Question

The Chicago Hope Hospital purchased a MRI machine for $5 million dollars, using a 6 year loan at 8% interest.

a. The above MRI machine which costs 5 million comes with a service charge for an additional amount of $20,000 each year for 5 years. What is the present value of cash flows for the MRI machine (use 8% as the discount rate)?

b. The salvage value of the machine is $100,000 five years from now. What is the present value of the salvage value of the MRI?

Answer 1

Calculation of PV of cash flows      
Cash Flows on Cost of machine at year 0 =       -5000000
Year 0 cash flows present value is same as        -5000000
      
Year 1 to 5 have single cash flows of $20000. So Present Value of Annuity formula will be used.      
Discount rate (i)=   8%  
Time (n)=   5  
Present value of Cash inflows = Annual amount * (1-(1/(1+r)^n) / r      
-20000*(1-(1/(1+8%)^5))/8%      
-79854.20

So Present Value of Cash flows = -5000000+(-79854.20)=   -$5,079,854.20  
      
Salvage value=   100000  
Present value of terminal value = Terminal value/(1+i)^n      
100000/(1+8%)^5      
68058.3197      
      
So Present Value of Salvage value is   $68,058.32