These are two independent questions.

a The Danforth Business sells a new type of macadamia nut shelling machine that it claims will save a constant amount of labour costs at a particular business each year for 10 years. Danforth suggests that this savings would have a present value (at 16 per cent) of \(\$ 21460.50\) to the business. What is the amount of the annual labour cost savings being claimed?

b The Solenoid Business sells a small mechanical apparatus with a complicated solid-state control unit that attaches to a car's carburettor. Solenoid claims the apparatus will save the average car owner \(\$ 120\) per year in fuel bills that should be worth over \(\$ 1000\) (present value) to the owner using a discount rate of 10 per cent. If the apparatus can save \(\$ 120\) per year, how many years would it have to be used for the present value of the savings to exceed \(\$ 1000\) ?

Required:

Prepare an analysis to answer each of the questions.