Question

1. Internal Rate of Return Method—Two Projects

Munch N’ Crunch Snack Company is considering two possible investments: a delivery truck or a bagging machine. The delivery truck would cost $44,209.44 and could be used to deliver an additional 40,000 bags of pretzels per year. Each bag of pretzels can be sold for a contribution margin of $0.38. The delivery truck operating expenses, excluding depreciation, are $0.52 per mile for 14,000 miles per year. The bagging machine would replace an old bagging machine, and its net investment cost would be $54,765. The new machine would require three fewer hours of direct labor per day. Direct labor is $15 per hour. There are 250 operating days in the year. Both the truck and the bagging machine are estimated to have seven-year lives. The minimum rate of return is 9%. However, Munch N’ Crunch has funds to invest in only one of the projects.

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. Compute the internal rate of return for each investment. Use the above table of present value of an annuity of $1. If required, round your present value factor answers to three decimal places and internal rate of return to the nearest percent.

	Delivery Truck	Bagging Machine
Present value factor
Internal rate of return	%	%

2.

Net Present Value Method and Present Value Index

Diamond and Turf Inc. is considering an investment in one of two machines. The sewing machine will increase productivity from sewing 110 baseballs per hour to sewing 198 per hour. The contribution margin per unit is $0.38 per baseball. Assume that any increased production of baseballs can be sold. The second machine is an automatic packing machine for the golf ball line. The packing machine will reduce packing labor cost. The labor cost saved is equivalent to $20 per hour. The sewing machine will cost $167,400, have a six-year life, and will operate for 1,400 hours per year. The packing machine will cost $85,800, have a six-year life, and will operate for 1,200 hours per year. Diamond and Turf seeks a minimum rate of return of 12% on its investments.

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 net present value for the two machines. Use the table of present values of an annuity of $1 above. Round to the nearest dollar.

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

b. Determine the present value index for the two machines. If required, round your answers to two decimal places.

	Sewing Machine	Packing Machine
Present value index

3.

Net Present Value—Unequal Lives

Bunker Hill Mining Company has two competing proposals: a processing mill and an electric shovel. Both pieces of equipment have an initial investment of $625,304. The net cash flows estimated for the two proposals are as follows:

	Net Cash Flow
Year	Processing Mill		Electric Shovel
1	$213,000		$266,000
2	190,000		247,000
3	190,000		228,000
4	151,000		234,000
5	115,000
6	96,000
7	83,000
8	83,000

The estimated residual value of the processing mill at the end of Year 4 is $270,000.

Present Value of $1 at Compound Interest
Year	6%	10%	12%	15%	20%
1	0.943	0.909	0.893	0.870	0.833
2	0.890	0.826	0.797	0.756	0.694
3	0.840	0.751	0.712	0.658	0.579
4	0.792	0.683	0.636	0.572	0.482
5	0.747	0.621	0.567	0.497	0.402
6	0.705	0.564	0.507	0.432	0.335
7	0.665	0.513	0.452	0.376	0.279
8	0.627	0.467	0.404	0.327	0.233
9	0.592	0.424	0.361	0.284	0.194
10	0.558	0.386	0.322	0.247	0.162

Determine which equipment should be favored, comparing the net present values of the two proposals and assuming a minimum rate of return of 15%. Use the present value table appearing above.

	Processing Mill	Electric Shovel
Present value of net cash flow total	$	$
Less amount to be invested	$	$
Net present value	$	$

Answer 1

Q1 a)

Cost of Delivery truck = $44,209.44

Depreciation = Cost/Useful Life = 44,209.44/7 = $6316(approx)

Free Cash Flow = EBIT + Depreciation

= ((40000*$0.38) - (14,000*$0.52) + $6,316

= $13596

PV of cash flow at 10% for 7 years = $13,596 * 4.868 = $66,185

NPV at 10% = PV of Cash Inflow - Cash Outflow

= $66,185 - $44,209.44 = $21,976(approx)

PV of cash flow at 15% for 7 years = $13,596 * 4.160 = $56,559

NPV at 15% = $56,559 - $44209.44 = $12,350

IRR (Delivery Truck) = L_r + L_rNPV/(L_rNPV-H_rNPV) * (H_r-L_r)

where, L_r = Lower discount rate   H_r= Higher Discount Rate

L_rNPV = NPV lower discount rate   H_rNPV = NPV higher discount rate

IRR (Delivery Truck) = 10 + 21976/(21976-12350)*(15-10)

= 21%

Cost of Bagging Machine = $54,765

Depreciation = Cost/Useful Life = 54765/7 = $7,824

Savings in Labour hour = 24hr*250days*$15 - 21hr*250*$15

= 90,000 - 78750

= $11,250

PV of Cash Flow at 10% for 7 years = 11,250*4.868 = $54,765

PV of cash flow at 15% for 7 years = 11,250*4.160 = $46,800

NPV at 10% = 54765-54765 = 0

So IRR (Bagging Machine) = 10%