Question

An airport is looking for some devices to support the luggage transportation services. There are 4 alternatives available (D1, D2, D3 and D4). To assist the evaluations, their purchase costs, service lives, possible salvages at the end of lives have been collected in Table Q2. In addition, the monthly variable costs of using these devices to perform the luggage transportation services in particular, and the numbers of corresponding devices needed are also provided in Table Q2. Given that the internal rate of return is set to 0.8% per month in that case.

1. (a) What are the Present Values of the end of life salvages (per unit) from these 4 devices? (4 marks)

2. (b) Determine the Capital Recovery Factors for the calculations of the monthly equivalent fixed costs (per unit) of the 4 devices. (4 marks)

3. (c) What are the fixed costs (per unit) in a monthly basis of the 4 devices? (4 marks)

4. (d) Prioritize the preference of choosing these 4 devices based on the cost minimization purpose and order them in the format of A > B > ..., where A is better than B and so on.

   (8 marks)

5. (e) What is the total monthly cost of the most preferred choice for providing the luggage

transportation services?

(5 marks)

Rubrics and Marking:

Table Q2

Device	D1	D2	D3	D4
Purchase Cost ($/unit)	38000	18000	35000	12000
Service Life (years)	5	7	8	4
End of Life Salvage ($/unit)	2500	2000	3200	3000
No. of Devices Required (units)	1	2	1	3
Variable Cost Required ($/month/unit)	450	220	380	150

Answer 1

Device	D1	D2	D3	D4
Purchase Cost ($/unit)	38000	18000	35000	12000
Service Life (years)	5	7	8	4
in months(yrs.*12)	60	84	96	48
End of Life Salvage ($/unit)	2500	2000	3200	3000
No. of Devices Required (units)	1	2	1	3
Variable Cost Required ($/month/unit)	450	220	380	150
Total variable cost(per unit*no.of units)	450	440	380	450
PV of annuity of variable costs
Device	D1	D2	D3	D4
A.Purchase Cost ($/unit)	38000	18000	35000	12000
1.Service Life (years)	5	7	8	4
2.                      in months(yrs.*12)	60	84	96	48
3.End of Life Salvage ($/unit)	2500	2000	3200	3000
(a) Present Values of the end of life salvages (per unit) (Row 3/1.008^Row 2)	2500/1.008^60=	2000/1.008^84=	3200/1.008^96=	3000/1.008^48=
	1549.92	1024.11	1489.15	2046.52
4.No. of Devices Required (units)	1	2	1	3
5.Variable Cost Required ($/month/unit)	450	220	380	150
6.Total variable cost for the device	450	440	380	450
7.Monthly Capital Recovery Factors (Ans.b)	(1-1.008^-60)/0.008=	(1-1.008^-84)/0.008=	(1-1.008^-96)/0.008=	(1-1.008^-48)/0.008=
	47.50421418	60.99331783	66.83001785	39.72838826
8.PV of variable costs for the device(6*7)(Ans.c)	21376.89638	26837.05985	25395.40678	17877.77472
9.Net PV of costs(A-a+8)	57826.98	43812.95	58906.26	27831.26
10.Equivalent monthly cost(NPV/Factor)(9/7)	1217.30	718.32	881.43	700.54
d..so, from the above
from cost minimisation point of view,
D4 > D2> D3 > D1
(e) Total monthly cost of the most preferred choice for providing the luggage = $ 700.54 (Uniform Equivalent Monthly Cost for the device D4)