Question

Waterways puts much emphasis on cash flow when it plans for capital investments. The company chose its discount rate of 8% based on the rate of return it must pay its owners and creditors. Using that rate, Waterways then uses different methods to determine the best decisions for making capital outlays.

This year Waterways is considering buying five new backhoes to replace the backhoes it now has. The new backhoes are faster, cost less to run, provide for more accurate trench digging, have comfort features for the operators, and have 1-year maintenance agreements to go with them. The old backhoes are working just fine, but they do require considerable maintenance. The backhoe operators are very familiar with the old backhoes and would need to learn some new skills to use the new backhoes.

The following information is available to use in deciding whether to purchase the new backhoes.

		Old Backhoes		New Backhoes
Purchase cost when new		$89,000		$198,095
Salvage value now		$41,900
Investment in major overhaul needed in next year		$55,130
Salvage value in 8 years		$15,000		$91,000
Remaining life		8 years		8 years
Net cash flow generated each year		$29,800		$44,500

(a) Evaluate in the following ways whether to purchase the new equipment or overhaul the old equipment. (Hint: For the old machine, the initial investment is the cost of the overhaul. For the new machine, subtract the salvage value of the old machine to determine the initial cost of the investment.)

(1) Using the net present value method for buying new or keeping the old. (For calculation purposes, use 5 decimal places as displayed in the factor table provided. If the net present value is negative, use either a negative sign preceding the number eg -45 or parentheses eg (45). Round final answer to 0 decimal places, e.g. 5,275.)

		New Backhoes		Old Backhoes
Net Present Value		$		$

Waterways should                                                           buy New Backhoesretain Old Backhoes equipment.

(2) Using the payback method for each choice. (Hint: For the old machine, evaluate the payback of an overhaul.) (Round answers to 2 decimal places, e.g. 1.25)

		New Backhoes		Old Backhoes
Payback Period		years		years

Waterways should                                                           buy New Backhoesretain Old Backhoes equipment.

(3) Comparing the profitability index for each choice. (Round answers to 2 decimal places, e.g. 1.25)

		New Backhoes		Old Backhoes
Profitability Index

Waterways should                                                           buy New Backhoes or retain Old Backhoes equipment.

Calculate the internal rate of return factor for the new and old blackhoes. (Round answers to 5 decimal places, e.g. 5.27647.)

		New Backhoes		Old Backhoes
IRR Factor

(4) Comparing the internal rate of return for each choice to the required 8% discount rate.

Waterways should                                                           buy New Backhoes or retain Old Backhoes equipment.

Answer 1

Part A:

Year	Particulars	Present Value factor @ 8%	Cash Flow - Old Backhoes	Discounted Cash Flow - Old Backhoes	Cash Flow - New Backhoes	Discounted Cash Flow - New Backhoes
0	Initial Investment	1.00000	$      -55,130.00	$      -55,130.00	$ -1,56,195.00	$ -1,56,195.00
1	Annual Net Cash Flow	0.92593	$       29,800.00	$       27,593.00	$       44,500.00	$       41,204.00
2	Annual Net Cash Flow	0.85734	$       29,800.00	$       25,549.00	$       44,500.00	$       38,152.00
3	Annual Net Cash Flow	0.79383	$       29,800.00	$       23,656.00	$       44,500.00	$       35,325.00
4	Annual Net Cash Flow	0.73503	$       29,800.00	$       21,904.00	$       44,500.00	$       32,709.00
5	Annual Net Cash Flow	0.68058	$       29,800.00	$       20,281.00	$       44,500.00	$       30,286.00
6	Annual Net Cash Flow	0.63017	$       29,800.00	$       18,779.00	$       44,500.00	$       28,043.00
7	Annual Net Cash Flow	0.58349	$       29,800.00	$       17,388.00	$       44,500.00	$       25,965.00
8	Annual Net Cash Flow	0.54027	$       29,800.00	$       16,100.00	$       44,500.00	$       24,042.00
8	Salvage Value	0.54027	$       15,000.00	$          8,104.00	$       91,000.00	$       49,165.00
Net Present Value		$   1,24,224.00		$   1,48,696.00

Net Present Value of New Backhoes = $ 148,696

Net Present Value of Old Backhoes = $ 124,224

Using the NPV method, Waterways should "buy" equipment

Part B:

Pay-Back period is the period by which Initial Investment is recovered.

