Question

Problem 25-03A 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 6%. Option A Option B Initial cost $181,000 $283,000 Annual cash inflows $73,000 $82,400 Annual cash outflows $30,200 $25,100 Cost to rebuild (end of year 4) $48,000 $0 $0 Salvage value $8,300 7 years 7 years Estimated useful life Click here to view the factor table. Compute the (1) net present value, (2) profitability index, and (3) internal rate of return for each option. (Hint: To solve for internal rate of return, experiment with alternative discount rates to arrive at a net present value of zero.) (If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round answers for present value and IRR to 0 decimal places, e.g. 125 and round profitability index to 2 decimal places, e.g. 12.50. For calculation purposes, use 5 decimal places as displayed in the factor table provided.) Internal Rate of Return Net Present Value Profitability Index Option A 2$ 0% Option B 2$ LINK TO TEXT LINK TO VIDEO Which option should be accepted? should be accepted.

Answer 1

Solution

Brooks Clinic

	Net Present Value	Profitability Index	Internal Rate of Return
Option A	$19,910	1.11	9%
Option B	$42,398	1.15	10%

From the above parameters, Option B has the highest net present value, highest profitability index as well as highest internal rate of return. Hence, Option B has to be chosen.

Computations for NPV, PI and IRR:

1. Computation of the net present value of the two options:

NPV of Option A –

Year	0	1	2	3	4	5	6	7	Total
Initial Outlay	($181,000)								($181,000)
Cash inflows		$42,800	$42,800	$42,800	($5,200)	$42,800	$42,800	$42,800
PV factor at 6%	1	0.9434	0.89	0.8396	0.7921	0.7473	0.705	0.6651
Present Value of cash flows	($181,000)	$40,378	$38,092	$35,935	($4,119)	$31,984	$30,174	$28,466	$200,910
Net Present Value									$19,910

Computations:

Net cash inflows = cash inflows – cash outflows for each year

Net cash inflows for year 1to 7 (except for Year 4) = $73,000 - $30,200 = $42,800

Net cash inflow for year 4 = 73,000 – 30,200 – 48,000 = ($5,200)

Salvage value =0

Initial outlay= $181,000

Cost of capital = 6%

Option B –

Year	0	1	2	3	4	5	6	7	Total
Initial Outlay	($283,000)								($283,000)
Cash inflows		$57,300	$57,300	$57,300	$57,300	$57,300	$57,300	$65,600
PV factor at 6%	1	0.9434	0.89	0.8396	0.7921	0.7473	0.705	0.6651
Present Value of cash flows	($283,000)	$54,057	$50,997	$48,109	$45,387	$42,820	$40,397	$43,631	$325,398
Net Present Value									$42,398

Computations:

Net cash inflows = cash inflows – cash outflows for each year

Net cash inflows for year 1to 6 = $82,400 - $25,100 = $57,300

Net cash inflow for year 7 = 82,400 – 25,100 + 8,300 = $65,600

Salvage value =8,300 at end of year 7

Initial outlay= $283,000

Cost of capital = 6%

2. Profitability Index –

Profitability index = present value of future cash flows/initial investment

Option A –

Present value of future cash flows = $200,910

Initial investment = $181,000

PI = 200,910/181,000 = 1.11

Option B –

Present value of future cash flows = $325,398

Initial investment = $283,000

PI = 325,398/283,000 = 1.15

3. Computation of the Internal Rate of Return (IRR)
4. At IRR rate the net present value is zero.

Since both the options are having positive NPV at 6%, the IRR could be higher. Assuming a discount rate of 9%,

The NPVs -

Option A –

Year	0	1	2	3	4	5	6	7	Total
Initial Outlay	($181,000)								($181,000)
Cash inflows		$42,800	$42,800	$42,800	($5,200)	$42,800	$42,800	$42,800
PV factor at 9%	1	0.917	0.842	0.772	0.708	0.65	0.596	0.547
Present Value of cash flows	($181,000)	$39,248	$36,038	$33,042	($3,682)	$27,820	$25,509	$23,412	($181,380)
Net Present Value

At 9% discount rate the NPV is almost zero the difference of $380 is attributable to +/- changes in computations. Hence, Internal Rate of Return for Option A is 9%

For Option B –

Year	0	1	2	3	4	5	6	7	Total
Initial Outlay	($283,000)								($283,000)
Cash inflows		$57,300	$57,300	$57,300	$57,300	$57,300	$57,300	$65,600
PV factor at 6%	1	0.9091	0.826	0.751	0.683	0.621	0.564	0.513
Present Value of cash flows	($283,000)	$52,086	$47,330	$43,032	$39,136	$35,583	$32,317	$33,653	$283,137
Net Present Value									$137

The net present value is almost zero at 10% for option B.

Hence, the internal rate of return for Option B is 10%