# CFA – Ethical & Professional Standards & Quantitative Methods – Discounted Cash Flow Applications

# LOS 6a

NPV – The NPV is the present value of a projects future cash flows, discounted at the firms cost of capital, less the projects cost.

NPV = PV of Cash Inflows – PV of Cash Outflows

IRR – Internal rate of return is the discount rate that makes the NPV == 0 (equates the PV of the expected future cash flows to the projects initial cost)

The NPV rule is to accept a project if NPV > 0; the IRR rule is to accept a project if IRR > required rate of return.

For an independent (single) project, these rules produce the exact same decision.

For mutually exclusive projects, IRR rankings and NPV rankings may differ due to differences in project size or in the timing of the cash flows. Choose the project with the higher NPV as long as it is positive.

A project may have multiple IRRs or no IRR.

The IRR method assumes all cashflows from the project are reinvested at the IRR

# LOS 6b

#### HPR

– Holding Period Return is the % change in the value of an investment over the period it is held.

The holding period return (or yield) is calculated as:

#### HPY

– Holding period yield is the actual return an investor will receive if the money market instrument is held until maturity

# LOS 6c

The money weighted rate of return is the IRR calculated using periodic cash flows into and out of an account and is the discount rate that makes the PV of cash inflows equal to the PV of cash outflows.

Time weighted rate of return – is calculated from the accounts periodic holding period returns and is the preferred performance measure.

# LOS 6d

#### BDY –

– Bank Discount Yield is the % discount from face value, annualized by multiplying by *360/days to maturity*

Bank discount yields are not true yields because they are based on a percentage of face (maturity) value instead of on the original amount invested. They are annualized without compounding since the actual discount from face value is simply multiplied by the number of periods in a “year”. The year used in 360 days.

#### EAY

– Effective annual yield is the annualized HPY on the basis of a 365 day year and incorporates the effects of compounding. It converts a t-day holding period to a compound annual yield based on a 365 day year.

#### MMY

– Money market yield (or rMM) is the annualized yield that is based on price and a 360 day year and does not account for the effects of compounding – it assumes simple interest

*NB:// easy in relation to the above!*

# Examples

## money weighted rate of return

Assume an investor purchases a share of stock for $50 at time t=0

and another share at $65 at time = t1

and at the end of year 1 and year 2, the stock paid a $2.00 dividend

Also at the end of year 2, the investor sold both shares for $70 each

- [CF]2nd [CLR WORK]
- 50 [+/-] [ENTER]
- 63 [+/-] [ENTER]
- 144 [+/-] [ENTER]
- [IRR] [CPT] ————–
*NB:// Watch your minus signs here or it wont work!*

## time weighted rate of return

HPR1 = (65+2)/50 – 1 = 34%

HPR2 = (140+4)/130 –1 = 10.77%

thus = [(1.34)()1.1077]^{.5 –}1 = 21.83%