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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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