Question

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Finance tutorial

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X plans to buy a new machine. The cost of the machine, payable immediately, is $800,000 and the machine has an expected life of five years. Additional investment in working capital of $90,000 will be required at the start of the first year of operation. At the end of five years, the machine will be sold for scrap, with the scrap value expected to be 5% of the initial purchase cost of the machine. The machine will not be replaced.

Production and sales from the new machine are expected to be 100,000 units per year. Each unit can be sold for $16 per unit and will incur variable costs of $11 per unit. Incremental fixed costs arising from the operation of the machine will be $160,000 per year. The production and sales are expected to increase by 2.5% per annum. It is also expected that selling price inflation will be 4.2% per year, variable cost inflation will be 5% per year and fixed cost inflation will be 3% per year

X has an after‐tax cost of capital of 11% which it uses as a discount rate in investment appraisal. The company pays profit tax one year in arrears at an annual rate of 30% per year. Tax‐allowable depreciation should be ignored.

Calculate Internal rate of return and Net Present Value.

Answer 1

In order to calculate the NPV and IRR, we need to evaluate the individual cash flows. The calculation as well as the steps for each is given in the below table.

	Cashflow analysis
1	Year	0	1	2	3	4	5		Remarks
2	Cost of the Machine	-800000
3	Working Capital	-90000	0	0	0	0	90000		Change in Working capital
4	Salvage value						40000		5% of cost of the machine
5	No. of units		100000	102500	105062.5	107689.1	110381.3		increase by 2.5% YoY
6	Cost per unit		16	16.672	17.37222	18.10186	18.86214		increase by 4.2% YoY
7	Variable cost per unit	11	11.55	12.1275	12.73388	13.37057		equals rows 5*6
8	Total sales		1600000	1708880	1825169	1949372	2082027		equals rows 5*7
9	Variable cost		1100000	1183875	1274145	1371299	1475861		increase by 5% YoY
10	Fixed cost		160000	164800	169744	174836.3	180081.4		increase by 3% YoY
11	Gross Profits		340000	360205	381279.8	403236.7	426084.8		Row 8-9-10
12	Tax		102000	108061.5	114383.9	120971	127825.4		Row 11*0.3
13	Net Profits		238000	252143.5	266895.9	282265.7	298259.4		Row 11 - 12
14	Net cashflow	-890000	238000	252143.5	266895.9	282265.7	428259.4		Sum of rows 2,3,4,13
15	Discount rate	1	0.900901	0.811622433	0.731191	0.658731	0.593451		Discounting by 11%
16	DCF	-890000	214414.4	204645.321	195152	185937.1	254151.1		Row 15*14
17	NPV	164299.9							sum of all the columns in row 16
18	IRR	17.46%

The IRR is calculated by using the keeping the discount rate as the variable and goal seeking the NPV to 0. Please refer to the remarks column for explanation of each steps.