Answer:
The break even cost is $0.0063825
Explanation:
Break-even cost is the amount of money, or change in value, which equates to the amount at which an asset must be sold to equal the cost of acquiring it. For easier understanding it can be thought the amount of money for which a product or service must be sold to cover the costs of manufacturing or providing it.
Wattage = W
Cost per kilo watt hour = C
Number of hours per year = H
Price per bulb/CFL = P
Discount rate = 11%
Life of bulb = 2 years
Price of bulb = $0.39
Wattage consumption of bulb per hours = 60
Life of CFL = 24 years
Price of CFL = $3.10
Wattage consumption of CFL per hour = 15
Calculate the Equated Annual Cost (EAC) of bulb
EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2years)}/ (PVIFA 11%, 2years)
PVIFA 11%, 2years = Annuity PV Factor = [1 – {(1 + r)^(-n)}]/r, where r is the rate per period and n is the number per periods
PVIFA 11%, 2 years = [1 – {(1 + 0.11)^(-2)}]/0.11 = 1.712523 (for 2 years)
PVIFA 11%, 24 years = [1 – {(1 + 0.11)^(-24)}]/0.11 = 8.348136 (for 2 years)
<u>Calculate the EAC of bulb</u>
EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 2 years)}/ (PVIFA 11%, 2 years)
EAC = {- 0.39 - (60/1000 x H x C) x (1.712523)}/ (1.712523)
EAC = {-0.39 – (51.37570 x C)}/ 1.712523, <em>consider this equation 1</em>
<u>Calculate the EAC of CFL</u>
EAC = {- P - (W/1000 x H x C) x (PVIFA 11%, 24 years)}/ (PVIFA 11%, 24 years)
EAC = {- 3.10 - (15/1000 x 500 x C) x (8.348136)}/ (8.348136)
EAC = {-3.10 – (62.61102 x C)}/8.348137, <em>consider this equation 2</em>
<u>Equate 1 and 2 to find the amount of C</u>
{-0.39 – (51.37570 x C)}/ 1.712523 = {-3.10 – (62.61102 x C)}/8.348137
{-0.39 – (51.37570 x C) x 8.348137} = {-3.10 – (62.61102 x C) x 1.712523}
C = $0.0063825
Thus, the break- even cost per kilo – watt is $0.0063825