Payback period of New Backhoes = $ 156,195 / $ 44,500 = 3.51 years

Payback period of Old Backhoes = $ 55,130 / $ 29,800 = 1.85 years

Using the Payback period method, Waterways should continue with old equipment.

Part C:

Profitability Index of New Backhoes = Discounted Cash Flows / Initial Investment

= $ 304,890 / $ 156,195

= 1.95 times.

Profitability Index of Old Backhoes = Discounted Cash Flows / Initial Investment

= $ 179,354 / $ 55,130

= 3.25 times.

Using Profitability Index, it is better to continue with old Backhoes.

Part D:

IRR for New Backhoes:

Year	Particulars	Cash Flow - New Backhoes	Present Value factor @ 27%	Discounted Cash Flow - New Backhoes - 27%	Present Value factor @ 26%	Discounted Cash Flow - New Backhoes - 26%
0	Initial Investment	$ -1,56,195.00	1.00000	$     -1,56,195.00	1.00000	$    -1,56,195.00
1	Annual Net Cash Flow	$       44,500.00	0.78740	$          35,039.00	0.79365	$          35,317.00
2	Annual Net Cash Flow	$       44,500.00	0.62000	$          27,590.00	0.62988	$          28,030.00
3	Annual Net Cash Flow	$       44,500.00	0.48819	$          21,724.00	0.49991	$          22,246.00
4	Annual Net Cash Flow	$       44,500.00	0.38440	$          17,106.00	0.39675	$          17,655.00
5	Annual Net Cash Flow	$       44,500.00	0.30268	$          13,469.00	0.31488	$          14,012.00
6	Annual Net Cash Flow	$       44,500.00	0.23833	$          10,606.00	0.24991	$          11,121.00
7	Annual Net Cash Flow	$       44,500.00	0.18766	$             8,351.00	0.19834	$            8,826.00
8	Annual Net Cash Flow	$       44,500.00	0.14776	$             6,575.00	0.15741	$            7,005.00
8	Salvage Value	$       91,000.00	0.14776	$          13,446.00	0.15741	$          14,324.00
Net Present Value		$           -2,289.00		$            2,341.00

IRR = 26% + [ $ 2,341 / ( $ 2,341 - ( - $ 2,289 ) ) ]

= 26% + 0.51%

= 26.51%

IRR for Old Backhoes:

Year	Particulars	Cash Flow - Old Backhoes	Present Value factor @ 52%	Discounted Cash Flow - Old Backhoes - 52%	Present Value factor @ 53%	Discounted Cash Flow - Old Backhoes - 53%
0	Initial Investment	$      -55,130.00	1.00000	$        -55,130.00	1.00000	$        -55,130.00
1	Annual Net Cash Flow	$       29,800.00	0.65789	$          19,605.00	0.65359	$          19,477.00
2	Annual Net Cash Flow	$       29,800.00	0.43283	$          12,898.00	0.42719	$          12,730.00
3	Annual Net Cash Flow	$       29,800.00	0.28475	$             8,486.00	0.27921	$            8,320.00
4	Annual Net Cash Flow	$       29,800.00	0.18734	$             5,583.00	0.18249	$            5,438.00
5	Annual Net Cash Flow	$       29,800.00	0.12325	$             3,673.00	0.11927	$            3,554.00
6	Annual Net Cash Flow	$       29,800.00	0.08108	$             2,416.00	0.07796	$            2,323.00
7	Annual Net Cash Flow	$       29,800.00	0.05335	$             1,590.00	0.05095	$            1,518.00
8	Annual Net Cash Flow	$       29,800.00	0.03510	$             1,046.00	0.03330	$                992.00
8	Salvage Value	$       15,000.00	0.03510	$                527.00	0.03330	$                500.00
Net Present Value		$                694.00		$              -278.00

IRR = 52% + [ $ 694 / ( $ 694 - ( - $ 278 ) ) ]

= 52% + 0.71%

= 52.71%

Considering the Internal rate of return for both models, Waterways should purchase the equipment.  

Note: There has been an alignment error for the above tables in the last row. Please do re-total the columns.