6 cost of capital solution
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1a
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 6,000,000.00 6/10 0.60 5.00% 3.00%
PS 1,000,000.00 1/10 0.10 10.00% 1.00%
CS 3,000,000.00 3/10 0.30 15.00% 4.50%TOTAL 10,000,000.00 1.00 8.50% WACC
1b
WACC dictates that all investments should have an internal rate of return above 8.5%.
1c
Debt is less costly because it is less risky from an investor's standpoint thus a lower
return iis demanded by investors. Moreover, interest expense is deductible for tax
purposes creaing cash savings from tax payment reduction.
2a
Capital Capital After Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 3,000,000.00 6/10 0.30 5.00% 1.50%
PS 1,000,000.00 1/10 0.10 10.00% 1.00%
CS 6,000,000.00 3/10 0.60 15.00% 9.00%
TOTAL 10,000,000.00 1.00 11.50% WACC
2b
There was an increase in WACC in No. 2
The higher the risks the higher the return. Risk and return trade-off.
3a
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 3,000,000.00 6/10 0.30 5.00% 1.50%
PS 1,000,000.00 1/10 0.10 10.00% 1.00%
CS 6,000,000.00 3/10 0.60 15.00% 9.00%
TOTAL 10,000,000.00 1.00 11.50% WACC
3b
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 2,500,000.00 6/10 0.19 5.00% 0.96%
PS 1,500,000.00 1/10 0.12 10.00% 1.15%
CS 9,000,000.00 3/10 0.69 15.00% 10.38%
TOTAL 13,000,000.00 1.00 12.50% WACC
3c
Market values are more reliable as they reflect the true value of the net assets.
3d
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Investments with IRR of 12% will be wrongfully accepted by using book values.
4a
Selling price 1,010.00
Less
Floatation cost 30.00
Net proceeds, Nd 980.00
4b
t1 t2 t3 … t15
980.00 (120.00) (120.00) … (120.00)
(1,000.00)
4c
Appproximation cost of debt formula:
kd = I + P1,000-Nd/n ki = kd x (1-tax rate)
Nd + P1,000
'2
kd = before tax cost of debt
I = stated interest
Nd = Net proceeds
n = term of the bond
P1,000 = assuimed face value of the bonds
2 = constant
ki - after tax cost of debt
kd= P120 + P1,000 - P980/15 years ,= P120 + 1.3333333 0.122556
P980 + P1,000 990 12.26%
'2
ki= 12.26% x 1-.40 = 0.073533
7.35%
4d
Cost to Maturity:
Step 1: Try 12%
V = 120 (6.811) + 1,000 (0.183)V = 817.32 + 183
V = $1,000.32
(Due to rounding of the PVIF, the value of the bond is 32 cents greater than expected.
At the coupon rate, the value of a $1,000 face value bond is $1,000.)
Try 13%:
V = 120 (6.462) + 1,000 (0.160)
n
ot n
t 1
I MB
(1 k) (1 k)=
= + + +
15
t 15t 1
$120 $1,000$980
(1 k) (1 k)=
= + + +
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V = 775.44 + 160
V = $935.44
The cost to maturity is between 12% and 13%.
Step 2: $1,000.32 $935.44 = $64.88
Step 3: $1,000.32 $980.00 = $20.32
Step 4: $20.32 $64.88 = 0.31Step 5: 12 + 0.31 = 12.31% = before-tax cost of debt
12.31 (1 0.40) = 7.39% = after-tax cost of debt
4e
12.26% and 12.31% after tax is 7.35% and 7.39% for approximation and IRR respectively, difference is
negligible.
4f
The value of bonds and interest rate have an inverse relationship.
4g
kd= P120 + P1,000 - P1,000/15 years ,= P120 + 0 0.12
P1,000 + P1,000 1000 12.00%
'2
ki= 12.00% x 1-.40 = 0.072
7.20%
4h
kd= P120 + P1,000 - P1020/15 years ,= P120 + -1.333333 0.117492
P1020 + P1,000 1010 11.75%
'2
ki= 11.75% x 1-.40 = 0.070495
7.05%
4i
Discounts increases cost of borrowings while premiums decreases cost of borrowing.
