Chapter 3 - Investment Appraisal - Discounted Cash Flow Techniques

Question 0

Discounting a single sum

Answer 0

P = F/ (1+r)^n = F(1+r)^-n

1+r)^-n is called the discount factor (DF

Question 1

Compounding

Answer 1

F = P(1+r)^n

F = Future value after n periods
P = Present or Initial value
r = Rate of interest per period
n = Number of periods

Question 2

The Net Present Value (NPV)

Answer 2

The NPV represents the surplus funds earned on the project.

1. If the NPV is positive - The project is financially viable.
2. If the NPV is zero - The project breaks even.
3. If the NPV is negative - The project is not financially viable.

Assumptions used in discounting:

1. All cash flows occur at the start or end of the year.
2. Initial investments occur at once (T0), other cash flows start in one year’s time (T1).

Question 3

Discounting annuities

Answer 3

An annuity is a constant annual cash flow for a number of years.

The annuity factor (AF) is the sum of the individual DF.

PV = Annual cash flow x AF

AF = [1- (1+r)^-n]/ r

Question 4

Discounting perpetuities

Answer 4

A perpetuity is an annual cash flow that occurs forever.

PV = Cash flow/ r

Or

PV = Cash flow x 1/ r

1/ r is known as the perpetuity factor.

Question 5

Advanced annuities and perpetuities

Answer 5

Some regular cash flows may start now (at T0) rather than in one year’s time.

Calculate PV by ignoring the payment at T0 and adding one to the annuity or perpetuity factor.

Question 6

Delayed annuities and perpetuities

Answer 6

Some regular cash flows may start later than T1.

These are dealt with by:

1. Applying the appropriate factor to the cash flow as normal
2. Discounting your answer back to T0.

Question 7

The Internal Rate of Return (IRR)

Answer 7

The IRR represents the discount rate at which the NPV of an investment is zero. It represents a break even cost of capital.

Question 8

Calculating the IRR using linear interpolation

Answer 8

The steps in linear interpolation are:
1. Calculate two NPVs for the project at two different costs of capital.

2. Use IRR = L + [N(L)/ [N(L)-N(H)] x (H-L)]

L = Lower rate of interest
H = higher rate of interest
N(L) = NPV at lower rate of interest
N(H) = NPV at higher rate of interest

Question 9

Calculating the IRR with even cash flows

Answer 9

To calculate the IRR with even cash flows which are annuities:

1. Find the cumulative DF, Initial investment/ Annual inflow.
2. Find the life of the project, n.
3. Look along the n year row of the cumulative DF until the closest value is found.
4. The column in which this figure is found is the IRR.

Question 10

Calculating the IRR with perpetuities

Answer 10

IRR of a perpetuity = Annual inflow/ Initial investment x 100%