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 6%.

	Option A	Option B
Initial Cost	$170,000	$274,000
Annual Cash InFlows	$72,200	$82,200
Annual Cash OutFlows	$31,400	$26,700
Cost to Rebuild (end of 4 years)	$50,100	$0
Salvage Value	$0	$8,200
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 $			%

Which option should be accepted?

Option A or Option B should be accepted?

Answer 1

Answer:

Option A:

Net Present Value:

Year	Flow	Net cash flow	Present value	Computation
0	-170,000	-170,000	-170,000
1	72,200-31,400	40,800	38,490.57	40,800 / 1.06
2	72,200-31,400	40,800	36,311.85	40,800 / 1.06^2
3	72,200-31,400	40,800	34,256.47	40,800 / 1.06^3
4	72,200-31,400-50,100	-9,300	-7,366.47	-9300 / 1.06^4
5	72,200-31,400	40,800	30,488.13	40,800 / 1.06^5
6	72,200-31,400	40,800	28,762.39	40,800 / 1.06^6
7	72,200-31,400	40,800	27,134.33	40,800 / 1.06^7

Add up the present value column to get the Net present value,

Net Present Value = $18,077.27

Profitability Index:

Profitability Index = Present value of future cash flows / Initial Investment

Present value of future cash flows can be found out by adding present value column values except initial investment.

Present value of future cash flows = 38,490.57 + 36,311.85 + 34,256.47 - 7,366.47 + 30,488.13

                                                                         + 28,762.39 + 27,134.33

                                                                = 188077.27

Profitability index = 188077.27 / 170000

                                    = 1.11

Internal Rate of Return:

If cost of capital is 8% then, NPV = 5,594.90279

For 9% cost of capital, NPV = -147.62740

Interpolating, (9% - 8%) / (5594.90279 + 147.62740) * 5594.90279 = 0.9743

IRR = 8 + 0.9743 = 8.9743%

Option B:

Year	Flow	Net cash flow	Present value	Computation
0	-274,000	-274,000	-274,000
1	82,200-26,700	55,500	52,358.49	55,500 / 1.06
2	82,200-26,700	55,500	49,394.8	55,500 / 1.06^2
3	82,200-26,700	55,500	46,598.87	55,500 / 1.06^3
4	82,200-26,700	55,500	43,961.2	55,500 / 1.06^4
5	82,200-26,700	55,500	41,472.83	55,500 / 1.06^5
6	82,200-26,700	55,500	39,125.31	55,500 / 1.06^6
7	82,200-26,700+8,200	63,700	42,364.14	63,700 / 1.06^7

Net Present Value = $41,275.64

Profitability Index:

Profitability Index = Present value of future cash flows / Initial Investment

Profitability index = 315275.64 / 274000

                                    = 1.15

Internal Rate of Return:

If cost of capital is 10% then, NPV = 405.14095

For 11% cost of capital, NPV = -8523.50834

Interpolating, (11%-10%) / (405.14095 + 8523.50834) * 405.14095 = 0.04538

IRR = 10 + 0.04538 = 10.04538%

	Net Present Value	Profitability Index	Internal Rate of Return
Option A	$18,077	1.11	8%
Option B	$41,276	1.15	10%

Option B should be accepted.