Investment appraisal Flashcards
Investment appraisal Discounting 1 Single cash flow (occurring at tn):
Present Value (PV) = cash flow at tn × discount factor (DF)
DF =
1
/
(1 + r)n
Or use tables
Investment appraisal Discounting 2 Annuity cash flow:
Annuity: A constant annual cash flow occurring for a set number of years.
PV = constant annual CF × annuity factor (AF)
AFt1 to tn =
(1/r) X (1-(1/(1+r)^n)
Or use tables
Note: if the annuity is growing at a constant rate of g each year, then r becomes: (1 + discount rate %) / (1 + growth %) – 1
Or as an approximation use (discount rate% – growth%)
Investment appraisal Discounting 3 Perpetuity cash flow:
Perpetuity: A constant annual cash flow occurring forever.
PV = constant annual CF × perpetuity factor (PF)
PF =
1/r
Perpetuity with growth: An annual cash flow occurring forever and growing at a constant rate g.
PV =
CF at t1 × PF (with growth)
PF with growth =
1/(r – g)
Note: All the perpetuity and annuity formulas assume the first cash flow occurs at t1.
If an annuity or perpetuity doesn’t start at t1 then the discount factor must be
adjusted. For example, if a cash flow is received each year for 5 years but starts at t4,
then the discount factor is: AF for 5 years × Simple DF for 3 years
Investment appraisal Discounting 4 Non-annual discount rates
(1 + R) = (1 + r)n
Where:
R = non-annual rate
r = annual rate
n = number of time periods
e.g. if we have an annual rate of 10% and want to discount cash flows that occur every six months, then the 6 month discount rate will be:
(1 + R6 months) = (1 + 10%)(6/12)
(1 + R6 months) = 1.0488
R6 months = 4.88%
Or, if we have a loan with interest paid quarterly of 2%, we can flex this up for the full year in the same way.
(1 + 2%)4 = (1 + r)
r = 8.24%
Investment appraisal Internal Rate of Return (IRR) 2.1 Internal rate of return
Traditionally the IRR method has been used as a form of investment appraisal as it
provides the average return generated from the inflows compared to the investment.
It can be calculated using the spreadsheet function:
=IRR(values)
Two main problems with the IRR
(1) It assumes the cash flows will be re-invested at the IRR rate, rather than the
actual cost of capital. This can lead to incorrect decisions being made when
comparing projects and lead to multiple IRRs. This can be overcome using the
modified internal rate of return (MIRR).
(2) It doesn’t consider when the actual cash flow takes place, which can be
overcome by calculating the extended internal rate of return (XIRR).
Investment appraisal Internal Rate of Return (IRR) 2.2 Modified internal rate of return (MIRR)
The MIRR is a modified version of IRR and takes account of the reinvestment rate that the company can achieve.
Calculation:
MIRR =
*(Terminal value of net annual inflows (TV)
/
PV of net annual outflows (PV))
(1/n)
– 1*
Or using the spreadsheet function
*=MIRR(range of cells t0 – tn, finance rate, return in reinvested funds) *
The cost of capital will be used for both the finance rate and return in reinvested funds in this exam, unless told otherwise.
Investment appraisal Internal Rate of Return (IRR) 2.3 Extended internal rate of return (XIRR)
The XIRR takes into account the dates when the actual cash flows take place and is
useful for a series of cash flows that are not periodic (irregular).
It can be calculated using the spreadsheet function:
=XIRR(values,dates)
Investment appraisal Foreign investment appraisal 3.1 Net Present Value (NPV)
NPV is still very examinable at this level, particularly:
Foreign NPV
Relatively simple NPVs as part of a wider strategy choice question.
NPV = PV of future cash flows associated with a project.
Decision rule:
Accept if NPV >0, as NPV = change in wealth for the investor
To find the NPV we can use a spreadsheet function:
=NPV(discount rate, CFs to be discounted)
Note: This only finds the present value of the cash flows that need to be discounted.
The cash flow at year 0 will also need to be included for the complete NPV.
More detail on NPV can be found in the recap section for Financial Management.
