Question

Net Present Value Method—Annuity

Briggs Excavation Company is planning an investment of $352,400 for a bulldozer. The bulldozer is expected to operate for 2,000 hours per year for five years. Customers will be charged $145 per hour for bulldozer work. The bulldozer operator costs $36 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 $47 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 12%. 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 12%.

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

Answer :

a. Calculation of equal annual net cash flow :

Particulars	Amount (in $)
Cash Inflows :
Revenue per year (2,000 hours x $145 per hour)	290,000
Cash Outflows :
Bulldozer operator costs (2,000 hours x $36 per hour)	(72,000)
Annual maintenance cost	(20,000)
Bulldozer fuel cost (2,000 hours x $47 per hour)	(94,000)
Annual net cash flow	104,000

b. Net present value :

Net present value = Present value of annual cash inflow - Amount invested

Particulars	Amount (in $)
Annual net cash flow (at the end of each year)	104,000
x Present value of annuity of $1 at 12% for five years	3.605
Present value of annual net cash flow	374,920
Less : Amount to be invested	352,400
Net present value	22,520

c. Yes, Briggs should accept the investment because the Bulldozer cost is less than the present value of cash flows at the minimum desired rate of return of 12%.

d. Calculation of number of operating hours such that the present value of cash flows equals the amount to be invested :

Net present value = Present value of annual cash inflow - Amount invested

3.605 x [(Hours x $110) - (Hours x $36) - (Hours x $47) - $20,000] = $22,520

(Hours x $397) - (Hours x $130) - (Hours x $169) - $72,100 = $22,520

Hours x $98 = $22,520 + $72,100

Hours x $98 = $94,620

Hours = $94,620 / $98

Hours = 966 hours (rounded off)