Quantitative Methods - Discounted Cash Flow Applications

There's a hefty 21 question problem set for the previous reading that I will save for a later date when I want to practice those.

For now I think I will take a look ahead to reading 6, another about 30 page reading about applications of the discounted cash flow approach.

Start time - 4:15 pm

Quantitative Methods - Discounted Cash Flow Applications

The candidate should be able to:

a. calculate and interpret the net present value (NPV) and the internal rate of return (IRR) of an investment;

b. contrast the NPV rule to the IRR rule, and identify problems associated with the IRR rule;

c. calculate and interpret a holding period return(total return);

d. calculate, interpret, and distinguish between the money-weighted and time-weighted rates of return of a portfolio, and evaluate the performance of portfolios based on these measures;

e. calculate and interpret the bank discount yield, holding period yield, effective annual yield, and money market yield for a U.S. Treasury bill;

f. convert among holding period yields, money market yields, effective annual yields, and bond equivalent yields. (Institute 311)"

Institute, CFA. Level I 2012 Volume 1 Ethical and Professional Standards and Quantitative Methods, 7th Edition. Pearson Learning Solutions. <vbk:9781256112754#page(311)>.

Net Present Value and the NPV Rule

• NPV = present value of cash inflows less present value of cash outflows
• 'Net' refers to the subtracting of the outflows
• Steps (5)
• Identify all cash flows
• Determine discount rate r
• Find PV of all cash flows
• Sum all PVs
• Apply the NPV rule - 
• NPV rule - if NPV positive, undertake project; if negative, do not undertake it.
• If there are two mutually exclusive projects, choose candidate with higher NPV
• Use 'opportunity cost of capital' as r

Internal Rate of Return and the IRR Rule

• IRR = discount rate that makes NPV equal to zero
• 'Internal' because it depends only on the cash flow of the investment - no external data needed
• Note: We will realize IRR only if we can reinvest all interim cash flows at the same IRR 
• Can work for or against you - e.g. IRR is 15% but you reinvest at 10% this is bad.  Conversely if you reinvest at 20% this is good.
• We typically use calculators and spreadsheets to calculate this (HP12c)
• IRR Rule: Accept investments for which IRR is greater than opportunity cost of capital

Weaknesses of IRR Rule

• Rankings according to IRR and NPV will not be the same if:
• Size or scale of the projects is different (where size = investment needed)
• Timing of the projects' cash flows differs
• When IRR and NPV conflict, default to NPV rule
• This maximizes shareholder wealth
• It is OK to take a lower IRR if it results in a higher NPV

Portfolio Return Measurement

• Two related but distinct tasks in assessing performance
• Performance measurement and performance appraisal
• Measurement provides basis for appraisal
• Holding Period Return (HPR)
• (P1 - P0 + D1) / P0
• Price at end of period, less price of initial investment, plus cash paid by investment at end of period, divided by initial investment
• Two solutions - money weighted rate of return and time weighted rate of return

Money Weighted Rate of Return

• This is the IRR - this is called Money Weighted because it accounts for timing and amount of all dollar flows into and out of the portfolio
• Drawback though: because clients determine when a manager gets money, and this can affect IRR (since it is money weighted), this can skew IRR performance - IRR is sensitive to the addition and withdrawal of funds in a portfolio
• A general principle is that a manager should only be evaluated on what he can control
• Therefore, we need a second measure to isolate the manager's effect - time weighted rate of return

Time-Weighted Rate of Return

• Measures the compound rate of growth of $1 initially invested over a stated period.  3 steps:
• Price portfolio immediately prior to any significant adds/withdrawals.  Break overall evaluation period into subperiods based on dates of cash inflows and outflows.
• Calculate HPR for each subperiod
• Link or compound HPRs to obtain annual rate for year
• If greater than 1 year, take geometric mean of annual returns to get TWR for that period
• Geometric mean
• Say you had returns of 15% and 6.67% in year 1 and 2
• (1+TWR)^2 = (1.15)(1.0667)
• (1+TWR)=sqrt((1.15)(1.0667))
• TWR)=sqrt((1.15)(1.0667)) - 1 = 10.76%
• Trick is to find all breaks where new money comes in and recalculate the basis for return each time
• E.g., if someone invests on May 1, calculate Jan 1 to April 30 first, then May 1 onward
• Next, see what 1 dollar does by multiplying it through

Break for now, end 6:00 PM

1.75 hours