SMU is considering replacing a broken furnace that has been in use for a very lo
ID: 2760062 • Letter: S
Question
SMU is considering replacing a broken furnace that has been in use for a very long time, with a newer and more efficient furnace. If the broken furnace is repaired, it could provide service for another five years, although SMU can sell it now to a potential buyer for $10,000. If the furnace is kept, it will require an immediate $2,500 overhaul to restore it to operable condition. The overhaul will neither extend the service life originally estimated nor increase the value of the furnace. The operating costs are estimated at $3,500 during the first year and these are expected to increase by $1,500 per year thereafter. Future market values are expected to decline by $2,000 per year. The new furnace will cost $20,000 and will have operating costs of $2,500 in the first year, increasing by $1000 per year thereafter. The expected salvage value is $12,000 after one year and will decline 12% each year. SMU requires a rate of return of 15%.
• Find the economic life for each option.
• Determine when the defender should be replaced.
Explanation / Answer
Furnace (old):
Current salvage value = $10,000, decreasing at an annual rate of $2,000 over the previous year’s value
Required overhaul = $2,500
O&M = $3,500 in year 1, increasing at the rate of $1,500 each year
Required Rate of return = 15%
Economic life:
n
Market Value
O & M Cost
CR
OC
AEC
0
$10,000.00
$2,500.00
1
$8,000.00
$3,500.00
$3,500.00
$6,375.00
$9,875.00
2
$6,000.00
$5,000.00
$3,360.47
$5,735.47
$9,095.93
3
$4,000.00
$6,500.00
$3,227.86
$5,955.63
$9,183.50
4
$2,000.00
$8,000.00
$3,102.12
$6,365.05
$9,467.17
5
$-
$9,500.00
$2,983.16
$6,830.01
$9,813.17
Hence, Furnace (Old) economic life is 2 years (n =2 years) and AEC = $9,095.93
Furnace (new):
Cost = $20,000
Salvage value = $12,000 after one year, will decline 12% each year
O&M = $2,500 in the first year, increasing by $1,000 per year thereafter
Required Rate of return = 15%
Economic life:
n
Market Value
O & M Cost
CR(15%)
OC(15%)
AEC
0
$20,000.00
$-
$-
$-
1
$12,000.00
$2,500.00
$11,000.00
$2,500.00
$13,500.00
2
$10,560.00
$3,500.00
$7,390.70
$2,965.12
$10,355.81
3
$9,292.80
$4,500.00
$6,083.43
$3,407.13
$9,490.55
4
$8,177.66
$5,500.00
$5,367.60
$3,826.26
$9,193.86
5
$7,196.34
$6,500.00
$4,898.98
$4,222.81
$9,121.80
6
$6,332.78
$7,500.00
$4,561.30
$4,597.19
$9,158.49
7
$5,572.85
$8,500.00
$4,303.64
$4,949.85
$9,253.49
8
$4,904.11
$9,500.00
$4,099.74
$5,281.33
$9,381.07
9
$4,315.61
$10,500.00
$3,934.38
$5,592.23
$9,526.61
10
$3,797.74
$11,500.00
$3,797.99
$5,883.20
$9,681.19
Hence, Furnace (New) economic life is 5 years (n =5 years) and AEC = $9,121.80
Since AECold=$9,095.93 < AECnew=$5,826, the answer is not to replace the furnance now.
To answer the question, we have to calculate the cost of keeping Furnace (old) for a third year from today i.e. marginal analysis. Meaning, what is the marginal cost of not selling Finance (old) after 2 years, using it for a 3rd year, and replacing it at the end of year 3.
Financial Data:
Step 1: Calculate the equivalent cost of retaining the defender one more from the end of its economic service life, say 2 to 3.
$6,000(F/P,15%,1) + $6,500 - $4,000 = $9,400
Step 2: Compare this cost with AECnew = $9,121.80 of the challenger.
Conclusion: Since keeping the furnace (old) for the 3rd year is more expensive than replacing it with the furnace (new), DO NOT keep the furnace (old) beyond its economic service life.
Please find the excel for calculation of economi life at below link for your refeernce: https://drive.google.com/file/d/0B9YbXjglpuuKbmtDVXBuTGR6TU0/view?usp=sharing
n
Market Value
O & M Cost
CR
OC
AEC
0
$10,000.00
$2,500.00
1
$8,000.00
$3,500.00
$3,500.00
$6,375.00
$9,875.00
2
$6,000.00
$5,000.00
$3,360.47
$5,735.47
$9,095.93
3
$4,000.00
$6,500.00
$3,227.86
$5,955.63
$9,183.50
4
$2,000.00
$8,000.00
$3,102.12
$6,365.05
$9,467.17
5
$-
$9,500.00
$2,983.16
$6,830.01
$9,813.17
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