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		$176,000		$292,000
Annual cash inflows		$71,500		$82,400
Annual cash outflows		$30,400		$25,400
Cost to rebuild (end of year 4)		$51,100		$0
Salvage value		$0		$8,800
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.)

		Net Present Value		Profitability Index		Internal Rate of Return
Option A		$				%
Option B		$				%

Answer 1

			Cost of capital 8%		Cost of capital 9%
	Option A	Option B	Option A	Option B	Option A	Option B
1.Initial cost	-176000	-292000	-176000	-292000	-176000	-292000
2.PV of annual cash inflows
71500*5.78637=	413725.46		372255.455		359855.93
82400*5.78637=		476796.89		429004.89		414715.08
3.PV of annual cash outflows
-30400*5.78637=	-175905.65		-158273.65		-153001.68
-25400*5.78637=		-146973.80		-132241.80		-127836.93
4. Cost to rebuild at end of 4 yrs.
-51100/1.05^4=	-42040.10	0	-37560.03	0	-36200.53	0
5.PV of salvage	0		0		0
8800/1.05^7=		6254.00		5134.72		4813.90
NPV(sum 1 to 5)	19779.71	44077.09	421.78	9897.81	-5346.28	-307.95
Profitability Index=
1+(NPV/Investment)
1+(19779.71/(176000+42040.1)=	1.09
1+(44077.09/292000)=		1.15
NOTE:Annuity Factor---P/A,i=5%; n=7=(1-1.05^-7)/0.05=
5.78637
P/A factors for COC-- 8% & 9%
(1-1.08^-7)/0.08=5.20637
(1-1.09^-7)/0.09=5.03295

IRR by Trial & Error
Trial Cost of capital(as in above   Table)	NPV	NPV
8%	421.78	9897.81
9%	-5346.28	-307.95
Diff. in NPV for 1%	5768.06	10205.76
For NPV to become 0
Disc. Rate to be added=	1%/5768.06*421.78=	1%/10205.76*9897.81=
	0.07%	0.97%
So, IRR=     8%+0.07%=	8.07%
IRR=    8%+0.97%=		8.97%

ANSWERS	Net Present Value	Profitability Index	IRR
Option A	$19,779.71	1.09	8.07%
Option B	$44,077.09	1.15	8.97%

IRR as per Equation method

ie. NPV=-PV of cash outflows+PV of cash inflows=0

Option A

-176000+(71500*(1-(1+r)^-7)/r)-(30400*(1-(1+r)^-7)/r)-(51100/(1+r)^4)=0

Solving for r, IRR= 8.07%

Option B

-292000+(82400*(1-(1+r)^-7)/r)-(25400*(1-(1+r)^-7)/r)+(8800/(1+r)^7)=0

Solving for r, IRR= 8.97%

IRR(as per Excel)
Option A	0	1	2	3	4	5	6	7
Initial cost	-176000
Cash inflow		71500	71500	71500	71500	71500	71500	71500
Cash outflow		-30400	-30400	-30400	-30400	-30400	-30400	-30400
Cost to rebuild					-51100
Total annual cash flows	-176000	41100	41100	41100	-10000	41100	41100	41100
IRR(as per Excel)	8.07%
Option B
Initial cost	-292000
Cash inflow		82400	82400	82400	82400	82400	82400	82400
Cash outflow		-25400	-25400	-25400	-25400	-25400	-25400	-25400
Salvage								8800
Total annual cash flows	-292000	57000	57000	57000	57000	57000	57000	65800
IRR(as per Excel)	8.97%