04. Discounted Cash Flow Techniques Flashcards
Where interest is charged on a non-annual basis, the effective annual interest rate (EAIR) or annual percentage rate (APR) may be utilized to compare the cost of finance of various sources. What is the formula for EAIR?
1 + R = (1 + r)^n
R = annual rate (EAIR)
r = interest rate per period (month/quarter)
n = number of periods in a year
What’re the formulas for PV and FV compounding interest?
PV = FV * 1/(1+r)^n
FV = P (1+r)^n
Why do investors prefer money today rather than in one year?
- Liquidity preference: if money is received today it can either be spent or reinvested to earn more in the future. Investors therefore have a preference for having cash/liquidity today.
- Risk: cash received today is safe, future cash receipts may be uncertain.
- Inflation: cash today can be spent at today’s prices but the value of future cash flows may be eroded by inflation.
What are the two primary Discounted Cash Flow (DCF) techniques?
- Net present value (NPV) - an absolute measure and
- Internal rate of return (IRR) - a relative measure.
Give two reasons why two methods of appraisal are superior to other appraisal methods.
- Take into account:
- the time value of money
- all of a project’s cash flows over its entire duration
- the timing of cash flows - Provide a more objective basis for evaluating and selecting investment projects as they are not affected by financial accounting policies (e.g. capitalisation and depreciation versus expense).
What are 4 possible reasons for companies’ reluctance to using DCF methods?
- The potentially complex and time-consuming process of calculating NPV and/or IRR.
- Difficulty in explaining DCF techniques to non-financial managers.
- Complexity of estimating an appropriate discount rate (ie the applicable interest rate), particularly for unquoted companies.
- Managers may feel little connection between DCF techniques and their own reported performance and bonus systems.
What is an annuity?
An annuity is a stream of identical cash flows arising each year for a finite period of time.
What is the formula for the PV annuity factor?
[1-(1+r)^-n]/r
What is a perpetuity?
A stream of identical cash flows arising each year to infinity.
What is the formula for the PV of a perpetuity?
CF * 1/r
What is the internal rate of return and what is the decision rule for it?
Internal rate of return (IRR) is a discount rate which, when used to discount the cash flows of a project to their present values, results in an NPV of zero.
The IRR represents the average annual percentage return from a project and therefore shows the highest finance cost that can be accepted for the project.
The decision rule for IRR is:
If IRR > cost of capital, accept project.
If IRR < cost of capital, reject project.
What is the formula for IRR when a project has equal cash flows receivable in perpetuity?
IRR = (annual cash inflows/initial investment) * 100
To get an NPV of zero, the PV of the cash inflows must equal the initial cash outflow. Outline the steps in calculating the IRR for an annuity.
- Calculate the annuity factor.
Annuity factor = (cash outflow/annual cash inflow)
- Use the table provided to identify the discount rate.
Outline the steps for calculating the IRR when cash flows are not perpetuities or annuities.
- Calculate the NPV of the project at a chosen discount rate.
- If NPV is positive, recalculate NPV at a higher discount rate (ie to get an NPV closer to zero).
- If the NPV is negative, recalculate at a lower discount rate (again to get an NPV closer to zero).
- Use the following formula to estimate the IRR by “linear interpolation”:
IRR ~ A + Na/[Na -NB] (B - A)
Where:
A = lower discount rate
B = higher discount rate
Na = NPV at rate A
No = NPV at rate B
