Question

Complex Cash Flow Problem - Data for the next six questions:

The firm is considering expanding into a new product line of solar-powered widgets. The CFO estimates that the firm will sell 150,000 solar-powered widgets per year for the next 10 years and that the widgets will sell for $125 each. The firm’s WACC is 15%. The CFO gives you the following data and asks you to use the WACC as the discount rate for the project.

Variable costs	$70 each
Annual fixed costs	$1,500,000
Initial robot production expenditure	$10,000,000 At the end of the project the value is $0. The robots are recycled and are not sold for cash.
Robot depreciation	straight-line method for 10 years, no residual value
Change in net working capital investment	One-time $500,000 initial investment in inventory to be recovered at the end of the project in 10 years
Marginal tax rate	25%

QUESTION: The Internal Rate of Return (IRR) for the project is:

Answer 1

Computation of annual cash flow:

Annual revenue ($ 125 x 150,000)	$18,750,000
Less: Variable cost ($ 70 x 150,000)	10,500,000
Contribution	8,250,000
Less: Fixed cost	1,500,000
Operating Profit	6,750,000
Less: Depreciation ($10,000,000/10)	1,000,000
Profit before tax	5,750,000
Less: Tax @ 25 %	1,437,500
Net income	4,312,500
Add: Depreciation	1,000,000
Annual cash flow	$5,312,500

Initial cash layout = Cost of equipment + Working capital investment

                              = $ 10,000,000 + $ 500,000 = $ 10,500,000

Final year cash flow = Annual cash flow + Working capital release

= $ 5,312,500 + $ 500,000 = $ 5,812,500

Computation of IRR using trial and error method:

Computation of NPV at discount rate of 49 %

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 49 % (F)	PV (C x F)
0	-$10,500,000	1/(1+0.49)^0	1	-$10,500,000
1	5,312,500	1/(1+0.49)^1	0.671140939597315	3,565,436.24161
2	5,312,500	1/(1+0.49)^2	0.450430160803567	2,392,910.22927
3	5,312,500	1/(1+0.49)^3	0.302302121344676	1,605,980.01964
4	5,312,500	1/(1+0.49)^4	0.202887329761528	1,077,838.93936
5	5,312,500	1/(1+0.49)^5	0.136165993128542	723,381.83850
6	5,312,500	1/(1+0.49)^6	0.091386572569491	485,491.16678
7	5,312,500	1/(1+0.49)^7	0.061333270180867	325,832.99784
8	5,312,500	1/(1+0.49)^8	0.041163268577763	218,679.86432
9	5,312,500	1/(1+0.49)^9	0.027626354750176	146,765.00961
10	5,312,500	1/(1+0.49)^10	0.018541177684682	107,770.59529
			NPV 1	$150,086.90222

As NPV is positive, let’s compute NPV at discount rate of 50 %

Year	Cash Flow (C)	Computation of PV Factor	PV Factor @ 50 % (F)	PV (C x F)
0	-$10,500,000	1/(1+0.50)^0	1	-$10,500,000
1	5,312,500	1/(1+0.50)^1	0.666666666666667	3,541,666.66667
2	5,312,500	1/(1+0.50)^2	0.444444444444444	2,361,111.11111
3	5,312,500	1/(1+0.50)^3	0.296296296296296	1,574,074.07407
4	5,312,500	1/(1+0.50)^4	0.197530864197531	1,049,382.71605
5	5,312,500	1/(1+0.50)^5	0.131687242798354	699,588.47737
6	5,312,500	1/(1+0.50)^6	0.087791495198903	466,392.31824
7	5,312,500	1/(1+0.50)^7	0.058527663465935	310,928.21216
8	5,312,500	1/(1+0.50)^8	0.039018442310623	207,285.47478
9	5,312,500	1/(1+0.50)^9	0.026012294873749	138,190.31652
10	5,312,500	1/(1+0.50)^10	0.017341529915833	100,797.64264
			NPV 2	-$ 50,582.99039

IRR = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 49 % + [$ 150,086.90222 x (50 % - 49 %)/ ($ 150,086.90222 – (-$ 50,582.99039))]

= 49 % + [($ 150,086.90222 x 1 %)/ ($ 150,086.90222 + $ 50,582.99039)]

= 49 % + ($ 1,500.8690222 / $ 200,669.89261)

= 49 % + 0.0074792934938

= 49 % + 0.74792934938 % = 49.74 %

IRR of the project A is 49.74 %