Question

Net Present Value Method—Annuity

Briggs Excavation Company is planning an investment of $420,800 for a bulldozer. The bulldozer is expected to operate for 2,000 hours per year for five years. Customers will be charged $135 per hour for bulldozer work. The bulldozer operator costs $25 per hour in wages and benefits. The bulldozer is expected to require annual maintenance costing $20,000. The bulldozer uses fuel that is expected to cost $33 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

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).

Learning Objective 3.

b. Determine the net present value of the investment, assuming that the desired rate of return is 20%. 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. Should Briggs Excavation invest in the bulldozer, based on this analysis?
No , because the bulldozer cost is more than the present value of the cash flows at the minimum desired rate of return of 20%.

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.

Briggs Excavation Company
Equal Annual Net Cash Flows
Cash inflows:
Hours of operation	2000
Revenue per hour		$        135
Revenue per year			$       270,000
Cash outflows:
Hours of operation	2000
Fuel cost per hour	$          33
Labor cost per hour	$          25
Total fuel and labor costs per hour		$          58
Fuel and labor costs per year			$ -116,000
Maintenance costs per year			$ -20,000
Annual net cash flows			$ 134,000

b.

Present value of annual net cash flows ($134000 x 2.991)	400794
Amount to be invested	420800
Net present value	-20006

c. No, because the bulldozer cost is more than the present value of the cash flows at the minimum desired rate of return of 20%.

d.  For the present value of cash flows to equal the amount to be invested, the annual net cash flows must be $420800/2.991 = $140688.73 = $140689

Assuming the number of operating hours to be "X"

$140689 = 135X - (58X + 20000)

140689 = 135X - 58X - 20000

77X = $160689

X = $160689/77 = 2086.87 = 2087 hours

The number of operating hours = 2087 hours

Check for 2087 operating hours:

Cash inflows:
Hours of operation	2087
Revenue per hour		$        135
Revenue per year			$   2,81,745
Cash outflows:
Hours of operation	2087
Fuel cost per hour	$          33
Labor cost per hour	$          25
Total fuel and labor costs per hour		$          58
Fuel and labor costs per year			$ -1,21,046
Maintenance costs per year			$     -20,000
Annual net cash flows			$   1,40,699
Present value of annual net cash flows ($140699 x 2.991)	420830.7
Amount to be invested	420800
Net present value	30.709