Answers
Answer 1
Cost of equity
The required rate of return on equity can be found using the capital asset pricing model:
E(ri) = Rf + i (E(rm) – Rf)
E(ri) = 4.7% + (1.2 x 6.5%)
= 12.5%
Cost of convertible debt
Conversion value = P0 (1 + g)nR
Where Po is the current share price
g is the expected annual growth of the share price
n is the number of years to conversion
R is the number of shares received on conversion
Conversion value = $5.50 x (1 + 0.06)6 x 15
= $117.03 per bond
We can therefore assume that conversion will take place as the conversion value is much greater than par
value.
The annual interest cost net of tax will be 7% (1 – 0.3) = $4.90 per bond
The cash flows will be as follows:
10% 5%
discount discount
Year Cash flow factors PV factors PV
$m $m $m
0 Market value (107.11) 1.000 (107.11) 1.000 (107.11)
1-6 Interest 4.90 4.355 21.34 5.076 24.87
6 Conversion value 117.03 0.564 66.00 0.746 87.30
(19.77) 5.06
Calculate the cost of convertible debt using an IRR calculation.
NPVa
IRR = a% (b – a) %
NPVa – NPVb
5.06(10% 5%)
= 5% + = 6.02%
5.06 19.77
The after tax cost of convertible debt is therefore 6.02%
Cost of bank loan
After-tax interest rate = 8% x (1 – 0.3)
= 5.6%
Market values
Market value of equity = 20m x $5.50 = $110m
Market value of convertible debt = 29m x 107.11/100 = $31.06m
Market value of bank loan = $2m
Total market value = $(110.00 + 31.06 + 2)m = $143.06m
Weighted average cost of capital
WACC = VE ke + VD kd
VE VD VE VD
In this case, we have two costs of debt so:
110 31.06 2
WACC = × 12.5% + × 6.02% + × 5.6%
143.06 143.06 143.06
= 9.61% + 1.31% + 0.08%
= 11%
Answer 2
Cost of equity
Using the CAPM: E(ri) = Rf + i (E(rm) – Rf)
E(ri) = 4% + 1.2(10.5% – 4%)
= 11.8%
Cost of debt
After-tax interest payment = 100 × 7% × (1 – 30%) = $4.90
10% 5%
discount discount
Year Cash flow factors PV factors PV
$m $m $m
0 Market value (94.74) 1.000 (94.74) 1.000 (94.74)
1-7 Interest 4.90 4.868 23.85 5.786 28.35
7 Capital repayment 100.00 0.513 51.30 0.711 71.10
(19.59) 4.71
Calculate the cost of debt using an IRR calculation.
NPVa
IRR = a% (b – a)%
NPVa – NPVb
4.71(10% 5%)
= 5% +
4.71 19.59
= 6%
The after tax cost of debt is therefore 6%
Number of shares issued by KFP Co = $15m/0.5 = 30 million shares
VE = 30 million $4.20
= $126 million
VD = 15 million 94.74/100
= $14.211
WACC = ke VE + k VD
d
VE VD VE VD
126 14.211
= 11.8 + 6
126 14.211 126 14.211
= 10.6% + 0.6%
= 11.2%
Answer 3
Cost of equity
Geometric average growth rate = 4 21.8 / 19.38 -1 = 0.0298 = 2.98% or 3%
Putting this into the dividend growth model gives ke = 0.03 + ((21.8 × 1.03) / 250)
= 0.03 +0.09 = 0.12 = 12%
Market values of equity and debt
Market value of equity = Ve = 100m × 2.50 = $250 million
Market value of bonds = Vd = 60m × (104/100) = $62.4 million
Total market value = $250 million + $62.4 million = $312.4 million
WACC Calculation
The current after tax cost of debt is 7%
WACC = ((ke × Ve) + (kd(1 –T) × Vd) / (Ve + Vd))
= ((12 × 250m) + (7 × 62.4m)) / 312.4m
= 11%
Cost of debt
After-tax interest payment = 100 × 8% × (1 – 30%) = 5.6%
5% 6%
discount discount
Year Cash flow factors PV factors PV
$ $ $
0 Market value (100.00) 1.000 (100.00) 1.000 (100.00)
1-10 Interest 5.60 7.722 43.24 7.360 41.22
10 Capital repayment 105.00 0.614 64.47 0.558 58.59
7.71 (0.19)
Calculate the cost of debt using an IRR calculation.
