Question

ME: I want ALL calculus work shown! I do NOT want a table. Specifically, explain your answer!

Von Broward is a regional director for a 24-hour Emergency Clinic franchise. Von is considering the purchase of a CT scanner to be installed in the Luckenbach, Texas location. A salesperson from ScansRUs has offered to sell CT scanner model 0731 for an initial purchase price of $650000 and a maintenance plan costing $25,000 per year for 10 years. Another company, MedEquip, has an on-line ad showing the same CT scanner model at a highly-discounted sales price. MedEquip will sell the scanner for $300,000, but the fine print reveals that the yearly maintenance costs will be $15000 t, where t is the number of years since purchase.

Von has contracted an actuary to perform a capital cost analysis* for previous purchase decisions. This time Von hires you to capitalize the cost of each of the two purchase options of CT Scanner 0731. Please prepare a report for Von determining the cost to acquire and keep the CT Scanner for 10 years. You may assume that the prevailing interest rate is 6%. Be sure to show all appropriate mathematical work with proper notation. Compare the results. Write a statement with your recommendation. Additionally, cite other issues that Von might consider in purchasing the CT Scanner 0731.

Answer 1

Discount rate (r) = 6%, Time (t) =10 yrs
Scan RUs CT scanner cash flow benefit   
At T=0 Initial Cash Investment = -650000 (CF₀)
AT T=1 to T =5 Maintenance costs = -25000/Year(CF_t)
Using NPV formula = -CF₀ - CF_t/(1+r)^t= 820042.3

MedEquip CT scanner cash flow benefit
At T=0  Initial Cash Investment = -300000 (CF₀)
AT T=1 to T =5 Maintenance costs = -15000t/Year(CFt)
CF₁= 15000*1 =15000,CF₂=15000*2 =30000,.................CF₁₀=15000*10
Using NPV formula = -CF₀ - CF_t/(1+r)^t=-854436
SINCE NPV of 1st case is more hence Scan RUs CT scanner must be bought..
Other issues include the salvage value of the CT scanner at the end of 10 years