• b.The Project Costs workbook and associated parts of the Renewable Energy textbook introduce you to Discounted Cash Flow. In this context you learn about Net Present Value (NPV), Internal Rate of Return (IRR) and the Average Annual Rate of Return (ROR). NPV and IRR calculations are likely to be useful in your project work (see SGB Section 2.3).

  The Present Value (PV) of an amount of money which arrives (or is paid out) at the end of year N in the future is given by the following formula:

  NOTE: to make this formula work, you must express the discount rate as a decimal fraction, not a percentage. E.g. 5% would be entered as 0.05.

  You can then get the NPV of a series of future monetary amounts by summing all the present values together.

  The table below shows information for two projects that are expected to generate incomes for 5 years, following the year during which infrastructure was installed ( also known as CF0 = cash flow year zero).

  Both projects initially cost the same, 5700.

  However, whereas Project Apollo is expected to produce a predictable income of the same amount in each of the following 5 years, Project Gemini will produce an income that varies significantly from year to year.

  Calculate the net present value of each project over the 5-year life of the projects:

  • i.at a discount rate of 5%

  • ii.at a discount rate of 12%

  • Show all your calculations. Put them in the Calculations column of the tables below.
  • Record your results by completing the blank cells in the Present value column of the table.
  • Work out the Net Present Value by summing all the cash flow years present values. NPV column totals should be rounded to the nearest valid monetary value in pounds and pence.

You should NOT use a spreadsheet to work out your answer to this part of the question as the TMA marker wants to see that an understanding of the process of this calculation is clearly demonstrated.

Table 1: cash flows for each year, for projects Apollo and Gemini. NOTE the set-up cost is negative because it is an outflow of money, whereas all the others are positive because they represent money coming in.

Cash flow year	0	1	2	3	4	5
Project option Apollo	-5700	1503	1503	1503	1503	1503
Project option Gemini	-5700	1580	1380	1490	1520	1595

Tables 2 and 3: Complete these tables for Project Apollo and Project Gemini. Some cells have been pre-populated as a start.

Table 2 Project Apollo
	Discount rate 5%		Discount rate 12%
Year	Calculation (Show your working)	Present value ()	Calculation (Show your working)	Present value ()
0	-5700/(1+0.05)0=	-5700.00	-5700/(1+0.12)0=	-5700.00
1	1503/(1+0.05)1=	1431.42857143	1503/(1+0.12)1=	1341.96428571
2
3
4
5
	Sum of all the present values (net present value, NPV)		Sum of all the present values (net present value, NPV)

Table 3 Project Gemini
	Discount rate 5%		Discount rate 12%
Year	Calculation (Show your working)	Present value ()	Calculation (Show your working)	Present value ()
0	-5700/(1+0.05)0=	-5700.00	-5700/(1+0.12)0=	-5700.00
1	1580/(1+0.05)1=	1504.76190476	1580/(1+0.12)1=	1410.71428571
2
3
4
5
	Sum of all the present values (net present value, NPV)		Sum of all the present values (net present value, NPV)