Discounted Cash Flow Applications

Capital Budgeting (资本预算)

The allocation of funds to relatively long-range projects or
investments. From the perspective of capital budgeting, a
company is a portfolio of projects and investments.

Capital Structure (资本结构)

The choice of long-term financing for the investments the
company wants to make

Working capital management (运营资本管理)

The management of the company’s short-term assets and
short-term liabilities(债务)

Net Present Value (NPV, 净现值)

The present value of its cash inflows(benefits) minus the
present value of its cash outflows(costs)

Calculation of NPV:

• Identify all cash flows;
• Determine the discount rate or opportunity cost ®;
• Find the present value of each cash flow;
• Sum up all present value to get NPV

$NPV = CF_0 +\frac{CF_1}{(1+r)} +\frac{CF_2}{(1+r)^2} + \dots +\frac{CF_n}{(1+r)^n}$

Apply the NPV rules:

• If NPV > 0, undertake the project
• If NPV ≤ 0, should not undertake the project;
• For mutually exclusive projects (can only invest in one),
  choose the one with higher positive NPV.

Internal rate of return (IRR, 内部收益率) :

The discount rate that makes net present value equal to
zero

$NPV = 0 = CF_0 +\frac{CF_1}{(IRR)} +\frac{CF_2}{(IRR)^2} + \dots +\frac{CF_n}{(IRR)^n}$

Apply the IRR rules:

IRR > opportunity cost of capital, undertake the project .

IRR ≤ opportunity cost of capital, should not undertake
the project

Problems with IRR rules

• NPV and IRR rules give the same accept or reject decision
  when projects are independent, but may rank projects
  differently if projects are mutually exclusive when:

  • The size or scale of the projects differs;

  • The timing of the projects’ cash flows differs.

• Stick to the NPV rule when NPV’s and IRR’s suggestions are
  conflict.

• When the signs of cash flows change more than once, there
  can be more than one IRR.

Holding period return (持有期收益率)

The return that an investor earns over a specified holding
period.

$HPR = \frac{P_1-P_0+D_1}{P_0}$

Example

Stock purchased nine months ago for $29 just paid a
dividend of $1.30 and is valued at $30.50. Calculate the
nine-month holding period return.

Answer:

HPR = (30.50 + 1.30 -29)/29 = 9.66%

Time-weighted return (TWR, 时间加权收益率)

The compound return that $1 initially invested in the
portfolio over a stated measurement period

Calculation of TWR:

• Break the overall evaluation period into sub-periods based
  on the dates of significant cash inflows and outflows;
• Calculate the HPRs for each sub-periods;
• Link or compound HPRs to obtain an annual rate of return

$TWR = {[(\frac{End\ Value_1}{Begin\ Value_1})(\frac{End\ Value_2}{Begin\ Value_2}) \dots (\frac{End\ Value_1}{Begin\ Value_1})]}$

Steps to compute thetime-weighted return

Price the portfolio prior to any significant addition or
withdrawal of funds. Break the overall evaluation period
into sub-periods based on the dates of cash inflows and
outflows

Steps to compute the time-weighted return (Cont.)

• Calculate the holding period return on the portfolio for
  each sub-period.
• Compound each holding period return to obtain an annual
  rate of return for the measurement period (the timeweighted rate of return for the measurement period)

Money-weighted return (MWR, 货币加权收益率)

MWR accounts for the timing and amount of all cash flows
into and out of the portfolio

• If more funds to invest at an unfavorable time, MWR will
  tend to be depressed;
• If more funds to invest at a favorable time, MWR will tend
  to be elevated

Calculation of MWR:

similar to IRR

$CF_0 +\frac{CF_1}{(1+MWR)} + \dots +\frac{CF_n}{(1+MWR)^n = 0}$

Steps to compute the money-weighted return

• Identify the cash inflows and cash outflows by time
  and then group the net cash flows.
• Find the money-weighted return based on the rule of
  NPV equal to zero.

TWR vs. MWR

Time weighted return:

• Not affected by cash withdrawals or additions;
• Periods can be any length between significant cash flows

Money weighted return

• Assign more weights to the return of larger cash flows;
• Affected by cash withdrawals or additions;
• Periods must be equal length

• Use shortest period with no significant cash flows

Money Market Yields

###　Money Market (货币市场)
The market for short-term debt instruments (one-year
maturity or less)

Pure Discount Instruments (纯贴现工具)

The financial instruments that pay interest as the difference
between the amount borrowed and the amount paid
back(e.g., US T-bill)

Face Value (面值)

The amount the issuer promises to pay back to the
investors if it is held at maturity

Discount (折扣)

The difference between the face value and the purchase
price.

Holding period yield (HPY)

HPY = (Ending Value/Beginning Value) - 1

Bank discount yield (BDY)

BDY = (Discount/Face Value) × (360/Days to maturity)

Discount rate, simple interest, 360-day annualized

Money Market Yield (MMY)

MMY = (Discount/Price) × (360/Days to maturity)

Add-on rate, simple interest, 360-day annualized

Bond Equivalent Yield (BEY, 债券等价收益率)

BEY = (Discount/Price) × (365/Days to maturity)

Add-on rate, simple interest, 365-day annualized;

Only for money market, not available for capital market

Effective annual yield (EAY, 有效年利率)

$EAY = (1+HPY)^{365/Days}-1$

Add-on rate, compound interest, 365-day annualized