Suppose you are the physical plant manager for a new hotel with many light fixtu
ID: 1168172 • Letter: S
Question
Suppose you are the physical plant manager for a new hotel with many light fixtures. You need to decide if you should use 15 watt compact fluorescents or 60 watt incandescent, each giving equivalent amount of lumens of light. The compact fluorescents cost $4.49 and last 8 years, while the incandescents cost $0.50 and last 1 year (thus have to be bought 8 times). However the compact fluorescents save $4.96 per year in electricity costs. (This assumes that electricity costs 11 cents/kWh, lighting is used 2.75 hours per day x 365 days x 45watt savings.) Which light bulb should you use? Make the calculation using two different discount rates: 3% or 6%. You can use the Excel chart below to start your work. Print your results.
Cash Outlay for Investing in Lighting
Year
Option
0
1
2
3
4
5
6
7
8
A. Compact fluorescents
-$4.49
B. Incandescents
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
Electricity Savings from compact fluorescents
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
PV Savings w/ discount rate
3.00%
?
?
?
?
?
?
?
?
?
6.00%
?
?
?
?
?
?
?
?
?
Cash Outlay for Investing in Lighting
Year
Option
0
1
2
3
4
5
6
7
8
A. Compact fluorescents
-$4.49
B. Incandescents
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
-$0.50
Electricity Savings from compact fluorescents
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
$4.96
PV Savings w/ discount rate
3.00%
?
?
?
?
?
?
?
?
?
6.00%
?
?
?
?
?
?
?
?
?
Explanation / Answer
Present Value of savings = Present value of benefits – Present value of cost
At 3% discount rate (R)
For Compact fluorescents,
No. of years (n) = 8
Yearly savings (P) = $4.96
Present value of cost= $ 4.49
Present value of benefits = CF*(1-1/ (1+R) ^n)/ R
Present value of benefits = 4.96*(1-1/1.03^8)/.03
Present value of benefits = $34.817
Thus
Present Value of savings = Present value of benefits – Present value of cost
Present Value of savings = 34.817 – 4.49 = $30.327
For Incandescent
Yearly Cost = $.5
Present value of benefits = 0
Present value of cost = .5 + .5*(1-1/(1+R)^N)/R
N= 7 years
Present value of cost = .5 + .5*(1-1/1.03^7)/.03
Present value of cost = $3.615
Present Value of savings = Present value of benefits – Present value of cost
Present Value of savings = 0-3.615 = -$3.615
Since present value of savings of Compact fluorescents is higher than that of Incandescent. Thus, compact fluorescents should be selected.
At 6% discount rate (R)
For Compact fluorescents,
No. of years (n) = 8
Yearly savings (P) = $4.96
Present value of cost= $ 4.49
Present value of benefits = CF*(1-1/ (1+R) ^n)/ R
Present value of benefits = 4.96*(1-1/1.06^8)/.06
Present value of benefits = $30.80
Thus
Present Value of savings = Present value of benefits – Present value of cost
Present Value of savings = 30.80 – 4.49 = $26.31
For Incandescent
Yearly Cost = $.5
Present value of benefits = 0
Present value of cost = .5 + .5*(1-1/(1+R)^N)/R
N= 7 years
Present value of cost = .5 + .5*(1-1/1.06^7)/.06
Present value of cost = $3.291
Present Value of savings = Present value of benefits – Present value of cost
Present Value of savings = 0-3.291 = -$3.291
Since present value of savings of Compact fluorescents is higher than that of Incandescent. Thus, compact fluorescents should be selected.
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