Question

Without using excel

Quasar Tech Ltd is investing $6 million in new machinery that will produce the next-generation routers. Sales to its customers will amount to $1 750 000 for the next 3 years and then increase to $2.4 million for 3 more years. The project is expected to last 6 years and cost the company annually $898 620 (excluding depreciation). The machinery will be depreciated to zero by year 6 using the straight-line method. The company’s tax rate is 30 per cent, and the cost of capital is 16 per cent.

(a) What is the payback period?

(b) What is the average accounting return (ARR)?

(c) Calculate the project NPV.

(d) What is the IRR for the project?

Answer 1

Answer :-

(a) Pay back period method

This method will tell that investment will be recoverd in how many years.

Year	Sales	Cost	Depreciation (6000000/6)	Earning Before Tax (Sales - Cost - Depreciation	Tax @ 30% (Note)	Earning after Tax	Cash Flow (EAT + Depreciation	Cumulative Cash flows
1	1750000	898620	1000000	(148620)	44586	(104034)	895966	895966
2	1750000	898620	1000000	(148620)	44586	(104034)	895966	1791932
3	1750000	898620	1000000	(148620)	44586	(104034)	895966	2687898
4	2400000	898620	1000000	501380	(150414)	350966	1350966	4038864
5	2400000	898620	1000000	501380	(150414)	350966	1350966	5389830
6	2400000	898620	1000000	501380	(150414)	350966	1350966	6740796

Payback Period = Complete Years + Remaining Cash flow / Cash flow for the year to be recovered

= 5 years +(6000000 - 5389830) / 1350966

= 5 years + 0.45 years

= 5.45 Years

(b) Average Accounting Return (ARR) = Average Earning After tax / Initial investment

  = [ (104034) + (104034) + (104034) + 350966 + 350966 + 350966 ] / 6000000

= [ 123466 ] / 6000000

= 0.02058 or 2.058 %

(c) Net Present Value :-

NPV = Present value of cash inflow - Present value of cash outflow

Year	Cash flow	PV factor @ 16%	Discounted cash flow
1	895966	0.8621	772412.29
2	895966	0.7432	665881.93
3	895966	0.6406	573955.82
4	1350966	0.5523	746138.52
5	1350966	0.4761	643194.91
6	1350966	0.4104	554436.45

Present Value of cash inflow	3956019.92
(-) Present value of cash outflow	6000000
Net Present Value	(2043980.08)

(d) Internal Rate of return (IRR)

IRR is rate where PV of cash inflow is equal to PV of cash outflow.

IRR is calculated by Hit & Trial Method.

Lets assume two rates @3% & 4% for purpose of calculation of NPV.

NPV @ 3%.

Year	Cash flow	PV factor @ 3%	Discounted cash flow
1	895966	0.9709	869893.39
2	895966	0.9426	844537.55
3	895966	0.9151	819898.49
4	1350966	0.8885	1200333.29
5	1350966	0.8626	1165343.27
6	1350966	0.8375	1131434.02

Present Value of cash inflow	6031440.01
(-) Present value of cash outflow	6000000
Net Present Value	31440.01

Now, we calculate NPV @ 4%

Year	Cash flow	PV factor @ 4%	Discounted cash flow
1	895966	0.9615	861471.31
2	895966	0.9245	828320.57
3	895966	0.8890	796513.77
4	1350966	0.8548	1154805.74
5	1350966	0.8219	1110358.96
6	1350966	0.7903	1067668.43

Present Value of cash inflow	5819138.78
(-) Present value of cash outflow	6000000
Net Present Value	(180861.22)

By Interpolation,

IRR = Lower Rate + Lower Rate NPV /(Lower Rate NPV - Higher Rate NPV) * Difference in Rate

Lower Rate = 3%

Lower Rate NPV = 31440.01

Higher Rate NPV = (180861.22)

Difference in Rate = 1% (4%-3%)

IRR = 3 + 31440.01 /[(31440.01 - (180861.22)]* 1

= 3 + 0.1481

= 3.1481%

Note --> In case of Negative Earning before tax, Tax saving has been taken in same year. Assuming that compnay have other income also to set off these losses.