5
k p = D p N p
Preferred
Stock
Calculation
A $11.00 $92.00 11.96%
B 3.20 34.50 9.28%
C 5.00 33.00 15.15%
D 3.00 24.50 12.24%
E 1.80 17.50 10.29%
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6a&b
6c
Because of floatation costs and underpricing
6d
Retained earnings rightfully belongs to common stockholders.
6e
Signalling theory - investors takes issuance of equity as a sign of companies poor prospects.
7a,b&c
7d
7e
Retained Earnings versus New Common Stock
1r
0
Dk g
P= +
1n
n
Dk g
N= +
Firm Calculation
A k r = ($2.25 $50.00) + 8% = 12.50%
k n = ($2.25 $47.00) + 8% = 12.79%
B k r = ($1.00 $20.00) + 4% = 9.00%
k n = ($1.00 $18.00) + 4% = 9.56%
C k r = ($2.00 $42.50) + 6% = 10.71%
k n = ($2.00 $39.50) + 6% = 11.06%
D k r = ($2.10 $19.00) + 2% = 13.05%
k n = ($2.10 $16.00) + 2% = 15.13%
k s = R F + [b (k m R F)]
k s = 6% + 1.2 (11% 6%)
k s = 6% + 6%
k s = 12%
(c) Risk premium = 6%
(b) Rate of return = 12%
(a) After-tax cost of common equity using the CAPM = 12%
k s = R F + [b (k m R F)]k s = 6% + 1 (11% 6%)
k s = 6% + 5%
k s = 11%
k s = R F + [b (k m R F)]
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7f
Risk free rate is the rate from t-bills or govt. bonds, market return is the return paid by the market whichis higher than the risk free rate and beta is a measure of volatility of the stock price which is measure of
risk.
8
9
k s = 6% + .90 (11% 6%)
k s = 6% + 4.5%
k s = 10.5%
(a)2006
k%,4
2002
Dg FVIF
D= =
$3.10g 1.462
$2.12= =
From FVIF table, the factor closest to 1.462 occurs at 10% (i.e., 1.464 for 4 years).Calculator solution: 9.97%
(b) Nn = $52 (given in the problem)
(c) 2007r
0
Dk g
P= +
r $3.40
k 0.10 15.91%$57.50
= + =
(d) K n 2007r
n
Dk g
N= +
K n=$3.40/$52+.10 = 16.54%
(a) Cost of Retained Earnings
r $1.26(1 0.06) $1.34
k 0.06 3.35% 6% 9.35%
$40.00 $40.00
+= + = = + =
(b) Cost of New Common Stock
s$1.26(1 0.06) $1.34
k 0.06 4.06% 6% 10.06%$40.00 $7.00 $33.00
+= + = = + =
(c) Cost of Preferred Stock
p$2.00 $2.00
k 9.09%= = =
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10a
It’s a wrong decision because an investment with an IRR of 8% was accepted while an investment with
10b
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 60,000.00 6/10 0.60 7.00% 4.20%
PS - 0 0.00 0.00% 0.00%
CS 40,000.00 4/10 0.40 16.00% 6.40%
TOTAL 100,000.00 1.00 10.60% WACC
Reject project Apple and acccept project Mona.
$25.00 $3.00 $22.00
(d) d
$1,000 $1,175$100
$65.005k 5.98%$1,175 $1,000 $1,087.50
2
+
= = =
+
k i = 5.98% (1 0.40) = 3.59%
(e) common equity$4,200,000 ($1.26 1,000,000) $2,940,000
BP $5,880, 0000.50 0.50
= = =
(f) WACC = (0.40)(3.59%) + (0.10)(9.09%) + (0.50)(9.35%)
WACC = 1.436 + 0.909 + 4.675
WACC = 7.02%
This WACC applies to projects with a cumulative cost between 0 and $5,880,000.
(g) WACC = (0.40)(3.59%) + (0.10)(9.09%) + (0.50)(10.06%)
WACC = 1.436 + 0.909 + 5.03
WACC = 7.375%
This WACC applies to projects with a cumulative cost over $5,880,000.
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1a
Liabilities Capital Capital
And Equity Structure Structure
Assets Source of Capital Book Value Weight Weight
Current Assets - C 10,000,000.00 Long Term Debt 6,000,000.00 6/10 0.60
Fixed Assets Preferred Stock 1,000,000.00 1/10 0.10
Common Stock 3,000,000.00 3/10 0.30TOTAL ASSETS 10,000,000.00 TOTAL 10,000,000.00 1.00
1b
WACC dictates that all investments should have an internal rate of return above 8.5%.
