Chapter 15 - financial mathematical techniques Flashcards
simple vs compound interest
SIMPLE = a % of the original amount invested or borrowed
S = X + nrX
where X = original sum, r = IR, n = number of periods, s = sum generated by investment after n periods
COMPOUND = interest is earned, added to investment and starts to earn interest itself
if no withdrawals are made, amount invested will grow by increasing amount each year because interest earns interest itself
S = X (1 + r) to power of n
what is an equivalent annual rate and formula
sometimes called effective annual rate
FORMULA:
(1 + R) = (1 + r) to power of n
R = effective annual rate
r = period rate
n = number of periods in a year
formula for cash inflow
cash inflow in one year’s time of £600,000 can be converted into a present value by multiplying it by:
1 / (1 + r) power of n
discount factor formula
1 / (1 + r) power of n
what is an annuity
ANNUITY = of cash inflows are equal each year they are described as an annuity
in this case you can discount annuity once using an annuity factor instead of discounting each cash inflow (quicker)
discount factor to perpetuity formula
1 / cost of capital
what is the internal rate of return
Internal Rate of Return (IRR) is another discounted cash flow technique which evaluates investments by calculating the % return generated by a project
the IRR of a project is compared to the return expected by investors to see if the project is acceptable
how to calculate IRR
- calculate NPV of the project at a low cost of capital
- calculate NPV of the project at a higher cost of capital
- calculate internal rate of return using the IRR formula
IRR formula
IRR = R1 + (R2 - R1) X NPV1 / NPV1 - NPV2
where 1 = lower cost of capital 2 = lower cost of capital
problem with IRR
might lead to a small project being chosen over a larger project because smaller project has a higher IRR despite a lower NPV (lower wealth for shareholders)
