Question

what is the payback period , net present Value, Initial rate of return , and MIRR for both machines

Question 2 Staten Island Construction Company is considering replacing an existing crane with one of two newer more effective models. The existing crane is 3 years old, cost $32,000 and is being depreciated under MACRS using a 5-year recovery period. Although the existing crane has only three years of depreciation remaining under MACRS, it has a remaining usable life of 5 years. Crane A, one of the two newer models cost $40,000 to purchase, and $8,000 to install. It has a 5-year usable life and will be depreciated under MACRS using a 5-yrear recovery period. Crane B cost $54,000 to purchase and $6,000 to install. It also has a 5-year usable life and will be depreciated under MACRS using a 5-year recovery period. The purchase of crane A would result in a $4,000 increase in net working capital; crane B would result in 6,000 increase in net working capital. The projected earnings before depreciation interest and taxes with each alternative crane is given in the following table. Earnings before depreciation, interest, and taxes Year Crane A $32,000 $32,000 $32,000 $32,000 $32,000 Crane B $28,000 $29,000 $36,000 $40,000 $40,000 Existing Crane $14,000 $14,000 $14,000 $14,000 $14,000 The existing crane can be sold for $18,000 and will not incur any removal or cleanup cost. At the end of five years the existing crane can be sold to net $1,000 before taxes. Crane A and B can be sold to net $12,000 and $20,000 respectively before taxes at the end of the 5-year period. The company is subject to a 40% tax rate. The company's discount rate is 10%.

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Answer 1

This question can be solved easily using excel

We have to find the cash flows for all three cranes and then we need to calculate the net present value. The crane which has the highest NPV will be selected.

The details of NPV for crane A is given below

Crane A
	5Yr MACR	20%	32%	19.20%	11.52%	11.52%	5.76%
	Year	0	1	2	3	4	5	Terminal Value
	Initial Outlay	-30000						12000
	EBITDA		32000	32000	32000	32000	32000
	Change in WC	-4000						4000
	Depreciation		9600	15360	9216	5530	5530
	EBIT		22400	16640	22784	26470.4	26470.4
	Tax		8960	6656	9114	10588	10588
	Net Income		13440	9984	13670	15882	15882
	PV	-34000	12218	8251	10271	10848	9862	9935
	NPV	27384

Description

1. The first row gives detail about the depreciation rate in MACR method

2. Initial Outlay is the amount paid in purchase and installation of the crane minus the

amount received by selling existing crane = 40000+8000-18000

3. EBITDA is the earnings before depreciation tax as given in the table in question

4. Change in working capital is the increase in working capital as mentioned in the question. This increase reduces the cash flows hence it is shown with a negative sign

5. Depreciation is (cost of machine + installation)* MACR rate for that year (eg for the first-year rate is 20%)

6.. EBIT = EBITDA - Depreciation

7. Tax = EBIT * 0.4 (since, tax rate is 40%)

8. Net income = EBIT - Tax

9. PV =present value of cash flow

10 NPV = net present value calculated using the sum of the present values

Similarly, we calculated NPV for crane B

Crane B
	5Yr MACR	20%	32%	19.20%	11.52%	11.52%	5.76%
	Year	0	1	2	3	4	5	Terminal Value
	Initial Outlay	-42000						20000
	EBITDA		28000	29000	36000	40000	40000
	Change in WC	-6000						6000
	Depreciation		12000	19200	11520	6912	6912
	EBIT		16000	9800	24480	33088	33088
	Tax		6400	3920	9792	13235	13235
	Net Income		9600	5880	14688	19853	19853
	PV	-48000	8727	4860	11035	13560	12327	16144
	NPV	18653

We also calculated the NPV for existing crane

The differences in this case from the previous two were

1. The initial outlay is zero as the cost to purchase the crane is a sunk cost

2. There is no change in working capital

3. the Depreciation rate for first-year is 19.2% (as on;y 3 years left in 5 yr MACR)

the NPV for the existing crane is as follows

Existing Crane
	5Yr MACR	20%	32%	19.20%	11.52%	11.52%	5.76%
	Year	0	1	2	3	4	5	Terminal Value
	Initial Outlay	0						1000
	EBITDA		14000	14000	14000	14000	14000
	Depreciation		6144	3686	3686
	EBIT		7856	10314	10314	14000	14000
	Tax		3142	4125	4125	5600	5600
	Net Income		4714	6188	6188	8400	8400
	PV	0	4285	5114	4649	5737	5216	621
	NPV	25623

Here, we can see that the NPV is maximum in case of crane A.

Hence they should replace the existing crane with crane A