32. Lavania Co
Lavania Co. is a construction company. It uses a large earth moving vehicle called the Buster to prepare foundations for buildings. It needs to decide whether the cheapest replacement interval for the Buster is three or four years.
The following details are available:
Lavania Co purchases the Buster from a manufacturer for $800,000, payable one year after delivery. Its resale value will fall by 40% of the purchase price at the end of its first year of operation. The resale value will then reduce by 25% of its previous year’s resale value for each further year of operation.
Yearly maintenance costs are $20,000 at the end of its first year of operations, rising by 5% per year. Maintenance must be provided in the year of sale.
Yearly fuel costs are $28,000 in the first year rising by $5,000 for each extra year it is operated.
If the Buster is operated beyond three years it is subject to a government safety and carbon emissions test. The test would be paid for and would take place at the beginning of the fourth year of operation. Correction of any faults discovered by this test is mandatory. There is an 80% chance that the test and remedial work will cost Lavania Co $50,000, and a 20% chance it will cost $120,000.
Lavania Co’s cost of capital is 8%.
Ignore taxation
A. Calculate the equivalent annual cost of the threeyear and fouryear replacement intervals for the Buster and advise Lavania Co which replacement interval to adopt.
Optimal replacement interval

Y0 
Y1 
Y2 
Y3 
Y4 

$000 
$000 
$000 
$000 
$000 
Threeyear interval 





Purchase cost 
(800·0) 




Maintenance cost (w1) 

(20·0) 
(21·0) 
(22·1) 

Fuel cost 

(28·0) 
(33·0) 
(38·0) 

Resale value (w2) 



270·0 

Net cash flow 
0·0 
(848·0) 
(54·0) 
210·0 

Present value factors at 8% 
1·000 
0·926 
0·857 
0·794 

Present value 
0·0 
(785·2) 
(46·3) 
166·7 

Net present value (664·8)
Equivalent annual cost (w3) (258·0)

Y0 
Y1 
Y2 
Y3 
Y4 

$000 
$000 
$000 
$000 
$000 
Fouryear interval 





Purchase cost 
(800·0) 




Maintenance cost (w1) 

(20·0) 
(21·0) 
(22·1) 
(23.2) 
Fuel cost 

(28·0) 
(33·0) 
(38·0) 
(43.0) 
Safety test (w4) 



(64·0) 

Resale value (w5) 




202·5 
Net cash flow 
0·0 
(848·0) 
(54·0) 
(124·1) 
136·3 
Present value factors at 8% 
1·000 
0·926 
0·857 
0·794 
0.735 
Present value 
0·0 
(785·2) 
(46·3) 
(98·5) 
100·2 
Net present value (829·8)
Equivalent annual cost (w6) (250·5)
Recommendation
The fouryear replacement interval has the lowest equivalent annual cost and on an expected cost basis, Lavania Co should replace the Buster every four years.
However, it is a close decision and there is a 20% chance that the cost of the government test will be $120,000 and this would make the fouryear interval more expensive than the threeyear option (working 7). Also, Lavania Co should consider that it has only looked at three and fouryear replacement intervals. Other, potentially cheaper, intervals should be considered.
Workings
Working 1 $20,000 x 1·05 = 21,000
$20,000 x 1·052 = 22,050
Working 2 $800,000 x 0·6 x 0·75 x 0·75 = $270,000
Working 3 NPV/3year annuity factor at 8% $664,800/2·577 = $258,000
Working 4 $50,000 x 0·8 + $120,000 x 0·2 = $64,000
Working 5 $800,000 x 0·6 x 0·75 x 0·75 x 0·75 = $202,500
Working 6 NPV/4year annuity factor at 8% = $829,800/3·312 = $250,500
Working 7 Effect of government test costing $120,000

Y0 
Y1 
Y2 
Y3 
Y4 

$000 
$000 
$000 
$000 
$000 
Purchase cost 
(800·0) 




Maintenance cost (w1) 

(20·0) 
(21·0) 
(22·1) 
(23.2) 
Fuel cost 

(28·0) 
(33·0) 
(38·0) 
(43.0) 
Safety test 



(120·0) 

Resale value 




202·5 
Net cash flow 
0·0 
(848·0) 
(54·0) 
(180·1) 
136·3 
Present value factors at 8% 
1·000 
0·926 
0·857 
0·794 
0.735 
Present value 
0·0 
(785·2) 
(46·3) 
(143.0) 
100·2 
Net present value (874·3)
Equivalent annual cost (264·0)
Note: Working 7 is not required to get the marks available.