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		$89,700		$201,044
Salvage value now		$42,900
Investment in major overhaul needed in next year		$54,000
Salvage value in 8 years		$15,100		$89,000
Remaining life		8 years		8 years
Net cash flow generated each year		$30,000		$44,800

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. (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 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

Calculation of NPV of Old Backhoes
Period	Overhaul cost (A)	Cash Inflows{B}	Salvage Value (C)	Net Cash Inflows (A+B+C)	P.V.F @ 8%	P.V.F @ 8%	P.V.F @ 60%	P.V.F @ 60%
1	-54,000	0		-54,000	0.92593	-50,000	0.62500	-33,750
1		30000		30,000	0.92593	27,778	0.62500	18,750
2		30000		30,000	0.85734	25,720	0.39063	11,719
3		30000		30,000	0.79383	23,815	0.24414	7,324
4		30000		30,000	0.73503	22,051	0.15259	4,578
5		30000		30,000	0.68058	20,417	0.09537	2,861
6		30000		30,000	0.63017	18,905	0.05960	1,788
7		30000		30,000	0.58349	17,505	0.03725	1,118
8		30000	15100	45,100	0.54027	24,366	0.02328	1,050
						1,30,557		15,437
Calculation of NPV of New Backhoes
Period	Cost (A)	Cash Inflows{B}	Salvage Value (C)	Net Cash Inflows (A+B+C)	P.V.F @ 8%	P.V.F @ 8%	P.V.F @ 30%	P.V.F @ 30%
0	-1,58,144	0		-1,58,144	1.00000	-1,58,144	1.00000	-1,58,144
1		44800		44,800	0.92593	41,482	0.76923	34,462
2		44800		44,800	0.85734	38,409	0.59172	26,509
3		44800		44,800	0.79383	35,564	0.45517	20,391
4		44800		44,800	0.73503	32,929	0.35013	15,686
5		44800		44,800	0.68058	30,490	0.26933	12,066
6		44800		44,800	0.63017	28,232	0.20718	9,281
7		44800		44,800	0.58349	26,140	0.15937	7,140
8		44800	89000	1,33,800	0.54027	72,288	0.12259	16,402
						1,47,390		-16,207
Solution 1)
NPV	Old Backhoes	1,30,557
NPV	New Backhoes	1,47,390
It is better to purchase the New bachoes, since its NPV is greater then Old Machine.
Solution 2)
PBP= Purchase price / Net Annual Cash flows
		Old Backhoes	New Backhoes
Purchase Price		54,000	1,58,144
Net Annual Cash Flows		30000	44800
PBP		1.80	3.53
As per PBP, better to go with Old Backhoes.
Solution 3)
Profitability Index=		(NPV+ initial Investment)
		initial investment
		Calculation of NPV of Old Backhoes		Calculation of NPV of New Backhoes
	NPV	1,30,557		1,47,390
	Initial Investment	54,000		1,58,144
	Total	1,84,557		3,05,534
	PI	3.42		1.93
As per PI, Old backhoes purchases is better option, since PI is higher.
Solution 4)
IRR= Lower Discount Rate + [ Lower Rate NPV / ( Lower Rate NPV - Higher Rate NPV )]*(Higher Discount Rate-Lower Discount Rate)
So By putting figure into this formula IRR is
IRR	Old Backhoes	54.29902%
IRR	New Backhoes	26.22224%
As per IRR, Old backhoes purchases is better option, since higher the IRR means greater the cash flows over iniital cost.