Question

Duo Co needs to increase production capacity to meet increasing demand for an existing product, ‘Quago’, which is used in food processing. A new machine, with a useful life of four years and a maximum output of 600,000 kg of Quago per year, could be bought for $800,000, payable immediately. The scrap value of the machine after four years would be $30,000. Forecast demand and production of Quago over the next four years is as follows: Year 1 2 3 4 Demand (kg) 1·4 million 1·5 million 1·6 million 1·7 million Existing production capacity for Quago is limited to one million kilograms per year and the new machine would only be used for demand additional to this. The current selling price of Quago is $8·00 per kilogram and the variable cost of materials is $5·00 per kilogram. Other variable costs of production are $1·90 per kilogram. Fixed costs of production associated with the new machine would be $240,000 in the first year of production, increasing by $20,000 per year in each subsequent year of operation. Duo Co pays tax one year in arrears at an annual rate of 30% and can claim capital allowances (tax-allowable depreciation) on a 25% reducing balance basis. A balancing allowance is claimed in the final year of operation. Duo Co uses its after-tax weighted average cost of capital when appraising investment projects. It has a cost of equity of 11% and a before-tax cost of debt of 8·6%. The long-term finance of the company, on a market-value basis, consists of 80% equity and 20% debt. Required: (a) Calculate the net present value of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000). (b) Calculate the internal rate of return of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000).

Answer 1

	A	Initial Cash flow	($800,000)
		Annual Operating cash flows:
		Year	0	1	2	3	4
	B	Demand (Kg)		1,400,000	1,500,000	1,600,000	1,700,000
	C	Existing machine capacity		1,000,000	1,000,000	1,000,000	1,000,000
	D=B-C	Production and sales from new machine		400,000	500,000	600,000	700,000
	E	Contribution per Kg($8-$5-$1.9)		$1.10	$1.10	$1.10	$1.10
	F=D*E	TotalContribution Margin		$         440,000	$         550,000	$         660,000	$         770,000
	G	Fixed cost		$240,000	$260,000	$280,000	$300,000
	H=F-G	Before tax operating cash flow		$         200,000	$         290,000	$         380,000	$         470,000
	I=H*(1-0.3)	After tax operating Cashflow		$         140,000	$         203,000	$         266,000	$         329,000
		Depreciation Tax Shield:
	J	Book Value at the beginning of year		$800,000	$600,000	$450,000	$337,500
	K=J*0.25	Depreciation expenses		$200,000	$150,000	$112,500	$84,375
	L=J-K	Book Value at the end of year		$600,000	$450,000	$337,500	$253,125
	M=K*0.3	Annual Depreciation Tax Shield		$60,000	$45,000	$33,750	$25,313
	P=I+M	Total annualAfter tax Cash Flow		$         200,000	$         248,000	$         299,750	$         354,313
		TerminalCash Flow
	Q	Salvage Value					$30,000
	R=L-Q	Balancing allowance					$223,125
	S=R*0.3	Tax shield due to balancing allowance					$66,938
	T=Q+S	Total TerminalCash Flow					$96,938
	N	YEAR	0	1	2	3	4
	U=A+P+T	Net Annual After Tax Cash Flow	($800,000)	$         200,000	$         248,000	$         299,750	$         451,250
		Internal Rate of Return	15.89%	(Using excelIRR function over the Net AnnualAfter Tax Cash flow)
		COST OF CAPITAL:
		After tax cost of debt=8.6*(1-0.3)=	6.02%	6.02
		Cost of Equity	11%
		Weighted Average Cost of Capital(WACC)	10%	(0.8*11+0.2*6.02)
		Present Value (PV) of Cash Flow:
		(Cash Flow)/((1+i)^N)
		i=Discount Rate=WACC=10%=0.1
		N=Year of Cash Flow
								SUM
	PV=U/(1.1^N)	Present Value of Net Annual aftertax Cashflow	$       (800,000)	$         200,000	$         248,000	$         299,750	$         451,250	$ 399,000
	NPV	Net Present Value=Sumof PV of Cash flows	$          399,000
	(a)	Based on NPV, the purchase of new machine is recommended because NPV is positive
	(b)	Based on IRR, the purchase of new machine is recommended because IRR is greater thanWACC