A freestanding imaging center is considering adding a new modality to its busine
ID: 2739056 • Letter: A
Question
A freestanding imaging center is considering adding a new modality to its business. They can either purchase a CT scanner or an MRI scanner. The CT scanner will cost $800,000, will have useful life of 10 years, salvage value of $50,000 and will return $100,000 annually. The MRI scanner will cost $1,500,000, will have a useful life of 8 years, salvage value of $100,000 and will return $140,000 annually. Using an 8% discount rate which modality do you recommend as the more profitable option? (If both are losses, you can recommend not pursuing either.)
Explanation / Answer
Year
CashFlow
PV Factor@ 8%
PV
0
(800,000)
1
(800,000)
1
100,000
0.9259
92,593
2
100,000
0.8573
85,734
3
100,000
0.7938
79,383
4
100,000
0.7350
73,503
5
100,000
0.6806
68,058
6
100,000
0.6302
63,017
7
100,000
0.5835
58,349
8
100,000
0.5403
54,027
9
100,000
0.5002
50,025
10
150,000
0.4632
69,479
NPV
(105,832.18)
C= r(NPV)/1-(1+r)-n
C= Equivalent Annuity cash flow
NPV= Net Present Value
r=rate per period
n= no of periods
C= 0.08(105,832.18)/1-(1+0.08)-10
=8,466.57/1-(1.08)-10
=8,466.57 /1-0.463193488’
=8,466.57/0.536806512
= $(15,772.12)
Year
CashFlow
PV Factor@ 8%
PV
0
(1,500,000)
1
(1,500,000)
1
140,000
0.9259
129,630
2
140,000
0.8573
120,027
3
140,000
0.7938
111,137
4
140,000
0.7350
102,904
5
140,000
0.6806
95,282
6
140,000
0.6302
88,224
7
140,000
0.5835
81,689
8
240,000
0.5403
129,665
NPV
(641,443.66)
C= r(NPV)/1-(1+r)-n
C= Equivalent Annuity cash flow
NPV= Net Present Value
r=rate per period
n= no of periods
C= 0.08(-641,443.66)/1-(1+0.08)-8
= (51,315.49)/1-(1.08)-8
= (51,315.49) /1- 0.540268885
=(51,315.49)/ 0.459731115
= $ (1,395,258.31)
Both projects NPV negative both are not profitable
Year
CashFlow
PV Factor@ 8%
PV
0
(800,000)
1
(800,000)
1
100,000
0.9259
92,593
2
100,000
0.8573
85,734
3
100,000
0.7938
79,383
4
100,000
0.7350
73,503
5
100,000
0.6806
68,058
6
100,000
0.6302
63,017
7
100,000
0.5835
58,349
8
100,000
0.5403
54,027
9
100,000
0.5002
50,025
10
150,000
0.4632
69,479
NPV
(105,832.18)
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