Brooks Clinic is considering investing in new heart-monitoring equipment. It has

Question

Brooks Clinic is considering investing in new heart-monitoring equipment. It has two options. Option A would have an initial lower cost but would require a significant expenditure for rebuilding after 4 years. Option B would require no rebuilding expenditure, but its maintenance costs would be higher. Since the Option B machine is of initial higher quality, it is expected to have a salvage value at the end of its useful life. The following estimates were made of the cash flows. The company’s cost of capital is 5%. Option A Option B Initial cost $183,000 $281,000 Annual cash inflows $70,000 $80,000 Annual cash outflows $28,000 $25,000 Cost to rebuild (end of year 4) $48,000 $0 Salvage value $0 $7,000 Estimated useful life 7 years 7 years

Compute the (1) net present value and (2) internal rate of return for each option. (Hint: To solve for internal rate of return, experiment with alternative discount rates to arrive at a net present value of zero.)

Explanation / Answer

Answer 1.

NPA of Option A:

NPV = Net present values of all the cashflows - present value of cost to rebuild - initial investment

= [42000/(1.05) + 42000/(1.05^2) + 42000/(1.05^3) + 42000/(1.05^4) + 42000/(1.05^5) + 42000/(1.05^6) + 42000/(1.05^7)] - [48000/(1.05^4)] - 183000

= 243027.682568251 - 39489.7188 - 183000

= 20537.9637191651

NPA of Option B:

NPV = Net present values of all the cashflows + present value of Salvage value - initial investment

= [55000/(1.05) + 55000/(1.05^2) + 55000/(1.05^3) + 55000/(1.05^4) + 55000/(1.05^5) + 55000/(1.05^6) + 55000/(1.05^7)] + 7000/(1.05^7) - 281000

= 31820.53657214 + 4974.7693 - 281000

= 42225.305

Answer 2:

IRR is the discount rate at which NPV will be equal to zero.

Option A:

0 = [42000/(1+IRR) + 42000/((1+IRR)^2) + 42000/((1+IRR)^3) + 42000/((1+IRR)^4) + 42000/((1+IRR)^5) + 42000/((1+IRR)^6) + 42000/((1+IRR)^7)] - [48000/((1+IRR)^4)] - 183000

Calculate the IRR value by hit and trial:

put IRR = 8 ==> NPV = 386.11

put IRR= 8.1 ==> NPV = (229.39)

put IRR= 8.06 ==> NPV = 16.41

put IRR = 8.063 ==> NPV = -2.05~0

Therefore, IRR ~ 8.0636

Option B:

0 = [55000/(1+IRR) + 55000/((1+IRR)^2) + 55000/((1+IRR)^3) + 55000/((1+IRR)^4) + 55000/((1+IRR)^5) + 55000/((1+IRR)^6) + 55000/((1+IRR)^7)] + 7000/((1+IRR)^7) - 281000

Calculate the IRR value by hit and trial:

put IRR = 9 ==> NPV = (358.35)

put IRR= 8.9 ==> NPV = 597.60

put IRR= 8.96 ==> NPV = 23.42

put IRR = 8.962 ==> NPV = 4.31

Therefore, IRR ~ 8.9624

Data Given Parameter Option A Option B Initial Cost 183000 281000 Cost to Rebuild (after 4 years) 48000 0 Cash Inflow (yearly) 70000 80000 Yearly Expenditure 28000 25000 Net yearly cash flow 42000 55000 Life 7 Years 7 Years Salvage Value 0 7000

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