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 $196,000 $291,000
Annual cash inflows $72,500 $82,500
Annual cash outflows $28,000 $25,600
Cost to rebuild (end of year 4) $49,100 $0
Salvage value $0 $8,500
Estimated useful life 7 years 7 years

Compute the
(1) net present value
(2) profitability index
(3) 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.) (If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round answers for present value and IRR to 0 decimal places, e.g. 125 and round profitability index to 2 decimal places, e.g. 10.50. For calculation purposes, use 5 decimal places as displayed in the factor table provided.)

Answer 1

Answer:

Project A:

NPV:$21,099 ; Profitability index: 10.76% IRR: 7.94%

Project A:

NPV: $44,285; Profitability index: 15.22%; IRR = 9.00%

Explanation:

* Project A:

We have the net cash flow each year as followed:

Y0 = -196,000; Y1-Y3: $44,500; Y4: -$4,600; Y5-Y7 = 44,500

=> Net present value = -196,000 + [ (44,500/5%) x ( 1 - 1.05^-3) ] +(-4,600/1.05^4) + [ (44,500/5%) x ( 1 - 1.05^-3) / 1.05^4 ] = $21,099

Profitability index = 21,099/ 196,000 = 10.76%

IRR calculation:

-196,000 + [ (44,500/IRR) x ( 1 - (1+IRR)^-3) ] +(-4,600/(1+IRR)^4) + [ (44,500/IRR%) x ( 1 - (1+IRR)^-3) / (1+IRR)^4 ] = 0 <=> IRR = 7.94%

* Project B:

We have the net cash flow each year as followed:

Y0 = -291,000; Y1-Y6: $56,900; Y7 = $65,400.

Carry out the calculation similar in Project A, we have

=> NPV = $44,285; Profitability index = 15.22%; IRR = 9.00%