Question

show your detailed work and how you arrived to the solution. Comprehensive Problems Consider the following information on Liquor Co. Debt: 4,000, 7% semiannual coupon bonds outstanding, $1,000 par value, 18 years to maturity, selling for 102 percent of par; the bonds make semiannual payments. Preferred Stock: 10,000 outstanding with par value of $100 and a market value of 105 and $10 annual dividend. Common Stock: 84,000 shares outstanding, selling for $56 per share, the beta is 2.08 The market risk premium is 5.5%, the risk free rate is 3.5% and Liquor Co tax rate is 32%. Liquor Co. is evaluating two mutually exclusive project that is somewhat riskier than the usual project the firm undertakes; management uses the subjective approach and decided to apply an adjustment factor of +2.1% to the cost of capital for both projects. Project A is a five-year project that requires an initial fixed asset investment of $2.4 million. The fixed asset falls into the five-year MACRS class. The project is estimated to generate $2,050,000 in annual sales, with costs of $950,000. The project requires an initial investment in net working capital of $285,000 and the fixed asset will have a market value of $225,000 at the end of five years when the project is terminated. Project B requires an initial fixed asset investment of $1.0 million. The marketing department predicts that sales related to the project will be $920,000 per year for the next five years, after which the market will cease to exist. The machine will be depreciated down to zero over four-year using the straight-line method (depreciable life 4 years while economic life 5 years). Cost of goods sold and operating expenses related to the project are predicted to be 25 percent of sales. The project will also require an addition to net working capital of $150,000 immediately. The asset is expected to have a market value of $120,000 at the end of five years when the project is terminated. Use the following rates for 5-year MACRS: 20%, 32%, 19.2%, 11.52%, 11.52%, and 5.76% 1) Calculate WACC for the firm. 2) What is the appropriate discount rate for project A and project B (Risk adjusted rate)? 3) Calculate project A’s cash flows for years 0-5 4) Calculate NPV, IRR and PI for project A 5) Calculate project B’s cash flows for year 0-5 6) Calculate NPV, IRR and PI for project B 7) Which project should be accepted if any and why? 8) What is the exact NPV profile’s crossover rate (incremental IRR)?

Answer 1

1]	COMPONENT COST OF CAPITAL:
	Cost of debt:
	Before tax cost = YTM of the bonds
	YTM of the bonds [using a calculator] = 6.81%
	After tax cost of debt = YTM*(1-t) = 6.81%*(1-32%) =	4.63%
	Cost of preferred stock:
	= Dividend/Price = 10/105 =	9.52%
	Cost of equity:
	Per CAPM, cost of equity = risk free rate+beta*market risk premium.
	= 3.5%+2.08*5.5% =	14.94%
	WACC:
	WACC is the weighted average of the cost of the
	components of the capital structure, the weights
	being the proportion in which the components are
	present in the capital structure. Here, the market
	value weights are to be used.
	WACC is calculated in the table below:
	COMPONENT	MARKET VALUE	WEIGHT	COMPONENT COST	WACC
	Debt [4000*1020]	$     40,80,000	41.49%	4.63%	1.92%
	Preferred stock [10000*105]	$     10,50,000	10.68%	9.52%	1.02%
	Common stock [84000*56]	$     47,04,000	47.83%	14.94%	7.15%
	Total	$     98,34,000	100.00%		10.08%
	WACC = 10.08%
2]	Discount rate = 10.08%+2.1% =	12.18%
3]	PROJECT A:
	The cash flows and calculations are done in the table below:
		0	1	2	3	4	5
	Capital expenditure	$     24,00,000
	Investment in NWC	$       2,85,000
	Sales		$      20,50,000	$    20,50,000	$    20,50,000	$    20,50,000	$    20,50,000
	Operating costs		$        9,50,000	$       9,50,000	$       9,50,000	$       9,50,000	$       9,50,000
	Depreciation rate [%]		20.00%	32.00%	19.20%	11.52%	11.52%	5.76%
	Depreciation		$        4,80,000	$       7,68,000	$       4,60,800	$       2,76,480	$       2,76,480	$   1,38,240
	NOI		$        6,20,000	$       3,32,000	$       6,39,200	$       8,23,520	$       8,23,520
	Tax at 32%		$        1,98,400	$       1,06,240	$       2,04,544	$       2,63,526	$       2,63,526
	NOPAT		$        4,21,600	$       2,25,760	$       4,34,656	$       5,59,994	$       5,59,994
	Add: Depreciation		$        4,80,000	$       7,68,000	$       4,60,800	$       2,76,480	$       2,76,480
	OCF		$        9,01,600	$       9,93,760	$       8,95,456	$       8,36,474	$       8,36,474
	Recapture of NWC						$       2,85,000
	After tax salvage value = 225000-(225000-138240)*32% =						$       1,97,237
	FCF [Cash flows]	$   -26,85,000	$        9,01,600	$       9,93,760	$       8,95,456	$       8,36,474	$    13,18,710
	PVIF at 12.18% [PVIF = 1/1.1218^t]	1	0.89142	0.79464	0.70836	0.63145	0.56289
	PV at 12.18%	$   -26,85,000	$        8,03,708	$       7,89,679	$       6,34,305	$       5,28,190	$       7,42,288
4]	NPV	$       8,13,170
	PI = Sum of cash inflows/Initial investment = (2685000+813170)/2685000 =	1.30
	IRR:
	IRR is that discount rate for which NPV = 0. It has to be found out by trying different discount rates [by trial and error] so that 0 NPV results.
	Discounting with 23%:
	PVIFA at 23%	1	0.81301	0.66098	0.53738	0.43690	0.35520
	PV	$   -26,85,000	$        7,33,008	$       6,56,858	$       4,81,204	$       3,65,453	$       4,68,408	$       19,930
	Discounting with 24%:
	PVIFA at 24%	1	0.80645	0.65036	0.52449	0.42297	0.34111
	PV	$   -26,85,000	$        7,27,097	$       6,46,306	$       4,69,655	$       3,53,806	$       4,49,822	$     -38,313
	IRR = 23%+1%*19930/(19930+38313) =	23.34%
7]	Project B with higher NPV is to be acceptedas it will result in higher addition to shareholders' worth.
8]	Incremental cash flows	$   -15,35,000	$        3,52,400	$       4,44,560	$       3,46,256	$       2,87,274	$       6,17,910
	PVIF at 10%	1	0.90909	0.82645	0.75131	0.68301	0.62092
	PV	$   -15,35,000	$        3,20,364	$       3,67,405	$       2,60,147	$       1,96,212	$       3,83,674	$       -7,199
	PVIF at 9%	1	0.91743	0.84168	0.77218	0.70843	0.64993
	PV	$   -15,35,000	$        3,23,303	$       3,74,177	$       2,67,373	$       2,03,512	$       4,01,599	$       34,964
	Incremental IRR [Cross over rate] = 9%+1%*34964/(34964+7199) =	9.83%