Question

10.8

(13 part question)

Project cash flow and NPV. The managers of Classic Autos Incorporated plan to manufacture classic Thunderbirds (1957 replicas). The necessary foundry equipment will cost a total of $4,300,000 and will be depreciated using a five-year MACRS life, B. The sales manager has an estimate for the sale of the classic Thunderbirds. The annual sales volume will be as follows: Year one: 230 Year two: 280 Year three: 330 Year four: 370 Year five: 330 If the sales price is $26,000 per car, variable costs are $17,000 per car, and fixed costs are $1,100,000 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 $600,000 at the beginning of the project (year O) 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.

Answer 1

Computation of Operating Cash flows

S.No	Particulars	Year 1	Year 2	Year 3	Year 4	Year 5
A	No.of Units sold	230	280	330	370	330
B	Sale price per unit	$26,000	$26,000	$26,000	$26,000	$26,000
C	Variable Cost per unit	$17,000	$17,000	$17,000	$17,000	$17,000
D	Total sales( A*B)	$5,980,000	$7,280,000	$8,580,000	$9,620,000	$8,580,000
E	Total Variable Cost( A*C)	$3,910,000	$4,760,000	$5,610,000	$6,290,000	$5,610,000
F	Fixed Cost	$1,100,000	$1,100,000	$1,100,000	$1,100,000	$1,100,000
G	Depreciation	$860,000	$1,376,000	$825,600	$495,360	$495,360
H	Profit Before Tax( D-E-F-G)	$110,000	$44,000	$1,044,400	$1,734,640	$1,374,640
I	Tax @ 30% on H	$33,000.0	$13,200.0	$313,320.0	$520,392.0	$412,392.0
J	Profit After Tax( H-I)	$77,000.0	$30,800.0	$731,080.0	$1,214,248.0	$962,248.0
K	Annual Operating Cashflow( J+G)	$937,000.0	$1,406,800.0	$1,556,680.0	$1,709,608.0	$1,457,608.0

Computation of Depreciation

Year	Depreciation Calculation	Depreciation Amount
1	$ 4300000*0.20=$ 860000.	$860,000
2	$ 4300000*0.32=$ 1376000	$1,376,000
3	$ 4300000*0.1920= $ 825600	$825,600
4	$ 4300000*0.1152=$ 495360	$495,360
5	$ 4300000*0.1152=$ 495360	$495,360
	Total	$4,052,320

Computation of after tax proceeds from the sale of Equipment

S.No	Particulars	Amount
A	Cost of Equipment	$4,300,000
B	Accumulated Depreciation	$4,052,320
C	Book Value of Equipment ( A-B)	$247,680
D	Salvage value	$500,000
E	Gain on sale of Equipment( D-C)	$252,320
F	Tax @ 30% on E	$75,696.0
G	After tax sale proceeds( D-F)	$424,304.0

Computation of IRR

Year	Cash flow	Disc @ 15%	Discounted Cashflows at 15%	Disc @ 16%	Discounted Cashflows at 16%	Disc @ 17%	Discounted Cashflows at 17%
0	-$4,900,000.00	1	-$4,900,000.00	1	-$4,900,000.00	1	-$4,900,000.00
1	$937,000.00	0.8696	$814,782.61	0.8621	$807,758.62	0.8547	$800,854.70
2	$1,406,800.00	0.7561	$1,063,742.91	0.7432	$1,045,481.57	0.7305	$1,027,686.46
3	$1,556,680.00	0.6575	$1,023,542.37	0.6407	$997,298.99	0.6244	$971,945.16
4	$1,709,608.00	0.5718	$977,473.92	0.5523	$944,201.28	0.5337	$912,332.39
5*	$2,481,912.00	0.4972	$1,233,948.91	0.4761	$1,181,670.61	0.4561	$1,132,027.74
			$213,490.72		$76,411.06		-$55,153.54

* Cash flow in Year 5 = OCF in year 5+ After tax sale procceds+ Working Capital recovery

= $ 1457608+$ 424304+$ 600000
= $ 2481912

* Cash flow in Year 0 = Equipment purchase price + Working capital

= -$ 4300000-$ 600000

=- $ 4900000

We know that at IRR NPV should be 0.

From the above table it is clear that IRR lies between 16% and 17%

We can find the exact rate by using interpolation technique

L.R +[ { NPV at L.R * ( H.R - L.R)}/ ( NPV at L.R - NPV at H.R) ]

Here L.R = Lower rate and H.R = Higher rate

16% + [ { $ 76411.06* ( 17% -16%) } / { $ 76411.06-( -$ 55153.54)}]

16% + [ $ 76411.06/ $ 131564.61]

16% + 0.5808%

16.58%

Internal rate of return is 16.58%.

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