This document discusses methods for evaluating investments, including net present value (NPV), gross present value, and internal rate of return. It provides definitions and formulas for each. As an example, it calculates the NPV, gross present value, and internal rate of return for a hypothetical investment that costs £1,000,000 upfront and generates £50,000 annual income for 5 years, at which point £1,200,000 capital is returned. It performs the calculations and determines that for a 10% target rate of return, the NPV is negative £65,355, while the gross present value and internal rate of return are also provided.

1. Calculating Net Present Value, Gross
Present Value and Internal Rate of
Return

2. Net Present Value
• Net Present Value is the standard technique in investment or
project appraisal for deciding whether a project is worth doing – or
an investment is worth making
• The NPV rule is that: when discounted at the target rate of return,
the NPV of the cash flow generated by an investment is not
negative, then the project is acceptable.
• It is simply the sum of the present values of all cash flows
generated by an investment or project
• The Gross Present Value is identical to the Net Present Value except
that the initial cost is ignored.

3. Answer five questions, set out the cash
flow and discount it
1.
2.
3.
4.
5.
How much is paid out?
When?
How much is received?
When?
What is the target rate of return?

4. Hypothetical investment
• Cost: £1,000,000
• Income received: £50,000 per annum
receivable annually in arrears for five years
• Capital received: £1,200,000 in five years
• TRR: 10% per annum.

5. Period
0
1
2
3
4
5
Capital Outlay
-£1,000,000
£0
£0
£0
£0
£0
Income
£0
£50,000
£50,000
£50,000
£50,000
£50,000
Capital receipt
£0
£0
£0
£0
£0
£1,200,000
Net Cash Flow
-£1,000,000
£50,000
£50,000
£50,000
£50,000
£1,250,000
PV factor @ 10%
1.0000
0.9091
0.8264
0.7513
0.6830
0.6209
Present Value
-£1,000,000
£45,455
£41,322
£37,566
£34,151
£776,152
NPV
What is the Gross Present Value?
-£65,355

6. Internal Rate of Return

7. Internal rate of return
• Technically - the Internal Rate of Return is the
discount rate at which the Net Present Value
is zero.
• It is the most important measure of actual or
expected investment performance.
• Broadly it is the average return (both capital
or income) on cash invested expressed as a %
per period

8. Period
0
1
2
3
4
5
Capital Outlay
-£934,645
£0
£0
£0
£0
£0
Income
£0
£50,000
£50,000
£50,000
£50,000
£50,000
Capital receipt Net Cash Flow PV factor @ 10% Present Value
£0
-£934,645
1.0000
-£934,645
£0
£50,000
0.9091
£45,455
£0
£50,000
0.8264
£41,322
£0
£50,000
0.7513
£37,566
£0
£50,000
0.6830
£34,151
£1,200,000
£1,250,000
0.6209
£776,152
NPV
£0