In: Finance
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 |
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