Question

Net Present Value Method-Annuity Briggs Excavation Company is planning an investment of $109,400 for a bulldozer. The bulldozer is expected to operate for 2,000 hours per year for five years. Customers will be charged $115 per hour for bulldozer work. The bulldozer operator costs $38 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 $50 per hour of bulldozer operation. Present Value of an Annuity of $1 at Compound Interest Year 6% 10% 12% 15% 20% 0.943 0.909 0.893 0.870 0.833 1.833 1.736 1.690 1.626 1.528 2.673 2.487 2.402 2.283 2.106 3.465 3.170 3.037 2.855 2.589 4.212 3.791 3.605 3.352 2.991 4.917 4.355 4.111 3.784 3.326 5.582 4.868 4.564 4.160 3.605 6.210 5.335 4.968 4.487 3.837 5.759 5.328 4.772 4.031 6.802 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.

Answer 1

Solution:

Briggs Excavation Company

1. Determination of equal annual net cash flows from operating the bulldozer:

Briggs Excavation
Equal annual net cash flow:
Cash Inflows:
Hours of operation	2,000
Revenue per hour	$115
Revenue per year		$230,000
Cash outflows:
Hours of operation	2,000
Fuel cost per hour	$50
labor cost per hour	$38
Total fuel and labor costs per year	$88 per hour	($176,000)
Annual maintenance cost		($20,000)
Annual net cash flow		$34,000

2. Determination of the net present value of investment assuming desired rate of return as 15%:

Present value of annual net cash flows –

= annual net cash inflows x present value of annuity of $1 at 15% for 5 years

= $34,000 x (P/A, 15%, 5)

= 34,000 x 3.352 = $113,968

Less: initial investment $104,900

Net present value = 113,968 – 104,900 = $9,068

3. Yes, Briggs Excavation should opt to invest in purchasing the bulldozer, as the investment earns a positive net present value at the company’s minimum desired rate of return of 15%.
4. Determination of the operating hours so that the present value of cash outflows equal the amount to be investe

Amount to be invested = (P/A, 15%, 5) x [(number of hours x 115) – (number of hours x 88) – 20,000] = $109,400

$109,400 = 3.352 x [(number of hours x 115) – (number of hours x $88) – 20,000

109,400 = number of hours x $385.50 – number of hours x $295 – 67,040

$176,440 = number of hours x $90.50

Number of hours = 176,440/90.50 = 1,950           

Hence, the bulldozer’s operating hours must exceed 1,950 each year so as to justify the investment of $109,400.