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Reading 06: Discounted Cash Flow Application (Various Yield Measures for…
Reading 06: Discounted Cash Flow Application
NPV & IRR
NPV
Definition
: Net Present Value
Formula:
\( NPV= \sum_{N}^{t=0}\frac{CF_{t}}{\left ( 1+r\right )^{t}}\)
Rule
: Choose project with NPV > 0; with highest NPV (if all NPV > 0)
IRR
Definition
: the discount rate that make NPV =0
Formula
: \(NPV_{IRR}= \sum_{N}^{t=0}\frac{CF_{t}}{\left ( 1+IRR\right )^{t}}=0\)
A project may have multiple IRRs or no IRR
Rule
: Choose project with IRR > Investor's required rate of return (cost of capital)
If NPV conflicts IRR
Prefer NPV over IRR
Holding Period Return
Definition
: Total return for holding an investment over a period of time.
Formula
: \(HPY=\frac{P_{1}-P_{0}+D_{1}}{P_{0}}= \frac{P_{1}+D_{1}}{P_{0}}-1\)
Money-weighted & Time-weighted Return Rates
Money-weighted Return Rate
MWR
Definition
: is the discount rate that make PV of cash inflows and outflows equal.
Formula
:\(\sum_{t=0}^{N}\frac{CF_{inflow}}{\left ( 1+MWR\right )^{t}}=\sum_{t=0}^{N}\frac{CF_{outflow}}{\left ( 1+MWR\right )^{t}}\)
If major amount of money is added just before a period with poor (good)-performance, MWR will be lower (higher) than TWR
MWR is appropriate performance measure if manager can control the money flows into and out of the portfolio.
Time-weighted Return Rate
TWR
Definition
: the rate at which $1 compounds over time.
Formula
: \( TWR_{Several Year}= \left [ \prod_{t=1}^{N}\left ( 1+HPR_{t} \right ) \right ]^{\frac{1}{N}}-1 \)
TWR is appropriate to measure a manager's ability to select investment.
Step to calculate
1) Price the portfolio immediately prior to any signicant addition or withdrawal of funds
2) Calculate the HPR on the portfolio for each sub-period \(HPR=\frac{EndValue}{Amount Invested}-1\)
3) Use the Formula (if all the total period is within a year, then don't need to take the root)
Various Yield Measures
for Money-market Security with n days to maturity
Bank discount Basis
: \(R_{BD}=\frac{Discount}{FaceValue}\times \frac{360}{t}\)
Holding Period Yield
: \(HPY=\frac{P_{1}-P_{0}+D_{1}}{P_{0}}=\frac{ R_{BD}\times \frac{n}{360}}{1 - \left ( R_{BD}\times \frac{n}{360} \right )} \)
Money Market Yield
: \(R_{MM} = \frac{360 \times R_{BD}}{360 - \left ( n\times R_{BD} \right )}= HPY \times \frac{360}{n}\)
Effective Annual Yield
: \(EAY=\left ( 1 + HPY \right )^{\frac{365}{n}} - 1\)
Bond Equivalent Yield
: \(BEY=\left [ \sqrt{\left ( 1 + EAY \right )} - 1 \right ]\times 2 \)