest rate = 5.5%. What is the semi-annual rate?
𝑟𝑠𝑒𝑚 = (1,055)1/2 − 1 = 2,71 % per semester
- De formule wordt ook gebruikt om meerjarige rendementen te berekenen
bv. You earn 3 % annually for 5 consecutive years, what is the compounded return you’ve made over the 5 year period?
𝑟5 𝑦𝑒𝑎𝑟𝑠 = (1,03)5 − 1 = 15,92 %
CHAPTER 2: FINANCIAL ALGEBRA 2 van 6
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