Question

Net Present Value Method—Annuity

Jones Excavation Company is planning an investment of $125,000 for a bulldozer. The bulldozer is expected to operate for 1,000 hours per year for five years. Customers will be charged $90 per hour for bulldozer work. The bulldozer operator costs $30 per hour in wages and benefits. The bulldozer is expected to require annual maintenance costing $7,500. The bulldozer uses fuel that is expected to cost $15 per hour of bulldozer operation.

Present Value of an Annuity of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	1.833	1.736	1.690	1.626	1.528
3	2.673	2.487	2.402	2.283	2.106
4	3.465	3.170	3.037	2.855	2.589
5	4.212	3.791	3.605	3.353	2.991
6	4.917	4.355	4.111	3.785	3.326
7	5.582	4.868	4.564	4.160	3.605
8	6.210	5.335	4.968	4.487	3.837
9	6.802	5.759	5.328	4.772	4.031
10	7.360	6.145	5.650	5.019	4.192

a. Determine the equal annual net cash flows from operating the bulldozer.

Jones Excavation Company
Equal Annual Net Cash Flows
Cash inflows:
Hours of operation
Revenue per hour		× $
Revenue per year			$
Cash outflows:
Hours of operation
Fuel cost per hour	$
Labor cost per hour
Total fuel and labor costs per hour		× $
Fuel and labor costs per year
Maintenance costs per year
Annual net cash flows			$

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a. Subtract the operating expenses (hourly fuel and labor costs, multiplied by the operating hours, plus the annual maintenance costs) from the revenues (operating hours multiplied by the hourly revenue).

b. Determine the net present value of the investment, assuming that the desired rate of return is 10%. Use the table of present value of an annuity of $1 table above. Round to the nearest dollar.

Present value of annual net cash flows	$
Amount to be invested
Net present value	$

c. Should Jones invest in the bulldozer, based on this analysis?
Yes , because the bulldozer cost is  less than  the present value of the cash flows at the minimum desired rate of return of 10%.

d. Determine the number of operating hours such that the present value of cash flows equals the amount to be invested. Round interim calculations and final answer to the nearest whole number.
hours

Answer 1

a
Jones Excavation Company
Equal Annual Net Cash Flows
Cash inflows:
Hours of operation		1000
Revenue per hour		90
Revenue per year			90000
Cash outflows:
Hours of operation		1000
Fuel cost per hour	15
Labor cost per hour	30
Total fuel and labor costs per hour		45
Fuel and labor costs per year			45000
Maintenance costs per year			7500
Annual net cash flows			37500
b
Present value of annual net cash flows	142163	=37500*3.791
Amount to be invested	125000
Net present value	17163

c

Yes,because the bulldozer cost is less than the present value of the cash flows at the minimum desired rate of return of 10%.

d

3.791*((Hours*90)-(Hours*45)-8000) = 125000

(Hours*341)-(Hours*171)-30328 = 125000

Hours*170 = 155328

Hours = 155328/170 = 914

Number of operating hours = 914 hours