# CFA I R7 Discounted Cash Flow (DCF) Applications

Thank you for visiting visiting WhitneyDiary CFA I Notes series, I have been using the notes below for my revision and have passed the CFA Level I on June 2018 Exam. Hereby, I share my notes with you and hope that they are helpful:

1. Net Present Value (NPV) = ∑{CF/[(1+r)^t]}
→ Calculated using opportunity cost, discount rate, expected cash flow, timing of expected cash flow from the project
→ IRR is not used to calculate NPV
2. a) Accept project with positive NPV;
reject project with negative NPV.
b) Mutually exclusive project: accept higher positive NPV project.
c) Accept project with IRR > required rate of return;
reject project with IRR < required rate of return.
3. Conflict between NPV & IRR [mutually exclusive projects]
a) Scale of investment may differ
b) Timing of cash flow may differ
4. Holding period return (HPR) = (Ending Value – Beginning Value)/Beginning Value
HPR = (Ending Value/Beginning Value) – 1
HPR = (Ending Value – Beginning Value + Cash Flow Received)/Beginning Value
5. Money-weighted return = Internal rate of return (IRR)
→ IRR on a a portfolio, taking into account all cash inflows & outflows
→ PV (inflows) = PV (outflows)
*Preferable performance measure if the manager has complete control over money flows into & out an account.
6. Time-weighted rate of return = geometric mean return
→ Measures compound growth [compute HPR for each holding period]
→ Time-weighted rate of return = [(1+HPR1)(1+HPR2)^(1/2)]-1
*Denominator of the power is determined by the number of holding period
*Preferable measure as it is not affected by timing of CF.
⇒ If funds are contributed to a portfolio before a relatively poor period, money-weighted rate of return tend to be lower than the time-weighted rate of return.
7. Bank discount yield (BDY) = (D/F) × (360/t)
*D = Difference between F & Purchase Price
→ Express dollar discount from F
→ Ignore opportunity to earn compound interest
8. Holding Period Yield (HPY) = (P1 – P0 +D1)/ P0
HPY = [(P1+D1)/P0] – 1
HPY = D/Selling Price [T-bills → Price]
→ Total return an investor earns between purchase date & the sale or maturity date
→ Reflects non-annualized return an investor will earn over a security’s life.
HPY = [BDY×(n/360)] / {1-[BDY×(n/360)]}
HPY = rMM × (t/360)
HPY = (1+EAY)^(n/365) – 1
9. Effective annual yield (EAY) = (1+HPY)^(365/t) – 1
→ Annualized value, based on 365-day year, that accounts for compound interest.
10. Money market yield (CD equivalent yield)
→ annualized HPY, assuming a 360-day year
a) rMM = HPY × (360/t)
b) Given rBD, rMM = (360 × rBD) / [360 – (t × rBD)
11. HPY ⇔ rMM ⇔ EAY ⇔ BEY
a) HPY = The actual return an investor will receive if the money market instrument is held until maturity
b) EAY = The annualized HPY on the basis of a 365-day year & incorporates the effects of compounding
c) rMM = The annualized yield that is based on price and a 360-day year & does not account for the effects of compounding – it assumes simple interest.
12. Bond Equivalent yield (BEY) = 2 × semiannual discount rate
BEY = [(1+EAY)^(t/365) – 1] × 365/t
BEY = HPY × (365/t)
BEY = 2 × (YTM^0.5) – 1