Question

Aguilera Acoustics, Inc. (AAI), projects unit sales for a new seven-octave voice emulation implant as follows:

Year	Unit Sales
1	8300
2	9200
3	10400
4	9800
5	8400

Production of the implants will require GH¢ 150,000 in net working capital to start and additional net working capital investments each year equal to 15 percent of the projected sales for that year. In the final year of the project, net working capital will decline to zero as the project is wound down. In other words, the investment in working capital is to be completely recovered by the end of the project’s life. Total fixed costs are GH¢ 240,000 per year, variable production costs are GH¢ 190 per unit, and the units are priced at GH¢ 345 each. The equipment needed to begin production has an installed cost of GH¢ 2,300,000. Because the implants are intended for professional singers, this equipment depreciated using the straight-line basis. In five years, this equipment can be sold for about 20 percent of its acquisition cost. The cost of acquisition and installation is to be financed partly by a loan from Swez Bank to the tune of GH¢ 1,000,000 at an interest rate of 15% and the remaining financed from the internal resource of the firm. The cost of equity is 20%. AAI is in the 25 percent marginal tax bracket. Based on these preliminary project estimates,

Required

Advise whether the company should buy the equipment or not using the NPV              

Answer 1

The Weighted Average cost of company = We X Ke + Wd x Kd x (1-t)

where We & Wd are weights of equity & debt in capital

Ke & Kd are costs of equity and debt respectively. t is the tax rate

Here, We = (230000-1000000) / 2300000 = 1,300,000/2,300,000 = & Wd = 1,000,000 / 2,300,000

Ke = 20% & Kd = 15% & t = 25%

WACC for the company = (1,300,000 / 2,300,000) x 20% + (1,000,000/2,300,000) x 15% x (1-25%)

= 56.52% x 20% + 43.48% x 11.25%

WACC = 16.20%

This is going to be discount rate for calculating NPVThe cash flows of the company are as follows

Revenue forecast	0	1	2	3	4	5
Units sold (A)		8300	9200	10400	9800	8400
Sales Price / Unit (B)		345	345	345	345	345
Variable cost/ Unit (C		190	190	190	190	190
Revenues (D = A x B)		2,863,500	3,174,000	3,588,000	3,381,000	2,898,000
Variable costs (E = A x C)		(1,577,000)	(1,748,000)	(1,976,000)	(1,862,000)	(1,596,000)
Fixed Costs (F)		(240,000)	(240,000)	(240,000)	(240,000)	(240,000)
Depreciation (G = (M+N) /5)		(368,000)	(368,000)	(368,000)	(368,000)	(368,000)
EBIT (H = D + E + F + G)		678,500	818,000	1,004,000	911,000	694,000
Taxes @ 25% (I = H x 25%)		(169,625)	(204,500)	(251,000)	(227,750)	(173,500)
Net Income (J = H - I)		508,875	613,500	753,000	683,250	520,500
Depreciation (G)		368,000	368,000	368,000	368,000	368,000
Net Working Capital Investments (K)	(150,000)	(279,525)	(46,575)	(62,100)	31,050
Return of Net working Capital (L)						507,150
Capital Expenditure in Plant & Mach(M)	(2,300,000)
Expenditure in Installation and other costs) N
Salvage Value of Equipment O						460,000
Free Cash Flow (O = J+G+K+L+M+N +O)	(2,450,000)	597,350	934,925	1,058,900	1,082,300	1,395,650
Working Capital (as 15% of sales)	150000	429,525	476,100	538,200	507,150
Cost of Capital (Discount Rate) R	16.20%
PV Of Free Cash Flow	(2,450,000)	514,071	692,412	674,896	593,640	658,788
NPV (Sum of PV of all CF)	683,806

All costs & values that impact cash flow negatively are shown in negative values

Fixed Costs are given.

Sales and variable costs are derived from units sold and the respective per unit revenue and variable costs

Depreciation = (Equipment cost - Salvage Value) / Number of years of depreciation

Depreciation = (2,300,000 - 20% x2,300,000) / 5 = 368,000

Tax is 25% on EBIT

Working Capital for year 0 = 150,000 . In subsequent years, it is the difference of previous and current year. If Working capital is increasing, it will bring down cash flow, thus shown as negative

So year, Working Capital = 15% x Sales = 429,525.

The investment in WC in year 1 = (429525-150000) = 279525. Because this will negatively impact cash flow, it is shown as negative. Like wise for subsequent years

In the terminal year, all investments in WC are returned back = (150000+ 279525+46575+62100-31050) = 507150

The salvage value of equipment is 460,000 (added back)

Cash Flow = (Net Income + Depreciation + Net working capital Investments + Return of Net working capital + Capital Expenditure + Salvage Value) *

*Sign of cash flows are important here. One which increases CF is positive, other which decreases Cf is negative

PV of cash flows = CFt/ (1+k)^t

where CFt is cash flow in year t, k = Cost of capital (WACC) & t is the year of Cash flow

Thus PV of 3rd Cashflow = 1058900 / (1+16.20%)^3 = 674896

Similarly other PVs are calculated

NPV = Sum of PV of all future cash flows - PV of Investment

NPV = (674896 + 514071 +692412 + 593640 + 658788) - 2,450,000

NPV = $683,806

Since the NPV is $683806 or greater than 0, at WACC of 16.20% , the equipment should be purchased.