Question

There is a project which has EBT, depreciation, interest, debt and equity of $4.5, $1.5, $1, $40 and $60 million respectively. Its tax rate is 20%. Market rates of interest for similar risk to this company are 8%. The rate of return of the market is 11%, while the T bond rate is 4%. The bheta of this firm is 1.2. The cost of the project is $13million. As a result of the increased sales, the account receivable, inventory and accounts payable increase by $3, $5 and $1 million respectively. The rise in sales continue for 7 years. Is this an investment the firm should pursue? (What is its NPV?)

Answer 1

Formula sheet

A	B	C	D	E	F	G	H	I	J	K	L
2
3		Free cash flow can be calculated as follows:
4		Free Cash Flow = Operating Cash Flow - Capital Expenditures - Change in working capital
5		Operating Cash Flow = EBIT*(1-Tax Rate)+Depreciation
6
7		Tax Rate	0.2
8
9		Free cash Flow can be calculated as follows:
10		Year	0	1	2	3	4	5	6	7
11		Initial Cost	-13
12		EBT		4.5	4.5	4.5	4.5	4.5	4.5	4.5
13		Less: Interest		1	1	1	1	1	1	1
14		EBIT		=E12-E13	=F12-F13	=G12-G13	=H12-H13	=I12-I13	=J12-J13	=K12-K13
15		Less: Tax Expense		=-E14*$D$7	=-F14*$D$7	=-G14*$D$7	=-H14*$D$7	=-I14*$D$7	=-J14*$D$7	=-K14*$D$7
16		EBIT*(1-T)		=E14+E15	=F14+F15	=G14+G15	=H14+H15	=I14+I15	=J14+J15	=K14+K15
17		Add Depreciation		1.5	=E17	=F17	=G17	=H17	=I17	=J17
18		Operatin Cash Flow		=E16+E17	=F16+F17	=G16+G17	=H16+H17	=I16+I17	=J16+J17	=K16+K17
19		Capex		0	0	0	0	0	0	0
20		Change in working Capital=(Change in current asset - change in current liabilities)		=(3+5-1)	0	0	0	0	0	0
21		Free Cash Flow	=D11	=E18-E19-E20	=F18-F19-F20	=G18-G19-G20	=H18-H19-H20	=I18-I19-I20	=J18-J19-J20	=K18-K19-K20
22
23		Calculation of cost of capital:
24
25		Formula for WACC is given as:
26		WACC = r(E) × w(E) + r(D) × (1 – t) × w(D)
27		Where, r(E) and r(D) are cost of equity and cost of debt, w(E) is weight of equity and W(D) is weight of debt and t is the tax rate
28
29		Calculation of cost of equity:
30		As Per CAPM, Expected rate of return can be calculated as
31		r(E) = rf + ?*(rm-rf)
32		Using the Following data
33		Beta (?)	1.2
34		Risk free rate ( rf )	0.04
35		Rate of return of the market (rm)	0.11
36
37		Expected rate of return can be calculated as follows:
38		Expected rate of return	= rf + ?*(rm-rf)
39			=4%+1.2*(11% - 4%)
40			=D34+D33*(D35-D34)	=D34+D33*(D35-D34)
41
42		Hence Cost of Equity is	=D40
43
44		Calculation of WACC:
45		Formula for WACC is given as:
46		WACC = r(E) × w(E) + r(D) × (1 – t) × w(D)
47		Where, r(E) and r(D) are cost of equity and cost of debt, w(E) is weight of equity and W(D) is weight of debt and t is the tax rate
48
49		Weight of equity, w(E)	=Market Value of equity / (Market Value of Debt + Market Value of equity)
50			=60/(40+60)
51
52		Weight of debt, w(D)	=1- Weight of equity
53			=1-D50
54
55		Calculation of WACC
56		Tax rate	0.3
57		Source of capital	Weight(w)	Cost(c)
58		Debt	=D53	0.08
59		Equity	=D50	=D42
60
61		WACC	= r(E) × w(E) + r(D) × (1 – t) × w(D)
62			=E59*D59+E58*(1-D56)*D58	=E59*D59+E58*(1-D56)*D58
63
64		Hence WACC is	=D62
65
66		NPV of the project can be calculated as follows:
67
68		NPV of the project is present value of future cash flows discounted at required rate of return less the initial investment.
69		Given the following cash flow and WACC, NPV for the project can be calculated as follows:
70		Year	0	1	2	3	4	5	6	7
71		Free Cash Flow (FCF)	=D21	=E21	=F21	=G21	=H21	=I21	=J21	=K21
72		MARR (i)	=D64
73		(P/F,i,n) for each year		=1/((1+$D72)^E70)	=1/((1+$D72)^F70)	=1/((1+$D72)^G70)	=1/((1+$D72)^H70)	=1/((1+$D72)^I70)	=1/((1+$D72)^J70)	=1/((1+$D72)^K70)
74		Present Value of cash flows = FCF*(P/F,i,n)		=E71*E73	=F71*F73	=G71*G73	=H71*H73	=I71*I73	=J71*J73	=K71*K73
75		Present value if future cash flows	=SUM(E74:K74)	=SUM(E74:K74)
76
77		NPV for Project	=Present value fo future cash flows - Initial investment
78			=D75+D71	=D75+D71
79
80		Hence NPV of the project is	=D78
81