ABMF4024 BUSINESS FINANCE
Tutorial 6(Cont.) Answer
November 10, 2010
Question 1 40% Debt; 60% Common equity; rd = 9%; T = 40%; WACC = 9.96%; rs= ? WACC = (wd)(rd)(1 T) + (wc)(rs) 0.0996 = (0.4)(0.09)(1 0.4) + (0.6)rs 0.0996 = 0.0216 0.0216 + 0.6rs 0.078 = 0.6rs rs = 13%.
Question 2 P0 = $30; D1 = $3.00; g = 5%; rs= ? D1
$3.00 + g = $30.00 + 0.05 = 15%.
a.
rs = P0
b.
F = 10%; re = ? D1
$3.00
re = P0 (1 F) + g = $30(1 0.10) + 0.05 =
.00 27.00 + 0.05 = 16.11%.
Question 3 D1 a.
rs =
P0
2.14
+g=
2
+ 7% = 9.3% + 7% = 16.3%.
b.
rs= rRF + (rM rRF)b = 9% + (13% 9%)1.6 = 9% + (4%)1.6 = 9% + 6.4% 6. 4% = 15.4%.
c.
rs = Bond rate + Risk premium = 12% + 4% = 16%.
d.
Since you have equal confidence in the inputs used for the three approaches, an average of the three methodologies probably would be warranted. 16.3% 15.4% 16% 3 rs = = 15.9%.
Question 4 Debt = 40%, Common equity = 60%. P0 = $22.50, D0 = $2.00, D1 = $2.00(1.07) = $2.14, g = 7%. D1 P0
$ .14 + g = $ .50 + 7% = 16.51%.
rs = WACC = (0.4)(0.12)(1 0.4) + (0.6)(0.1651) = 0.0288 + 0.0991 = 12.79%.
ABMF4024 BUSINESS FINANCE
Tutorial 6(Cont.) Answer
November 10, 2010
Question 5 .
a
rd = 10%, rd(1 T) = 10%(0.6) = 6%. D/A = 45%; D 0 = $2; g = 4%; P 0 = $20; T = 40%. Project A: Rate of return = 13%. Project B: Rate of return = 10%. rs = $2(1.04)/$20 + 4% = 14.40%.
b.
WACC = 0.45(6%) + 0.55(14.40%) = 10.62%.
c.
Since the firms WACC is 10.62% and each of the projects is equally risky and as risky as the firms other assets, MEC should accept Project A. Its rate of return is greater than the firms WACC. Project B should not be accepted, since its rate of return is less than MECs WACC.
Question 6 If the firm's dividend yield is 5% and its stock price is $46.75, the next expected annual dividend can be calculated. Dividend yield = D1/P0 5% = D1/$46.75 D1 = $2.3375. Next, the firm's cost of new common stock can be determined from the DCF approach for the cost of equity. re = D1/[P0(1 F)] + g = $2.3375/[$46.75(1 0.05)] + 0.12 = 17.26%.
Question 7 .
a
Examining the DCF approach to the cost of retained earnings, the expected growth rate can be determined from the cost of common equity, price, and expected dividend. However, first, this problem requires that that the formula for WACC be used to determine the cost of common equity. WACC 13.0% 10.6% rs
= wd(rd)(1 T) + w crs = 0.4(10%)(1 0.4) + 0.6(r s) = 0.6r s = 0.17667 or 17.67%.
From the cost of common equity, the expected growth rate can now be determined. rs = D1/P0 + g 0.17667= $3/$35 + g g = 0.090952 or 9.10%. b.
From the formula for the long-run growth rate: g = (1 Div. payout ratio) v ROE = (1 Div. payout ratio) v (NI/Equity) 0.090952 = (1 Div. payout ratio) v ($1,100 million/$6,000 million) 0.090952 = (1 Div. payout ratio) v 0.1833333 0.496104 = (1 Div. payout ratio) Div. payout ratio= 0.503896 or 50.39%.
ABMF4024 BUSINESS FINANCE
Tutorial 6(Cont.) Answer
November 10, 2010
Question 8 .
a
With a financial calculator, input N = 5, PV = -4.42, PMT = 0, FV = 6.50, and then solve for I/YR = g = 8.02%
}
8%.
b.
D1 = D0(1 + g) = $2.60(1.08) = $2.81.
c.
rs = D1/P0 + g = $2.81/$36.00 + 8% = 15.81%.
Question 9 a.
b.
rd(1 T) = 0.10(1 0.3) = 7%. rp = $5/$49 = 10.2%. rs = $3.50/$36 + 6% = 15.72%.
WACC: After-tax Component Debt[0.10(1 T)] Preferred stock Common stock
Weight 0.15
v
0.10 0.75
Cost 7.00%
Weighted =
10.20 15.72 WACC
c.
Projects 1 and 2 will be accepted since their rates of return exceed the WACC.
Question 10 .
a
If all project decisions are independent, the firm should accept all projects whose returns exceed their risk-adjusted costs of capital. The appropriate costs of capital are summarized below:
Project A B C D E F G H
Required Investment $4 million 5 million 3 million 2 million 6 million 5 million 6 million 3 million
Rate of Return 14.0% 1.5 9.5 9.0 12.5 12.5 7.0 11.5
Therefore, Ziege should accept projects A, C, E, F, and H.
Cost of Capital 12% 12 8 10 12 10 8 8
Cost 1.05% 1.02 _11.79__ = 13.86%
ABMF4024 BUSINESS FINANCE b.
Tutorial 6(Cont.) Answer
November 10, 2010
With only $13 million to invest in its capital budget, Ziege must choose the best combination of Projects A, C, E, F, and H. H. Collectively, the projects would account for an investment of $21 million, so naturally not all these projects may be accepted. Looking at the excess return created by the projects (rate of return minus the cost of capital), we see that the excess returns for Projects A, C, E, F, and H are 2%, 1.5%, 0.5%, 2.5%, and 3.5%. The firm should accept the projects which provide the greatest excess returns. By that rationale, the first project to be eliminated from consideration is Project E. This brings the total investment required down to $15 million, therefore one more project must be eliminated. The next lowest excess return is Project C. Therefore, Ziege's optimal capital budget consists of Projects A, F, and H, and it amounts to $12 million.
c.
Since Projects A, F, and H are already accepted projects, we must adjust the costs of capital for the other two value producing projects (C and E).
Project
Required Investment
Rate of Return
C
$3 million
9.5%
E
6 million
12.5
Cost of Capital 8% +1%= 9% 12% +1% = 13%
If new capital must be issued, Project E ceases to be an acceptable project. On the other hand, Project C's expected rate of return still exceeds the risk-adjusted cost of capital even after raising additional capital. Hence, Ziege's new capital budget should consist of Projects A, C, F, and H and requires $15 million of capital, so $3 million of additional capital must be raised.
