Question

Net Present Value Method—Annuity

Briggs Excavation Company is planning an investment of $320,100 for a bulldozer. The bulldozer is expected to operate for 2,000 hours per year for six years. Customers will be charged $105 per hour for bulldozer work. The bulldozer operator costs $26 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 $34 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	3.352	2.991
6	4.917	4.355	4.111	3.784	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
Equal Annual Net Cash Flow
Cash inflows:
		$
			$
Cash outflows:
	$
		$
			$

b. Determine the net present value of the investment, assuming that the desired rate of return is 10%. 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?
, because the bulldozer cost is 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

Cost of bulldozer	= $ 320,100.00
Bulldozer operating hours per year	= 2000 hours

a.

Calculation of annual net cash flow:

	Particulars	For each hour (A)	For the year in (B=A*2000)
A	Revenue per hour in	$          105.00	$    210,000.00
B	Operator cost per hour	$            26.00	$      52,000.00
C	Fuel cost per hour	$            34.00	$      68,000.00
D	Annual maintenance cost (as given)		$      20,000.00
E=A-B-C-D	Annual net cash flow for each year		$      70,000.00

Equal annual net cash flow:

Year	Cash flow
0	$ -320,100.00
1	$      70,000.00
2	$      70,000.00
3	$      70,000.00
4	$      70,000.00
5	$      70,000.00
6	$      70,000.00

From the table, equal annual cash inflow = $70,000.

b.

Calculation of NPV of investment:

	Particulars	Amount in $
1	Initial cash outflow	320,100.00
2	Annual cash inflow	70,000.00
3	Present value annuity factor for 6 years,10% (from the table)	4.355
4=2*3	The total present value of cash inflows	304,850.00
5=4-5	Net present value	-15,250.00

From the computation table, the NPV of the project is (15,250.00) which is negative.

c.

Briggs Excavation should not invest in the Bulldozer since net cash flow from the investing activity is negative ($ -15,250)

d.

The calculation to find the number of operating hours such that the present value of cash flows equals the amount to be invested:

A	Present value annuity factor for 6 years,10% (from the table)	4.355
B	Initial cash outflow	$                   320,100
C=B/A	Required minimum cash inflow so that present value of cash inflow equals to cash outflow	$                     73,502
D	Present annual cash inflow	$                     70,000
E=C-D	The required increase in annual cash inflow	$                        3,502
F	Revenue per hour in	$                           105
G	Operator cost per hour	$ 26
H	Fuel cost per hour	$ 34
I=F-G-H	Net revenue contribution per hour (Before considering the fixed cost)	$ 45
J=E/I	Additional hours to be worked (Number of hours)	78 hours

The required number of operating hours to match the present value of inflows with outflows = 2,000 + 78

= 2,078 hours for each year