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		$90,000		$202,784
Salvage value now		$41,600
Investment in major overhaul needed in next year		$55,510
Salvage value in 8 years		$15,000		$90,000
Remaining life		8 years		8 years
Net cash flow generated each year		$30,500		$43,800

Click here to view PV table.

(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.

		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 Backhoesretain 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 Backhoesretain Old Backhoes equipment.

Answer 1

a) 1) Calculation of Net present value in case of buying the new backhoes.

Discounting factor at 8%

Particulars	Calculation	Amount ($)
Cashinflows:
Salvage value of old backhoes		41,600
Present cashflows of 8 years	43,800*5.74	251,412
Present salvage value of new backhoes	90,000*0.54	48,600
A. Total cash inflows		341,612
B. Cashoutflows:
Cost of new backhoes		202,784
Net Present value (A-B)		$138,828

Net present value of keeping the old backhoes

Particulars	Calculation	Amount
Cash inflows:
Present cashflows of 8 years	30,500*5.74	175,070
Present salvage value of old backhoes	15,000*0.54	8,100
A. Total cash inflows		183,170
B. Investment in next year		55,510
Net present value (A-B)		$127,660

Net present value of new backhoes is greater than the Net present value of keeping the old backhoes. Hence, Waterways should buy the New backhoes.

2. Calculation of Payback period :

Particulars	Old Backhoes	New Backhoes
A. Initial cost	55,510	161,184
		(202784 - 41600)
B. Annual cashflows	30,500	43,800
Payback period (A/B)	1.82 years	3.68 years

If the period is high, then there is more risk. New blackhoes payback period is more than old backhoes. Hence, Old backhoes is to be retained.

3. Calculation of Probability index: from the answer (1)

Particulars	Old Backhoes	New Backhoes
A. Present value of Cashflows	183,170	341,612
B. Cash outflow	55,510	202,784
Probability index (A/B)	3.30 times	1.68 times

Since, probability index of 2 projects is more than 1. Ranking should be given on highest calculation. Hence, Old backhoes is to be retained.

Calculation of Internal rate of return :

For New Backhoes,

First discounting rate is 8% and assuming second discount rate @9%.

Calculation of Net present value @9%

Particulars	Calculation	Amount ($)
Cash inflows:
Salvage value of old backhoes		41,600
Present cash flow generated for 8 years	43,800*5.53	242,214
Present salvage value of new backhoes	90,000*0.50	45,000
A. Total Cashinflows		328,814
B. Cash outflow		202,784
Net Present value @9% (A -B)		126,030
Net Present value @ 8% (from 1)		138,828

Internal rate of return of New Backhoes =

NPVOL 1 1NPVOL, - NPVOL" -(L2 – L1)

L1 = lowest discount rate, L2 = Highest discount rate

Irr = 8% +

138828 -19-8) 126030 - 138828

= 8% - 138,828/12,798 * 1

= 8% - 10.84% = - 2.84%

For Old backhoes, Calculation of net present value

Particulars	Calculation	Amount ($)
Cash inflow :
Present cash flows for 8 years	30,500*5.53	168,665
Present salvage valueof old backhoes	15,000*0.50	7,500
Total cash inflows (A)		176,165
Cash outflow (B)		55,510
Net present value ( A-B) @9%		120,655
Net present value @8%		$127,660

Internal rate of return = 8% + 127660/(120655 -127660) * (9-8)

= 8% - 127660/7005 * 1

=8% - 18.22 = -10.22%

	New Backhoes	Old backhoes
Irr factor	-2.84%	-10.22%

4. If the Internal rate of return is greater than the cost of capital, the project is to be pursued. But the internal rate of return of 2 projects is in negative that is the cashflows is less than the initial investment.

And Irr is not to be trusted in taking a decision. Waterways may face negative returns by considering IRR