Answer to Question #173796 in Financial Math for Meden

Question

Project R delegates all the development work to outside companies. The estimated cashflows for Project R are (where brackets indicate expenditure): Beginning of Year 1 (£150,000) (contractors’ fees) Beginning of Year 2 (£250,000) (contractors’ fees) Beginning of Year 3 (£250,000) (contractors’ fees) End of Year 3 £1,000,000 (sales) Project S carries out all the development work in-house by purchasing the necessary equipment and using the company’s own staff. The estimated cashflows for Project S are: Beginning of Year 1 (£150,000) (New equipment) Continuous payments Through Year 1 (£75,000) (Staff Cost) Continuous payments Through Year 2 (£250,000) (Staff Cost) Continuous payments Through Year 3 (£250,000) (Staff Cost) End of Year 3 £1,000,000 (sales) REQUIRED a) Calculate the net present value for Project R and Project S using a risk discount rate of 20% per annum.

Answer 1

Project R

NPV = PV of cash inflows - PV of cash outflows

PV of inflows=1,000,000(1/1.2^3)

=578,703.70

PV of outflows=150,000(1/1.2^1)+250,000(1/1.2^2)+250,000(1/1.2^3)

=125000+144,675.9259+83,333.333

=353,008.33

NPV=578,703.70-353,008.33

=225,695.37

Project S

PV of cash inflows=1,000,000(1/1.2^3)

=578,703.70

PV of cash outflows=150,000(1/1.2^1)+75,000(exp(1*0.2))+(250,000(exp(2*0.2))+250,000(exp(3*0.2))

=125,000+91,605.21+375,956.1744+455,529.700

=1,048,091.084

NPV=578,703.70-1,048,091.084

=-469,387.3845