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Rate of Return (:check: External Rate of Return (ERR Calculation (Equate…
Rate of Return
:check: External Rate of Return
ERR can be used when
:star: All net receipts is reinvest at IRR
:star: Having problem in IRR
:star: Used to workout a project is worth or not
ERR Calculation
Outflow Discounted (PV)
Inflow Compounded (FV)
Equate Outflow & Inflow
Rejected
:red_cross: ERR < MARR
Accepted
:check: ERR > MARR
How to do ERR > MARR
All net cash outflows are discounted
All net cash inflows are compounded at 𝜖% to period N
The ERR, which is the interest rate that establishes an equivalence between the two quantities, is determined
ERR Graphical Method
ERR is an interest rate(ε), from the external sources to a project account at which net cash flows required over the period can be reinvested.
Payback Period Method
The payback period is the amount of time of an investment that reaches a breakeven point.
Payback Period Formula
Simple Payback Period Method
The simple payback period, 𝜃, ignores the time value of money and all cash flows that occur after payback period, 𝜃.
To overcome the shortfalls, the discounted payback period, 𝜃′ (𝜃′ ≤ 𝑁) is introduced, where i% is the MARR, I is the capital investment usually made at present time (k = 0).
Simple Payback Period Formula
Bonds
An interesting bearing certificate that provides future net cash flows at a specified interest rate and has a cash value that can be redeemed at some future date.
The PW method is one way to find the value of a bond.
Commonly known as a long term debt instrument which the borrower agree to make payment of principal and interest on the specific dates to the holders of the bond
Bond value
VN=C(P/F , i%, N) + r.Z(P/A, i%, N)
The owner of a bond is paid two types of payments:
A series of periodic interest payments (r.Z) until the bond is retired
A single payment (C) when the bond is retired.
:check: Internal Rate of Return (IRR)
IRR is the way of evaluating a project whether it is
accepted:check: or rejected:red_cross:
:warning:IRR is the discount rate that makes Net Present Value (NPV) = 0
Relationship between IRR and NPV
Example Project: Say Mr.Senuh :beer_mugs: invest $100(PV) in a bank for a year. At the end of year, Mr. Snow will receive $130(FV).
NPV
given discount rate,r =8%
NPV=PV+FV/(1+r)
=$100+$130/(1.08)
NPV = $20.37
if NPV > 0, project is accepted :check:
Comparing R and r
If R>r, then project is accepted
Since R>r
30%>8%
then, project is accepted :check:
IRR
calculate the R
:warning:NPV=PV+FV/(1+R)
0=$100+$130/(1+R)
R=30%
When NPV = 0, it means the project is at breakeven point where money is neither being added nor destroyed
