Question

A  firm is considering the purchase of one of two machines to replace an existing one. MachineA will cost GBP £18,000 and has a four-year life. Annual net cash flows are expected to be GBP£7,200, beginning one year after the machine is purchased. Machine B will cost GBP £26,000and has a six-year life. Annual net cash flows are expected to be GBP £7,500, beginning oneyear after the machine is purchased. Assume the firm's cost of capital is a constant 15%forever, and there is no value to flexibilityas these machines will continue to be manufactured

Which of the following statements is incorrect?

a)The NPV of Machine A is greater than the NPV of Machine B

b)Machine B has a lower equivalent annual cash flow (or equivalent rental value) thanMachine A

c)Machine B has an equivalent annual cash flow (or equivalent rental value) greater than GBP£700

d)Machine A has an equivalent annual cash flow (or equivalent rental value) greater than GBP£700

e)Machine B has an equivalent annual cash flow (or equivalentrental value) that is less thanGBP £2000 per year higher than Machine A (to the nearest pound).

Answer 1

Machine A NPV

Year	0	1-4
Cost of machine	(18,000.00)
Annual net cashflows		7,200.00
Net cashflows	(18,000.00)	7,200.00
PV factor @ 15% ---> Year0--> 1/(1+15%)^nth year Year 1 to 4 ---> (1-(1+15%)^-no. of years)/15%	1.00	2.85
PV of cashflows ---> Net cashflows x PV factor	(18,000.00)	20,555.84
NPV	2,555.84

Machine B NPV

Year	0	1-6
Cost of machine	(26,000.00)
Annual net cashflows		7,500.00
Net cashflows	(26,000.00)	7,500.00
PV factor @ 15% ---> Year0--> 1/(1+15%)^nth year Year 1 to 6 ---> (1-(1+15%)^-no. of years)/15%	1.00	3.78
PV of cashflows ---> Net cashflows x PV factor	(26,000.00)	28,383.62
NPV	2,383.62

NPV of Machine A is greater than NPV of Machine B.

Equivalent Annual cashflow of Machine A

Equivalent Annual cashflows= NPV / PV annuity factor

Equivalent Annual cashflows= NPV / ((1-(1+interest rate)^-no. of years)/interest rate)

Equivalent Annual cashflows= 2555.84 / ((1-(1+15%)^-4)/15%)

Equivalent Annual cashflows= 2555.84 / 2.85

Equivalent Annual cashflows= $ 895.22

Equivalent Annual cashflow of Machine B

Equivalent Annual cashflows = NPV / PV annuity factor

Equivalent Annual cashflows= NPV / ((1-(1+interest rate)^-no. of years)/interest rate)

Equivalent Annual cashflows= 2,383.62/ ((1-(1+15%)^-6)/15%)

Equivalent Annual cashflows= 2,383.62/ 3.78

Equivalent Annual cashflows= $ 629.84

NPV of Machine A has higher equivalent annual cashflows in comparison to that of Machine B

Therefore the incorrect answers are:

c). Machine B has an equivalent annual cash flow (or equivalent rental value) greater than GBP£700

e). Machine B has an equivalent annual cash flow (or equivalentrental value) that is less thanGBP £2000 per year higher than Machine A (to the nearest pound).

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