Non-financial aspects are more important at this level.
Investment appraisal Foreign investment appraisal 3.2 Interpreting exchange rate information
The examiner will expect you to forecast the future exchange rates in a project and
will provide you with details about how the exchange rate will move. For example:
“The current exchange rate is $1.3/£ and the £ is expected to depreciate at 10% per
year”.
Note: As in FM you can expect the examiner to quote rates in terms of F.C./£ (this is
the normal convention in the UK).
This means the £ buys 10% less $s each year, so the T1 rate =
$1.3/£ × 0.9 = $1.17/£
Investment appraisal Foreign investment appraisal 3.2 Interpreting exchange rate information If the foreign currency is appreciating or depreciating
If the question says “The current exchange rate is $1.3/£ and the $ is expected to appreciate against the £ at 10% per year”.
This means each year the $ will buy 10% more £’s each year.
The $ appreciating at 10% per year, is roughly equivalent to the £ depreciating at
10% per year, therefore it is permissible to use the same approach as above:
$1.3/£ × 0.9 = $1.17/£
Investment appraisal Foreign investment appraisal 3.2 Interpreting exchange rate information Alternative approach (foreign currency appreciating/depreciating):
If the question says “The current exchange rate is $1.3/£ and the $ is expected to appreciate against the £ at 10% per year”.
The future exchange rate could also be calculated as:
$1.3/£ ÷ 1.1 = $1.18/£
This alternative approach is technically more accurate but either approach would get
full credit in the exam.
Investment appraisal Foreign investment appraisal 3.2 Interpreting exchange rate information Perpetuities shortcut
For a perpetuity we cannot predict the future exchange rate for all cash flows.
Instead we need to think about how the exchange rate will impact the cash flows
overall.
For example, if we have a receipt in $ every year for the foreseeable future and the $
appreciates against the £ by 1% per year. The £ can afford less $s per year and we
will translate our receipt at a smaller number each year. Effectively our receipt in £s
will grow by 1% per year. We can therefore discount our perpetuity as a growing
perpetuity with growth of 1%.
Investment appraisal Foreign investment appraisal 3.3 Foreign investment appraisal approach
There are two alternative approaches to working out the NPV of a foreign project,
with the first method being used for the majority of questions:
1 Convert foreign cash flows into the home currency, then discount using the
firm’s normal cost of capital.
2 Leave the cash flows in foreign currency and discount using a foreign (adjusted)
cost of capital. Then translate back into the home currency at the current spot
rate.
This foreign (adjusted) cost of capital can be found using the International
Fisher Effect equation:
1 + radjusted =
FX rate t1 × (1 + r) FX rate t0
Method 1 is generally more flexible as it can:
Deal with exchange rates which are not changing at a constant rate
Be adapted more easily to incorporate additional UK cash flows.
However method 2 may be preferable in some circumstances (e.g. where the foreign
cash flows are a long annuity or perpetuity).
Investment appraisal Foreign investment appraisal 3.3 Foreign investment appraisal approach Method 1 approach
Prepare a standard NPV schedule for foreign currency CFs (including any F.C.
tax)
Calculate FX rates for each year (as above)
Use the calculated FX rates to translate the net flows into £s
Add in any additional £ CFs
Discount net £ flows at the UK discount rate (normally cost of capital). The sum
of the discounted cash flows can be calculated using the spreadsheet function:
= NPV(discount rate, cell range)
Remember to deduct the investment at T0 to get the NPV.
Investment appraisal Foreign investment appraisal 3.3 Foreign investment appraisal approach Method 2 approach
Prepare a standard NPV schedule for foreign currency CFs (including any F.C.
tax)
Calculate the FX rate for T1 if not given (as above)
Calculate the adjusted discount rate, using the following formula to adjust the
UK discount rate using the T0 and T1 FX rates
1 + radjusted = (FX rate t1) / (FX rate t0) × (1 + r)
Discount the net FC flows at the adjusted discount rate using the NPV function
Convert the PV to £s using the current spot rate
Add in the PV of any additional £ cash flows discounted at the standard UK cost
of capital.
