Question

A hospital is considering the purchase of a piece of medical equipment that costs $1,500,000 and has a useful life of five years and no salvage value at the end of its useful life. The equipment generates revenues of $650,000 per year and operating expenses of $300,000. Calculate NPV, payback, BCR, and IRR, should the equipment be purchased if the discount rate is 6% or 10%?

           Revenue   Expense

   Year 0       -      $1,500,000 (investment)

   Year 1       $650,000   $300,000

   Year 2       $650,000   $300,000

   Year 3       $650,000   $300,000

   Year 4       $650,000   $300,000

   Year 5       $650,000   $300,000

Answer 1

Initial cost = $1,500,000

Revenue = $650,000 and operating expenses = $300,000

The cashflow every year will be = (650,000 - 300,000) = 350,000

Depreciation is (1,500,000 / 5) = 300,000 per annum

when discount rate is 6%, NPV = [350000/ (1.06) + 350000 / (1.06)² + 350000 / (1.06)³ + 350000 / (1.06)⁴ + 350000 / (1.06)⁵ ] - 1,500,000 = -25672.67

Inflows = 330188.67 + 311498.75 + 293866.74 + 277232.78 + 261540.36 = 1162828.55

when discount rate is 10%, NPV = -173224.63

Inflows when rate is 10% = 318181.81 + 300171.52 + 283180.68 + 267151.59 +252029.80 = 1420715.40

Payback period = Investment required / Net annual cashflow

=> 1500000/ 350000 = 4.28 years

Benefit cost ratio or BCR is the relationship between cost and benefit and the formula is BCR = Benefits/ Cost

when rate is 6% , BCR = 1162828.55 / 1500000 = 0.77

and when rate is 10% , BCR = 1420715.40 / 1500000 = 0.94

IRR = 5.3%

Since, the NPV is negative for both the scenariosat rate 6% and 10% , we will not accept the project and alsothe IRR = 5.3% which is less than the discount rate ( 6% and 10%) hence, we will reject the project and not purchase the equipment