Question

Net Present Value Method—Annuity

Briggs Excavation Company is planning an investment of $1,077,200 for a bulldozer. The bulldozer is expected to operate for 3,000 hours per year for 10 years. Customers will be charged $150 per hour for bulldozer work. The bulldozer operator costs $29 per hour in wages and benefits. The bulldozer is expected to require annual maintenance costing $30,000. The bulldozer uses fuel that is expected to cost $38 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. Use a minus sign to indicate cash outflows.

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

Feedback

b. Determine the net present value of the investment, assuming that the desired rate of return is 15%. Use the present value of an annuity of $1 table above. Round to the nearest dollar. If required, use the minus sign to indicate a negative net present value.

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

C. 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.

Cash inflows:
Hours of operation		3000
Revenue per hour		$150
Revenue per year	(A)	$450,000
Cash outflows:
Hours of operation		3000
Fuel cost per hour		$38
Labor cost per hour		$29
Total fuel and labor costs per hour		$67
Fuel and labor costs per year	(B)	$201,000
Maintenance costs per year	(C)	$30,000
Annual net cash flows	(A-B-C)	$219,000

B.  

Present value of annual net cash flows = Annual net cash flow * annuity factor (15%, 10years) = $219,000 * 5.019 = $1,099,161

Present value of annual net cash flows	$1,099,161
Amount to be invested	$1,077,200
Net present value	$21,961

C. To find out number of operating hours to equalise our investment and present value of cash flows , If we assume annual hours of operation as X in table in above point A and B, then we have following equation

(150X - 67X - 30,000) * 5.019 = $ 1,077,200

83X - 30,000 = $214,624

83X = 214,624 +30000

83X = 244,624

X = 244,624 / 83

X = 2947 hours

Therefore, if buldozer operates for 2947 hours every year then the present value of cash flows will be equal to the amount of investment.