NPVa
IRR = a% (b – a) %
NPVa – NPVb
= 5% + 7.71(6% 5%)
7.71 0.19
= 5.98% or 6%
Note: Other discount factors and therefore costs of debt are acceptable.
Revised WACC Calculation
Market value of the new issue of bonds is $40 million
New total market value = $312.4m + $40 m = $352.4m
Cost of debt of bonds is 6% (from above)
WACC = ((12 × 250m) + (7 × 62.4m) + (6 × 40m)) / 352.4m
= 10.4%
Answer 4
Cost of equity
The geometric average dividend growth rate in recent years:
(36·3/30·9)0·25 – 1 = 1·041 – 1 = 0·041 or 4·1% per year
Using the dividend growth model:
Ke = 0·041 + [(36·3 x 1·041)/470] = 0·041 + 0·080 = 0·121 or 12·1%
Cost of preference shares
As the preference shares are not redeemable:
Kp = 100 x [(0·04 x 100)/40] = 10%
Cost of debt of bonds
The annual after-tax interest payment is 7 x 0·7 = $4·9 per bond.
Using linear interpolation:
Year Cash flow $ 5% DF PV ($) 4% DF PV ($)
0 Market price (104·50) 1·000 (104·50) 1·000 (104·5)
1–6 Interest 4·9 5·076 24·87 5·242 25·69
6 Redemption 105 0·746 78·33 0·790 82·95
–––––– ––––––
(1·30) 4·14
–––––– ––––––
After-tax cost of debt = 4 + [((5 – 4) x 4·14)/(4·14 + 1·30)] = 4 + 0·76 = 4·8%
Cost of debt of bank loan
If the bank loan is assumed to be perpetual (irredeemable), the after-tax cost of debt of the bank loan will be its after-tax
interest rate, i.e. 4% x 0·7 = 2·8% per year.
Market values
Number of ordinary shares = 4,000,000/0·5 = 8 million shares
$000
Equity: 8m x 4·70 = 37,600
Preference shares: 3m x 0·4 = 1,200
Redeemable bonds: 3m x 104·5/100 = 3,135
Bank loan (book value used) 1,000
–––––––
Total value of AMH Co 42,935
–––––––
WACC calculation
[(12·1 x 37,600) + (10 x 1,200) + (4·8 x 3,135) + (2·8 x 1,000)]/42,935 = 11·3%
Answer 5
Cost of equity
Using the capital asset pricing model, Ke = 4 + (1·15 x 6) = 10·9%
Cost of debt of loan notes
After-tax annual interest payment = 6 x 0·75 = $4·50 per loan note.
Year $ 5% discount PV 4% discount PV
($) ($)
0 (103·50) 1·000 (103·50) 1·000 (103·50)
1–6 4·50 5·076 22·84 5·242 23·59
6 106·00 0·746 79·08 0·790 83·74
–––––– ––––––
(1·58) 3·83
–––––– ––––––
Kd = 4 + [(1 x 3·83)/(3·83 + 1·58)] = 4 + 0·7 = 4·7% per year
Market values of equity and debt
Number of ordinary shares = 200m/0·5 = 400 million shares
Market value of ordinary shares = 400m x 5·85 = $2,340 million
Market value of loan notes = 200m x 103·5/100 = $207 million
Total market value = 2,340 + 207 = $2,547 million
Market value WACC
K0 = ((10·9 x 2,340) + (4·7 x 207))/2,547 = 26,479/2,547 = 10·4%
Book value WACC
K0 = ((10·9 x 850) + (4·7 x 200))/1,050 = 10,205/1,050 = 9·7%
Comment
Market values of financial securities reflect current market conditions and current required rates of return. Market values
should therefore always be used in calculating the weighted average cost of capital (WACC) when they are available. If book
values are used, the WACC is likely to be understated, since the nominal values of ordinary shares are much less than their
market values. The contribution of the cost of equity is reduced if book values are used, leading to a lower WACC, as
evidenced by the book value WACC (9·7%) and the market value WACC (10·4%) of Tinep Co.