1c
Debt is less costly because it is less risky from an investor's standpoint thus a lower
return iis demanded by investors. Moreover, interest expense is deductible for tax
purposes creaing cash savings from tax payment reduction.
2a
Capital Capital After
Structure Structure Tax WeightSource of Capital Book Value Weight Weight Costs Costs
LTD 3,000,000.00 6/10 0.30 5.00% 1.50%
PS 1,000,000.00 1/10 0.10 10.00% 1.00%
CS 6,000,000.00 3/10 0.60 15.00% 9.00%
TOTAL 10,000,000.00 1.00 11.50%
2b
There was an increase in WACC in No. 2
The higher the risks the higher the return. Risk and return trade-off.
3a
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 3,000,000.00 6/10 0.30 5.00% 1.50%
PS 1,000,000.00 1/10 0.10 10.00% 1.00%
CS 6,000,000.00 3/10 0.60 15.00% 9.00%
TOTAL 10,000,000.00 1.00 11.50%
3b
Capital Capital After
Structure Structure Tax Weight
Source of Capital Market Value Weight Weight Costs Costs
LTD 2,500,000.00 0.19 0.19 5.00% 0.96%
PS 1,500,000.00 0.12 0.12 10.00% 1.15%CS 9,000,000.00 0.69 0.69 15.00% 10.38%
TOTAL 13,000,000.00 1.00 12.50%
3c
Market values are more reliable as they reflect the true value of the net assets.
3d
Investments with IRR of 12% will be wrongfully accepted by using book values.
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4a
Selling price 1,010.00
Less
Floatation cost 30.00
Net proceeds, Nd 980.00
4b
t0 t1 t2 …
980.00 (120.00) (120.00) …
4c
Appproximation cost of debt formula:
kd = I + P1,000-Nd/n ki = kd x (1-tax rate)
Nd + P1,000
'2
kd = before tax cost of debt
I = stated interest
Nd = Net proceeds
n = term of the bond
P1,000 = assuimed face value of the bonds
2 = constant
ki - after tax cost of debt
kd= P120 + P1,000 - P980/15 years ,= P120 +
P980 + P1,000 990
'2
ki= 12.26% x 1-.40 = 0.073533333
7.35%
4d
Cost to Maturity:
Step 1: Try 12%
V = 120 (6.811) 1,000 (0.183)
V = 817.32 183V = $1,000.32
(Due to rounding of the PVIF, the value of the bond is 32 cents greater than expected.
At the coupon rate, the value of a $1,000 face value bond is $1,000.)
Try 13%:
V = 120 (6.462) 1,000 (0.160)
V = 775.44 160
V = $935.44
n
ot n
t 1
I MB
(1 k) (1 k)=
= + + +
15
t 15t 1
$120 $1, 000$980
(1 k) (1 k)=
= + + +
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The cost to maturity is between 12% and 13%.
Step 2: $1,000.32
$935.44=
$64.88
Step 3: $1,000.32
$980.00=
$20.32
Step 4: $20.32
$64.88=
0.31
Step 5: 12 0.31=
12.31%=
before-tax cost of debt
12.31 (1 0.40) = 7.39% = after-tax cost of debt
4e
12.26% and 12.31% after tax is 7.35% and 7.39% for approximation and IRR respectively, differ
negligible.
4f
The value of bonds and interest rate have an inverse relationship.
4gkd= P120 + P1,000 - P1,000/15 years ,= P120 +
P1,000 + P1,000 1000
'2
ki= 12.00% x 1-.40 = 0.072
7.20%
4h
kd= P120 + P1,000 - P1020/15 years ,= P120 +
P1020 + P1,000 1010
'2
ki= 11.75% x 1-.40 = 0.0704950697.05%
4i
Discounts increases cost of borrowings while premiums decreases cost of borrowing.
5
6a&b
k p = D p N p
PreferredStock
Calculation
A $11.00 $92.00 11.96%
B 3.20 34.50 9.28%
C 5.00 33.00 15.15%
D 3.00 24.50 12.24%
E 1.80 17.50 10.29%
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6c
Because of floatation costs and underpricing
6d
Retained earnings rightfully belongs to common stockholders.
