Summary
Summary Formulas
- Institution
- The University Of York (UOY)
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FINANCE FORMULASThe Net Present Value:
NPV = PV(benefits)-PV(costs)
- For a Perpetuity
C
NPV =Initial investment +
r
Expected return of a risky investment = expected gain at the end of
the year/initial cost
Future value of a cash flow = F V n =C∗( 1+ r )n
C
Present value of a cash flow = PV = ( 1+ r )n
PV of a perpetuity = C/r
Perpetuity = stream of equal cash flows that occur at regular intervals
and last forever.
Annuity = stream of N equal cash flows paid at regular intervals and
ends at a fixed number of payments.
C∗1 1
PV(Annuity of C for N periods) ¿ r
(1−
( 1+r )N
)
C∗1
FV(Annuity) ¿ ( ( 1+r ) N−1 )
r
A perpetuity growing at a constant rate, g.
c
PV(growing perpetuity) ¿ r−g
( ( ))
N
C∗1 1+ g
PV(growing annuity) ¿ r−g 1−
1+r
Loan or annuity payment:
P
C=
1
r(1−
1
( 1+r ) N )
, For finding the IRR, write out the formula for the particular NPV in
the question, where r is supposed to be, replace with IRR, and solve
for IRR setting the NPV = 0.
NPV rule: accept a project if it has a positive NPV.
Internal Rate of Return (IRR) investment rule: Take any investment
where IRR exceeds the cost of capital. Turn down any investment
whose IRR is less than the cost of capital. Limits: some projects can
have multiple IRRs or none at all.
When the NPV rule and IRR rule conflict, the NPV decision rule
should be followed.
The Payback rule: if the payback period (the amount of time it takes
to recover of pay back the initial investment) is less than a pre-
specified length of time, you accept the project, otherwise you reject
the project. Limitations of rule: it ignores project’s cost of capital and
the time value of money and the cash flows after the payback period,
relies on an ad-hoc decision criterion about the cut-off period. A
project accepted based on these criteria may not have a positive
NPV. Advantages: it is easy to understand and apply, focuses on the
liquidity of investment projects.
Profitability index (PI)
PI = NPV/ Resources consumed
One year discount factor = 1/(1+r)
Bonds
Coupon payment:
CPN = (Coupon rate * Face value)/Number of coupon payments per
year
IRR of an investment in a bond = Yield to maturity
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