CFA 1.6 DISCOUNTED CASH FLOW
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Three primary areas of financial decision-making:
- 1. Capital budgeting
- 2. Capital Structure
- 3. Working Capital Management
Allocation of funds to relatively long-range projects or investments. Looks at a company as a portfolio of investments & projects.
The choice of long-term financing of the investments the company wants to make.
Working capital management
Management of the company's short term assets (inventory, cash) and short-term liabilities (accounts payable)
Net Present Value (NPV)
Present value of cash inflows minus the present value of outflows. Way of characterizing the value of an investment
Method for choosing among alternative investments.
If the investment's NPV is positive, take it. If negative, don't take it. Always choose the project with the highest NPV if there are multiple mutually exclusive options.
- 1. Identify all cash flows (inflows & outflows) - do not include sunk costs
- 2. Determine discount rate/opportunity cost (r) for the investment
- 3. Using the rate from 3, find the PV of each cash flow (inflows + ; outflows -)
- 4. Sum the present values
- 5. Apply the NPV rule to determine whether to invest
Alternative return that investors forgo in undertaking an investment.
*When NPV is positive, the investment adds value because it more than covers the opportunity cost of capital needed to undertake it.
Net Present Value (NPV)
*Inputs must be compatible (time) - cash flows are annual, life should be in years and r should be annual rate.
- = the expected net cash flow at time t
- N = investment's projected life
- r = discount rate/opportunity cost of capital
NPV of perpetuity
- CF = cash flow
- r = discount rate/opp cost of capital
Internal Rate of Return (IRR)
Discount rate that makes net present value equal to zero.
Rate of return most often used in investment applications including capital budgeting.
Makes PV of inflows = PV of outflows. Known as internal rate because only relies on cash flows of investment.
IRR calculation vs. IRR actual
Compound rate of return over life of investment will only equal our IRR if both cash flow projections are accurate and re-investment of cash flows is exactly at the IRR rate.
= initial investment @ time 0
*Finding the IRR is the same as finding the discount rate that makes NPV = 0
Accept projects for which the IRR is greater than the opportunity cost of capital (hurdle rate).
Hurdle Rate (opportunity cost of capital)
Rate that a project's IRR must exceed for the project to be accepted
If Opp Cost of Capital = IRR, NPV = 0
IRR & NPV rules rank differently when (2):
- 1. Size or scale of projects differs (size of investment needed to undertake the project)
- 2. Timing of the project's cash flows differ
When IRR & NPV rules differ for a project, we should take the ____ rule...why?
NPV rule. NPV represents the addition to shareholder wealth from an investment which is the goal of the investment.
NPV better than IRR because:
- 1. IRR rankings not affected by external interest rates (internal cash flows only). Re-investment assumptions can be unrealistic.
- 2. NPV uses external market-determined discount rate and re-investment is based on that rate. - more realistic and economically relevant.
Calculating returns in a logical and consistent manner
Holding Period Return (HPR)
Money Weighted Rate of Return
Same as IRR - accounts for the timing and amount of all dollar flows in and out of the portfolio.
Drawback for porfolio evaluation because it weighted based on $ amount which can be at the discretion of the investor (i.e. when they give more money). Does not correctly identify the investment professional's performance.
Time-Weighted Rate of Return
Investment measure that unlike the money weighted return, is not sensitive to additions/withdrawals of funds.
Preferred performance measure.
Measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period.
Time-Weighted Return Steps:
- 1. Price the portfolio prior to any addition/withdrawal of funds. Evaluation periods should be broken up based on dates of cash inflows/outflows.
- 2. Calculate the holding period return for each sub-period
- 3. Link the holding period returns to obtain annual rate of return. For more than 1 year, take the geometric mean of annual returns over the measurement period.
Linking holding period returns for Time-Weighted Formula:
Holding period return =
Liking = ((1+
Market for short-term debt instruments (less than 1 yr)
T-bills, commercial paper, CDs
Pure discount instrument
Pay interest as the difference between the amount borrowed and the amount paid back (bonds)
I.e. US T-BILL
Reduction from the face value amount that gives the price for a bond. The discount becomes the interest that accumulates.
Bank Discount Basis
Quoting convention for t-bills that annualizes based on a 360 day year. Discount is a % of the face value.
Yield on Bank Discount Basis
- = yield on bank discount basis
- D = dollar discount (difference between the face value of the bill and the purchase price)
- F = face value of the bill
- t = actual # of days remaining to maturity
- 360 = bank convention for # of days in the year
Assumes simple interest (no compounding)
Holding Period Yield (HPY)
Accrued interest on interest instrument
Coupon interest that the seller earns from the last coupon date but does not receive as a coupon because the next coupon date occurs after the date of the sale.
Effective Annual Yield (EAY)
Takes the holding period yield + 1 and compounds it forward to one year then subtracts the 1 to recover an annualized return that accounts for the effect of compounding interest.
- Bank discount yield is less than EAY
Money Market Yield (CD Equivalent Yield)
- t = # of days to maturity
- rBD = Bank discount yield
Makes the quoted yield on a t-bill comparable to the yield quotations on interest bearing mm instruments that pay interest on a 360 day basis.
MM Yield is equal to annualized HPY assuming a 360 day year. MM yield is larger than the bank discount yield.
Three Commonly used yield measures:
- 1. Holding Period Yield (HPY)
- 2. Effective Annual Yield (EAY)
- 3. Money Market Yield (CD Equivalent Yield)
Money Market Yield > Bank Discount Yield
Bond Equivalent Yield
Annualizing a semi-annual yield to annual yield by simply doubling it as opposed to compounding it via the EAY method.
I.e. semiannual YTM = 4%, yield = 8%.
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