Question

The managers of Classic Autos Incorporated plan to manufacture classic Thunderbirds (1957 replicas). The necessary foundry equipment will cost a total of $4,200,000 and will be depreciated using a five-year MACRS life, The sales manager has an estimate for the sale of the classic Thunderbirds. The annual sales volume will be as​ follows:

Year one:   260   Year four:   350
Year two:   290 Year five:   300
Year three:   360      

If the sales price is ​$28,000 per​ car, variable costs are ​$19,000 per​ car, and fixed costs are ​$1,400,000 ​annually, what is the annual operating cash flow if the tax rate is 30​%? The equipment is sold for salvage for ​$500,000 at the end of year five. Net working capital increases by ​$500,000 at the beginning of the project​ (year 0) and is reduced back to its original level in the final year. Find the internal rate of return for the project using the incremental cash flows.

1:what is the annual operating cash flow of the project for year​ 1, 2, 3, 4, 5, 6?

2: what is the​ after-tax cash flow of the equipment at​ disposal?

3: what is the incremental cash flow of the project in year​ 0, 1, 2, 3, 4, 5?

4: What is the IRR of the project?

MACRS Fixed Annual Expense Percentages by Recovery Class:        

Year	​3-Year	​5-Year	​7-Year	​10-Year
1	​33.33%	​20.00%	​14.29%	​10.00%
2	​44.45%	​32.00%	​24.49%	​18.00%
3	​14.81%	​19.20%	​17.49%	​14.40%
4	​ 7.41%	​11.52%	​12.49%	​11.52%
5		​11.52%	​8.93%	​9.22%
6		​ 5.76%	​8.93%	​7.37%
7			​8.93%	​6.55%
8			​4.45%	​6.55%
9				​6.55%
10				​6.55%
11				​3.28%

Answer 1

1)		0	1	2	3	4	5
	Sales volume [cars]		260	290	360	350	300
	Sales revenue at $28000/car		$      72,80,000	$   81,20,000	$    1,00,80,000	$    98,00,000	$    84,00,000
	Variable cost at $19000/car		$      49,40,000	$   55,10,000	$        68,40,000	$    66,50,000	$    57,00,000
	Depreciation		$        8,40,000	$   13,44,000	$          8,06,400	$       4,83,840	$      4,83,840	241920
	Fixed costs		$      14,00,000	$   14,00,000	$        14,00,000	$    14,00,000	$    14,00,000
	NOI		$        1,00,000	$    -1,34,000	$        10,33,600	$    12,66,160	$      8,16,160
	Tax at 30%		$            30,000	$        -40,200	$          3,10,080	$       3,79,848	$      2,44,848
	NOPAT		$            70,000	$        -93,800	$          7,23,520	$       8,86,312	$      5,71,312
	Add: Depreciation		$        8,40,000	$   13,44,000	$          8,06,400	$       4,83,840	$      4,83,840
	OCF		$        9,10,000	$   12,50,200	$        15,29,920	$    13,70,152	$    10,55,152
2)	Sale value of the equipment						$      5,00,000
	Book value of the equipment						$      2,41,920
	Gain on sale						$      2,58,080
	Tax on gain at 30%						$          77,424
	After tax cash flow of the equipment on disposal						$      4,22,576
3)	Initial investment	$         42,00,000					$     -4,22,576
	Change in NWC	$           5,00,000					$     -5,00,000
	Incremental cash flow of the project	$       -47,00,000	$        9,10,000	$   12,50,200	$        15,29,920	$    13,70,152	$    19,77,728
4)	IRR is that discount rate for which NPV = 0. Such a discount rate is to be found out by trial and error to get 0 NPV.
	Incremental cash flow of the project	$       -47,00,000	$        9,10,000	$   12,50,200	$        15,29,920	$    13,70,152	$    19,77,728
	Discounting at 14%:
	PVIF at 14%	1	0.87719	0.76947	0.67497	0.59208	0.51937	NPV
	PV at 14%	$       -47,00,000	$        7,98,246	$      9,61,988	$        10,32,652	$       8,11,240	$    10,27,170	$      -68,704
	Discounting at 13%:
	PVIF at 13%	1	0.88496	0.78315	0.69305	0.61332	0.54276
	PV at 13%	$       -47,00,000	$        8,05,310	$      9,79,090	$        10,60,311	$       8,40,340	$    10,73,432	$        58,482
	IRR lies between 13% and 14%.
	By simple interpolation IRR = 13%+1%*58482/(68704+58482) =	13.46%