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          $194,000      $291,000

cash inflows      $72,600         $82,000

cash outflows    $28,100.       $25,100

Cost to rebuild   $51,200        $0
(end of year 4)

Salvage value    $0                 $9,000

Estimated
useful life            7 years        7 years

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.)

Answer 1

Facts:

	Option A	Option B
Initial outlay	$ 194,000	$ 291,000
Useful Life(years)	7	7
Cost to rebuild	$ 51,200	$ 0
Net Annual Cash inflows	$ 44,500	$ 56,900
Salvage value	$ 0	$ 9,000

NPV of Option A
Year	Events	Amount	PV/PVA @5%	PV of Cash flows
0	Initial Outlay	(194,000)	1	(194,000)
1-7	Annual Cash inflows	44,500	5.7864	257,494
4	Cost to rebuild	(51,200)	0.823	(42,122)
	Net Present Value			21,371
NPV of Option B
Year	Events	Amount	PV/PVA @5%	PV of Cash flows
0	Initial Outlay	(291,000)	1	(291,000)
1-7	Annual Cash inflows	56,900	5.7864	329,245
7	Residual value	9,000	0.711	6,396
	Net Present Value			44,641

Profitability Index: PV of future cash flows/Initial Outlay

Option A : (257494-42122)/194000 = 1.11

Option B : (329245+6396)/291000 = 1.15

IRR for each option:

IRR is the discount rate at which NPV is '0'.

Lets Experimenting with other discount rates (greater than 5%) for NPV to become 0.

Lets take discount rates 8% and 9% for option A and find NPV

NPV of Option A
Year	Events	Amount	PV/PVA @8%	PV/PVA @9%	NPV(7%)	NPV(8%)
0	Initial Outlay	(194,000)	1	1	(194,000)	(194,000)
1-7	Annual Cash inflows	44,500	5.2064	5.0330	231,683	223,966
4	Cost to rebuild	(51,200)	0.7350	0.7084	(37,634)	(36,271)
					50	(6,305)

IRR = L + NPV(L)/[NPV(L)-NPV(H)] * (H-L)

= 8% + 50/(50+6305)*1%

= 8.02%

Lets take discount rates 9% and 10% for option B and find NPV

NPV of Option B
Year	Events	Amount	PV/PVA @9%	PV/PVA @10%	NPV(9%)	NPV(10%)
0	Initial Outlay	(291,000)	1	1	(291,000)	(291,000)
1-7	Annual Cash inflows	56,900	5.0330	4.8684	286,375	277,013
7	Residual value	9,000	0.5470	0.5132	4,923	4,618
	Net Present Value				298	(9,369)

IRR = 9% + 298/(298+9369) * 1%

= 9.03%