Answer the following compounding/discount questions assuming year end cash flows
ID: 2804303 • Letter: A
Question
Answer the following compounding/discount questions assuming year end cash flows: A. The west bend community hospital purchased an MRI machine for $50 million, using a 10 year loan at 10.5% interest. What will be the annual payment for this machine? B. The price of the MRI nxchibd($50 million) is rising at a fixed rate of 2.2% each year. How much would it costs to replace the MRI machine ten years from now? Answer the following compounding/discount questions assuming year end cash flows: A. The west bend community hospital purchased an MRI machine for $50 million, using a 10 year loan at 10.5% interest. What will be the annual payment for this machine? B. The price of the MRI nxchibd($50 million) is rising at a fixed rate of 2.2% each year. How much would it costs to replace the MRI machine ten years from now? A. The west bend community hospital purchased an MRI machine for $50 million, using a 10 year loan at 10.5% interest. What will be the annual payment for this machine? B. The price of the MRI nxchibd($50 million) is rising at a fixed rate of 2.2% each year. How much would it costs to replace the MRI machine ten years from now?Explanation / Answer
A. To compute the annual payments or any periodic payment of a loan divide the loan amount with the present value factor annuity for that period at the given rate.
Annual Payment = $50,000,000 / PVFA (10.5%, 10) = $50,000,000 / 6.01477274026 = $8,312,866.03154 or $8,312,866
PVF is computed as 1 / (1+ r)t where r is rate of interest and t is year for which it is computed. For example in our case PVF for year 1 would 1 / (1 + 0.105)1 and for year 4 would be 1 / (1 + 0.105)4 . PVFA is computed by adding all the values of PVF for the given period.
B. We need the future value in this case, which would be computed as -
Future value of MRI machine = $50,000,000 x (1 + r)t = $50,000,000 x (1 + 0.022)10 = $62,155,413.827 or $62,55,414