6e
Signalling theory - investors takes issuance of equity as a sign of companies poor prospects.
7a,b&c
7d
7e
Retained Earnings versus New Common Stock
1r
0
Dk g
P= +
1n
n
Dk g
N= +
Firm Calculation
A k r = ($2.25 $50.00) + 8% = 12.50%
k n = ($2.25 $47.00) + 8% = 12.79%
B k r = ($1.00 $20.00) + 4% = 9.00%
k n = ($1.00 $18.00) + 4% = 9.56%
C k r = ($2.00 $42.50) + 6% = 10.71%
k n = ($2.00 $39.50) + 6% = 11.06%
D k r = ($2.10 $19.00) + 2% = 13.05%
k n = ($2.10 $16.00) + 2% = 15.13%
k s = R F + [b (k m R F)]
k s = 6% + 1.2 (11% 6%)
k s = 6% + 6%k s = 12%
(c) Risk premium = 6%
(b) Rate of return = 12%
(a) After-tax cost of common equity using the CAPM = 12%
k s = R F + [b (k m R F)]
k s = 6% + 1 (11% 6%)
k s = 6% + 5%
k s = 11%
k s = R F + [b (k m R F)]
k s = 6% + .90 (11% 6%)
k s = 6% + 4.5%
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7f
Risk free rate is the rate from t-bills or govt. bonds, market return is the return paid by the mark
is higher than the risk free rate and beta is a measure of volatility of the stock price which is m
risk.
8
9
s = .
(a)2006
k%,4
2002
Dg FVIF
D= =
$3.10g 1.462
$2.12= =
From FVIF table, the factor closest to 1.462 occurs at 10% (i.e., 1.464 for 4 years).Calculator solution: 9.97%
(b) Nn = $52 (given in the problem)
(c) 2007r
0
Dk g
P= +
r $3.40
k 0.10 15.91%$57.50
= + =
(d) K n 2007r
n
Dk g
N= +
K n=$3.40/$52+.10 = 16.54%
(a) Cost of Retained Earnings
r $1.26(1 0.06) $1.34
k 0.06 3.35% 6% 9.35%$40.00 $40.00
+= + = = + =
(b) Cost of New Common Stock
s$1.26(1 0.06) $1.34k 0.06 4.06% 6% 10.06%$40.00 $7.00 $33.00
+= + = = + =
(c) Cost of Preferred Stock
p$2.00 $2.00
k 9.09%$25.00 $3.00 $22.00
= = =
$1,000 $1,175$100
+
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10a
It’s a wrong decision because an investment with an IRR of 8% was accepted while an investment with
10b
Capital Capital After
Structure Structure Tax Weight
Source of Capital Book Value Weight Weight Costs Costs
LTD 60,000.00 6/10 0.60 7.00% 4.20%
PS - 0 0.00 0.00% 0.00%
CS 40,000.00 4/10 0.40 16.00% 6.40%
TOTAL 100,000.00 1.00 10.60%
Reject project Apple and acccept project Mona.
(d) d.
k 5.98%$1,175 $1,000 $1,087.50
2
= = =
+
k i = 5.98% (1 0.40) = 3.59%
(e) common equity$4,200,000 ($1.26 1,000,000) $2,940,000
BP $5,880, 000
0.50 0.50
= = =
(f) WACC = (0.40)(3.59%) + (0.10)(9.09%) + (0.50)(9.35%)
WACC = 1.436 + 0.909 + 4.675
WACC = 7.02%
This WACC applies to projects with a cumulative cost between 0 and $5,880,000.
(g) WACC = (0.40)(3.59%) + (0.10)(9.09%) + (0.50)(10.06%)
WACC = 1.436 + 0.909 + 5.03
WACC = 7.375%
This WACC applies to projects with a cumulative cost over $5,880,000.
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After
Tax Weight
Costs Costs
5.00% 3.00%
10.00% 1.00%
15.00% 4.50%8.50% WACC
WACC
WACC
WACC
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t15
(120.00)
(1,000.00)
1.333333333 0.122556
12.26%
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nce is
0 0.12
12.00%
-1.33333333 0.117492
11.75%
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