Question

Problem 26-7A 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 year 4) $50,100 $0 Salvage value $0 $8,200 Estimated useful life 7 years 7 years Click here to view PV table. Click here to view PV of Annuity table. Compute the (1) net present value and (2) 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 to 0 decimal places, e.g. 125. For calculation purposes, use 5 decimal places as displayed in the factor table provided.) Net Present Value Internal Rate of Return Option A $ % Option B $ % Link to Text Link to Text Which option should be accepted? should be accepted.

Answer 1

	Option A	Option B
Initial Investment	170000	274000
Inflows	72200	82200
Outflows	31400	26700
Cost to rebuild at the end of year 4	50100	0
Salvage Value	0	8200
Term	7 years	7 years
Discount Rate	6%	6%
Net Annual Cash Flow (Inflow - Outflow)	40800	55500

NPV (Option A) = -170000 + 40800 * PVIFA (6%,7) – 50100 * PVIF (6%,4)

NPV (Option A) = -170000 + 40800 * 5.582381 – 50100 * 0.792094 = 18077.24

NPV (Option B) = -274000 + 55500 * PVIFA (6%,7) + 8200 * PVIF (6%,7)

NPV (Option B) = -274000 + 55500 * 5.582381 + 8200 * 0.665057 = 41275.61

If ‘i’ is the IRR of option A, then,

V = -170000 + 40800 * PVIFA (i,7) – 50100 * PVIF (i,4) = 0

For i = 6%, V = 18077.24

For i = 8%, V = 5594.903

For i = 9%, V = -147.627

By interpolation, i = 8% + (9% - 8%) * (0 – 5594.903)/(-147.627 – 5594.903) = 8.97%

IRR of Project A is 8.97%

If ‘i’ is the IRR of option B, then,

V = -27400 + 55500 * PVIFA (i,7) + 8200 * PVIF (i,7) = 0

For i = 6%, V = 41275.61

For i = 10%, V = 405.141

For i = 11%, V = -8523.508

By interpolation, i = 10% + (11% - 10%) * (0 – 405.141)/(-8523.508 – 405.141) = 10.04%

IRR of Project B is 10.04%

Since, both NPV and IRR are greater for Project B, it is a better alternative.