Question

Low-energy lightbulbs typically cost $3.75, have a life of nine years, and use about $1.85 of electricity a year. Conventional lightbulbs are cheaper to buy, for they cost only $.55. On the other hand, they last only about a year and use about $6.85 of energy.   

a. If the real discount rate is 6%, what is the equivalent annual cost of the two products? (Do not round intermediate calculations. Enter your answers as a positive value rounded to 2 decimal places.)

	Equivalent Annual Cost
Low-energy lightbulbs	$
Conventional lightbulbs	$

b. Which product is cheaper to use?

	Low-energy lightbulbs
	Conventional lightbulbs

Answer 1

a]

EAC = (NPV * r) / (1 - (1 + r)^-n),

where NPV = net present value

r = discount rate

n = time period in years

NPV of Low-energy lightbulbs = initial cost + present value of yearly expenses

NPV of Low-energy lightbulbs = $3.75 + $1.85 * (PVAF(6%, 9) (where PVAF is the present value annuity factor)

NPV of Low-energy lightbulbs = $3.75 + ($1.85 * 6.8017) = $16.33

EAC of Low-energy lightbulbs = (16.33 * 0.06) / (1 - (1 + 0.06)^-9) = $2.40

NPV of conventional lightbulbs = initial cost + present value of yearly expenses

NPV of conventional lightbulbs = $0.55 + $6.85 * (PVAF(6%, 1) (where PVAF is the present value annuity factor)

NPV of conventional lightbulbs = $0.55 + ($6.85 * 0.9434) = $7.01

EAC of conventional lightbulbs = (0.7.01 * 0.06) / (1 - (1 + 0.06)^-9) = $1.03

b]

The EAC of  conventional lightbulbs is lower than the EAC of Low-energy lightbulbs

conventional lightbulbs are cheaper to use