Discounted Cash Flows Flashcards
Net Present Value
present value of expected cash inflows associated with the project less the present value of the projects expected outflows, discounted at the appropriate cost of capital.
Procedure to compute NPV
- indentify all inflow and outflow
- determine approp discount rate
- use discount rate, find PV of each cash flow. inflows (+) increase NPV outflows (-) decrease NPV
- compute NPV, sum the DCFs
Internal Rate of Return
rate of return that equates the PV of an investments expected benefits (inflows) with the PV of its costs (outflows). - defined as the discount rate which the NPV of an investment is zero.
NPV Decision Rule
if project has + NPV, this amount goes to shareholders
- Accept projects with + NPV
- Reject projects with - NPV
- Two projects mutually exclusive, higher NPV accepted
IRR Analysis
Accept project with IRR greater than firms required rate of return
-Reject projects with an IRR that is less than the firms required rate of return
Hurdle Rate
rate that a projects IRR must exceed for the project to be accepted.
Opportunity Cost = IRR
NPV = 0
Opportunity Cost < IRR
NPV > 0
Why should we accept projects with a positive NPV?
Positive NPV projects will increase shareholder wealth.
IRR Rule
NPV Rule
Interpret NPV
When NPV > 0, the investment adds value because it covers the opportunity cost of capital needed to undertake it.
Positive NPV increases shareholder wealth.
Problems with IRR rule
IRR and NPV rules give the same accept/reject decision when projects are independent, but rankings may not be the same when
- project sizes differ
- timing of cash flows differ.
=> Use NPV to rank projects.
IRR will have multiple solutions when CF signs change more than once.
The IRR decision rule says:
Accept projects with an IRR that is greater than the firm’s required rate of return; Reject projects with an IRR that is less than the firm’s required rate of return.
The IRR is defined as the rate of return that equates the PV of an investment’s expected benefits with the PV of its costs…
OK
Any discount rate less than the IRR will result in a positive or negative NPV?
Positive NPV
When given NPV vs. IRR, which should you use?
You should always use the project with the greatest NPV when the IRR and NPV rules provide conflicting decisions. This is because shareholder wealth maximization is the ultimate goal of the firm.
When 2 projects are mutually exclusive (only one can be accepted), the project with the higher positive NPV should be accepted?
Yes
Time-weighted rate of return
measures compound growth. The rate at which $1 compounds over a specified performance horizon.
-Preferred method of performance measurement, because it is not affected by the timing of cash inflows and outflows.
What is the “Time-weighted rate of return”?
It measures compound growth. It is the rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time.
Steps in Time Weighted Return
1 - value portfolio immediately preceding significant additions or withdrawals.
2 - computer HPR of each subperiod
3 - compute product of (1+HPR) for each subperiod to obtain a total return for entire measurement period. If total investment period is greater than one year, must take the geometric mean of measurement period return to find annual time-weighted rate of return
Money Weighted Return
Concept of IRR to investment portfolio. defined as he internal rate of return on a portfolio, taking into account all cash inflows and outflows
- Like an IRR measure => PV(outflows) = PV(inflows)
- Periods must be equal length
- Calculating an equal HPR for all periods
Because the return rate is the same for all holding periods, the period with the most “money” has the greatest effect on the calculation.
What is the “money-weighted return”?
It’s defined as the IRR of a portfolio, taking into account of all cash inflows and outflows.
Money-Weighted vs Time-Weighted in evaluating portfolio managers
Money-weighted drawbacks:
- Clients determine size and frequency of cash flows
- General principle of evaluation is that a person should be judged only on the basis of their own actions
- Tool should isolate the effect of investment manager’s action
Time-weighted not affected by withdrawals or additions to the portfolio.
Holding Period Return
:- % change in value of an investment over the period it is held.
:- total return if it has cash flows such as dividend or interest payments
What is the holding period return?
it’s simply the percentage change in the value of an investment over the period it is held.
Holding Period Year (HPY)
Total return an investor earns between the purchase date and the sale or maturity date.
(P1 - Po + D1) / Po ((P1 + D1)) / Po) -1
What is Holding period yield?
It’s the total return an investor earns between the purchase date and the sale or maturity date.
HPY
actual return an investor will receive if the money market instrument is held to maturity
EAY
annualized HPY on the basis of a 365-day year and incorporates the effects of compounding
Effective Annual Yield (EAY)
annualized value, 365-day year, accounts for compound interest
EAY = (1 + HPY)³⁵⁶/ⁿ -1
What is the EAY?
It’s the annualized HPY on the basis of a 365-day year and incorporates the effects of compounding.
What is the effective annual yield (EAY)?
It’s an annualized value, based on a 365-day year, that accounts for compound interest.
Bank Discount Yield
D/F) x (360/t)
d - dollar discount
F - face value of the bill
t - number of days remaining until maturity
key distinction - expresses dollar discount from face (par) value as fraction of the face value, not the market price. And annualized 360 (simple interest)
Money Market Yield
equal to annualized holding period yield, assuming 360-day year. Makes quoted yield on tbill comparable to yield quotes for interest-bearing money market instruments that pay interest on 360-basis
(360/#days) x HPY
Other equation page 145 book 1
rMM
annualized yield that is based on price and a 360-day year and does not account for the effects of compounding - assumes simple interest
Bond equivalent Yield
2 x semiannual discount rate. Yields on US bonds are quoted as twice the semiannual rate, because the coupon interest is paid in two semiannual payments
The money market yield is equal to what?
It’s equal to the annualized holding period yield, assuming a 360-day year.
What is a bond-equivalent yield?
It refers to 2 x the semiannual discount rate. This convention stems from the fact that yields on U.S. bonds are quoted as twice the semiannual rate, because the coupon interest is paid in 2 semiannual payments.
Bank Discount Basis
T-bills quoted, based on face value of instrument instead of purchase price.
RMM and EAY are just _______ of HPY
annualized versions
Bank discount yield not representative of return earned by an investor:
- BD yield annualizes using simple interest and ignores the effects of compound interest
- BD yield is based on FV of the bond not its purchase price
- BD yield is annualized based on a 360 day year rather than 365
What is the beginning value of a portfolio?
The beginning value of the account is an inflow, as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.
Why is the time-weighted rate of return the preferred method of performance measurement?
Because it is not affected by the timing of cash inflows and outflows.
Bank discount yield annualizes using simple interest and ignores the effects of what?
It ignores the effects of compound interest.
Bank discount yield is based on the face value of the bond, not its purchase price- investment returns should be evaluated relative to what?
Investment returns should be evaluated relative to the amount invested.
Bank discount yield is annualized based on a 360-day year or a 365-day year?
It’s annualized based on a 360-day year
Effective Annual Rate
rMM
Money Market Yield
rBD
Bank Discount Yield
Yield on Discount Basis
Bank Discount Yield
How can you calculate HPY when only Bank Discount Yield is only given
How will you calculate EAY when Money Market Yield is given
