Chapter 2 Investment appraisal

Question 1

1.1 Discounting

Answer 1

Single cash flow: Present value (PV) = cash flow at tn x discount factor
- DF = 1 / (1+r)^n
Annuity cash flow: a constant annual cash flow occurring for a set number of years. PV = constant annual CF x annuity factor
- Aft-tn = 1 / r (1 – 1/(1+r)^n)
Perpetuity cash flow: a constant annual cash flow occurring forever. PV = constant annual CF x perpetuity factor
- PF = 1/R
Perpetuity with growth: an annual cash flow occurring forever and growing at a constant rate. PV = CF at t1 x PF (with growth)
- PF (with growth) = 1 / r -g
Non-annual discount rates: (1+R) = (1+r)^n, where
R is the non-annual rate; r is the annual rate and n is the number of time periods

Question 2

2.1 Internal rate of return

Answer 2

IRR method is used to provide the average return generated from the inflows compared to the investment. It can be calculated using the IRR spreadsheet function. Two main problems include:
- It assumes cash flows are re-invested at the IRR rate, rather than 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.
- It does not consider when actual cash flows take place, which can be overcome by calculating the extended internal rate of return.

Question 3

2.2 Modified internal rate of return.

Answer 3

MIRR = (Terminal value of net annual inflows / PV of net annual outflows) ^ (1/n) – 1
Or the spreadsheet function: =MIRR (range of cells t0 – tn, finance rate, return in reinvested funds).

Question 4

2.3 Extended internal rate of return

Answer 4

The XIRR takes into account the dates when the actual cash flows takes place and is useful for a series of cash flows that are not periodic. It can be calculated using the spreadsheet function, = XIRR(values, dates).

Question 5

3.1 Foreign investment appraisal: Net present value

Answer 5

NPV = PV of future cash flows associated with a project. If NPV is above 0 then accept, as NPV is change in wealth for the investor. Spreadsheet function: =NPV(discount rate, CFs to be discounted).

Question 6

3.2 Foreign investment appraisal approach

Answer 6

There are two alternative approaches to working out the NPV of a foreign project:
- Convert foreign cash flows into the home currency, then discount using the firm’s normal cost of capital
- Leave the cash flows in foreign currency and discount using a foreign cost of capital. Then translate back into home currency at the current spot rate. The foreign cost of capital is found using the fisher effect equation:
o 1 + r(adjusted) = FX rate t1 / FX rate t0 x (1+r)
The first approach is more flexible as it can deal with exchange rates which are not changing at a constant rate and be adapted easily to incorporate additional UK cash flows. Method 2 is preferable where the foreign cash flows are a long annuity or perpetuity.
Under method 1:
- Prepare a standard NPV schedule for foreign currency cashflows.
- Calculate FX rates for each year.
- Use the calculated FX rates to translate the net flows into £s.
- Add in any additional UK cashflows.
- Discount net flows at the UK discount rate
Under method 2:
- Prepare a standard NPV schedule for foreign currency CFs.
- Calculate the FX rate for T1.
- Calculate the adjusted discount rate.
- 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.

Question 7

3.4 Possible further complications in foreign NPV

Answer 7

Double taxation: under an agreement a UK company will only pay UK tax on foreign income to the extent the UK rates exceeds the foreign rate.
Subsidies: the benefit of any foreign subsidies should be included in the NPV calculation
Exchange restrictions: any CFs that cannot be repatriated to the UK should not be included in the NPV calculation.

Question 8

4.1 Environmental and social costing

Answer 8

this needs to be considered as part of the appraisal process:
- They are likely to influence consumer and investor decisions.
- It may be a requirement if the company has used green finance or the industry is regulated.
- Understanding the key costs will help with pricing decisions and may generate savings.
- Fines may be incurred without compliance.
If a company does proceed with a project that results in a negative environmental impact, it should consider the clean-up costs under IAS37. These costs are difficult to measure and quantify, making it difficult to include with the appraisal process.