Weighted Average Cost of Capital

WEIGHTED AVERAGE COST OF CAPITAL
SOLUTION 1
Project’s initial, (Year0) cash flows.
The project’s initial cash flow is the initial investment less net working capital less the lost
opportunity cost of the sale of land (after tax). i.e.
t=0
Initial (depreciable) investment -$ 265,000,000.00
CF due to change in net working
capital -$ 11,950,000.00
Opportunity cost of lost land sale
(after tax) -$ 11,250,000.00
-$ 288,200,000.00
SOLUTION 2
Weighted average cost of capital (WACC) of Perfect Image NZ Ltd
WACC = Cost of equity* Weight of Equity + Cost of debt* Weight of Debt*1- Corporate tax rate +
Cost of non-redeemable preference shares * Weight of preference shares (CFI, 2019).
Step 1: Cost of Equity
It is given that that Perfect image holds 18,000,000 ordinary shares selling for $38 per share.
Furthermore, the company pays regular dividends.
The cost of equity can be determined using the Dividend growth model formula
Re= D1/P0 + g
Where D1 = dividend paid for period, P0 = share price at the beginning and g = growth factor
(Investing Answers, 2019).
Perfect Image NZ made a dividend payment of $3.81 and the initial share price was $38. To
calculate the constant growth factor, we take the average growth rates across each dividend year
to get 2.59% (see appendix).
Thus, using the dividend growth model, the cost of equity is 12.6163% (3.81/38+2.59%).

Step 2: Cost of Debt
It is given that the company borrowed $150,000,000, 7.25% coupon bonds outstanding with 20
years to maturity redeemable at par, selling for 95 per cent of par; the bonds have a $1000 par
value each and make semi-annual coupon payments.
To calculate the cost of debt we need to determine the yield to maturity using the variables below.
n= 40
Market Value = 0.95*150,000,000= $142,500,000
Coupon Payment = 150,000,000*7.5%*6/12=5,625,000
Face Value=$150,000,000
142,500,000= 5625000
(1+ ytm /2)+ 5625000
(1+ ytm /2)2 + .....+ 155,625,000
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Solving the above equation gives a Yield to maturity of 8.005%. Hence, the cost of debt is given
as 8.01%. The corporate tax is given as 28% and will be applied to the cost of debt when
calculating WACC.
Step 3: Cost of Preference Shares
It is given that Perfect image holds 11,000,000 non-redeemable preference shares (par value $ 10
per share) with 6.5% dividends (after taxes), selling for $24 per share.
The cost of preference shares is given by formula below:-
Cost of preference shares = Dividend/market price of preference share (Efinance, 2019)
=6.5%*10/24
=2.7083%
Step 4: Weight of Debt, Equity and Preference shares
The market value of Equity (E) (both ordinary and preference) and the market value of Debt (D)
will be required to determine the Weights of Equity and Debt.
The market value of ordinary equity is the current share price, P0, multiplied by its shares
outstanding i.e.
Market Value (E) = 18, 0000, 0000*38 = $684,000,000

The market value of Non-redeemable Preference shares (P) is the current share price, P0,
multiplied by the number of shares outstanding i.e.
Market Value (P) = 11, 0000, 0000*24 = $264,000,000
The market value of Debt (D) is the current selling price at par, multiplied by the face value of the
bond i.e.
Market Value (D) =0.95*150,000,000= $142, 500, 0000
Weight of Debt, Wd= D/D+E+P = 13.07%
Weight of Equity, We= E/D+E+= 62.72%
Weight of Preference shares, Wp= P/D+E+P = 24.21%
,
Weighted Average Cost of Capital
WACC =Weight Debt * cost of debt *(1 – T) + Weight equity *cost of equity+ Weight Preference
shares *cost of Preference shares
Where T is the corporate tax given as 28% (CFI, 2019)
WACC =13.07%*8.01 %*( 1-28%) +62.72%*12.6163%+24.21%*2.7083%
WACC =9.3224%
The cost of capital for Perfect Image NZ is calculated as 9.32%.
SOLUTION 3
General assumptions
Initial (depreciable) investment $265,000,0
00
Diminishing value depriciation per year 25%
unit sales per year
385,000
variable costs $550
net working capital $11,950,00
0
Selling price per year $1,350
fixed cost p.a $225,000,0
00
Income tax rate 28%
Discount rate 9.32%
Salvage value $32,000,00
0
book sale $47,164,30
7

Net income 1 2 3 4 5 6
Revenues $519,750,00
0
$519,750,00
0
$519,750,00
0
$519,750,00
0
$519,750,00
0
$519,750,00
0
– Cost variable $211,750,00
0
$211,750,00
0
$211,750,00
0
$211,750,00
0
$211,750,00
0
$211,750,00
0
– Cost fixed $225,000,00
0
$225,000,00
0
$225,000,00
0
$225,000,00
0
$225,000,00
0
$225,000,00
0
– Depreciation
expense $66,250,000 $49,687,500 $37,265,625 $27,949,219 $20,961,914 $15,721,436
Taxable income $16,750,000 $33,312,500 $45,734,375 $55,050,781 $62,038,086 $67,278,564
– Taxes $4,690,000 $9,327,500 $12,805,625 $15,414,219 $17,370,664 $18,837,998
After-tax
income $12,060,000 $23,985,000 $32,928,750 $39,636,563 $44,667,422 $48,440,566
Annual Net Cash
Flow Estimates 0 1 2 3 4 5 6
Investment in fixed
assets -$265,000,000 $0 $0 $0 $0 $0 $36,246,006
CF due to change in
net working capital -$11,950,000 $0 $0 $0 $0 $0 11,950,000
Opportunity cost of
lost land sale (after
tax) -$11,250,000 $0 $0 $0 $0 $0 15,500,000
Net income $0 $12,060,000 $23,985,000 $32,928,750
39,636,56
3
44,667,42
2 48,440,566
Add back
depreciation (non-
cash expense) $0 $66,250,000 $49,687,500 $37,265,625
27,949,21
9
20,961,91
4 15,721,436
Net cash flows -$288,200,000 $78,310,000 $73,672,500 $70,194,375
67,585,78
1
65,629,33
6 127,858,008
Cumulative cash
flows ($288,200,000
)
($209,890,000
)
($136,217,500
)
($66,023,125
) 1,562,656
67,191,99
2
$195,050,00
0
Discounted cF (PV) (288,200,000)
71,632,166 61,643,477 53,724,810
47,317,17
1
42,029,31
4 74,898,495
Net present value- $ $63,045,433
Internal Rate of Return -16.01%
Profitability Index-1.22
Based on the above Net Present Value and IRR analysis, Perfect Image should proceed
with the investment in the new plant. This is because the NPV is greater than zero.
SOLUTION 4
Factors affecting Cost of capital