Answer 6
Cost of equity
The dividend growth model can be used to calculate the cost of equity.
Ke = ((0·25 x 1·04)/4·26) + 0·04 = 10·1%
Cost of preference shares
Kp = (0·05 x 1·00)/0·56 = 8·9%
Cost of debt of loan notes
After-tax annual interest payment = 6 x (1 – 0·25) = 6 x 0·75 = $4·50 per year
Year Cash Flow 5% discount PV 6% discount PV
($) ($) ($)
0 (95·45) 1·000 (95·45) 1·000 (95·45)
1–5 4·50 4·329 19·48 4·212 18·95
5 100·00 0·784 78·40 0·747 74·70
–––––– ––––––
2·43 (1·80)
–––––– ––––––
After-tax cost of debt of loan notes = Kd = 5 + (1 x 2·43)/(2·43 + 1·80) = 5 + 0·57 = 5·6%
Cost of debt of bank loan
The after-tax fixed interest rate of the bank loan can be used as its cost of debt. This will be 5·25% (7 x 0·75). Alternatively,
the after-tax cost of debt of the loan notes can be used as a substitute for the after-tax cost of debt of the bank loan.
Market values
$000
Equity: 4·26 x (23,000,000/0·25) = 391,920
Preference shares: 0·56 x (5,000,000/1·00) = 2,800
Loan notes: 95·45 x (11,000,000/100) = 10,500
Bank loan 3,000
––––––––
408,220
––––––––
After-tax weighted average cost of capital
((10·1 x 391,920) + (8·9 x 2,800) + (5·6 x 10,500) + (5·25 x 3,000))/408,220 = 9·9%
Answer 7
Cost of equity
Cum div share price ($ per share) 7·52
Ex div share price ($ per share) 7·07
–––––
Dividend for 20X7 ($ per share) 0·45
Dividend for 20X3 ($ per share) 0·37
Dividend growth rate (%) 5·02 [(0·45/0·37)0·25 – 1]
Cost of equity (%) 11·7 [((0·45 x 1·05)/7·07) + 0·05]
Cost of preference shares
Nominal value ($ per share) 0·50
Market price ($ per share) 0·31
Dividend rate (%) 5
Cost of preference shares (%) 8·06 [(0·5 x 0·05)/0·31]
Interest rate of loan notes (%) 7
Nominal value of loan notes ($) 100·00
Market price of loan notes ($) 102·34
Time to redemption (years) 4
Redemption premium (%) 5
Tax rate (%) 30
Year Item $ 5% DF PV ($) 6% DF PV ($)
0 MV (102·34) 1·000 (102·34) 1·000 (102·34)
1–4 Interest 4·90 3·546 17·38 3·465 16·98
4 Redeem 105·00 0·823 86·42 0·792 83·16
––––––– –––––––
1·45 (2·20)
––––––– –––––––
IRR (%) (5 + (1·45/(1·45 + 2·20))) = 5·40
Cost of bank loan (%) 5·40 Use cost of loan notes as a proxy value.
Market values and WACC calculation
BV ($000) Nominal MV MV ($000) Cost (%) WACC
Ordinary shares 12,000 0·50 7·07 169,680 11·7 10·67
Preference shares 5,000 0·50 0·31 3,100 8·06 0·13
Loan notes 10,000 100·00 102·34 10,234 5·40 0·30
Bank loan 3,000 3,000 5·40 0·09
–––––––– ––––––
186,014 11·19
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