# Cost of Capital

**Topics:**Trigraph, Weighted average cost of capital, Stock

**Pages:**14 (2737 words)

**Published:**August 12, 2013

E9-1. Answer: Weighted average cost of capital N 10, PV $20,000 (1 0.02) $19,600, PMT Solve for I 8.30% 0.08 $20,000 $1,600, FV $20,000

E9-2. Cost of preferred stock Answer: The cost of preferred stock is the ratio of the preferred stock dividend to the firm’s net proceeds from the sale of the preferred stock. rp Dp Np rp (0.15 $35) ($35 $3) rp $5.25 $32 16.4% E9-3. Cost of common stock equity Answer: The cost of common stock equity can be found by dividing the dividend expected at the end of year 1 by the current price of the stock and adding the expected growth rate. rs (D1 P0) g rs ($6.50 $78) 7% 15.33% E9-4. Weighted average cost of capital (0.35 0.08) (0.65 0.13) 0.0280 (0.35 0.0845 0.106) 11.25% 0.0832 8.32% Answer: ra

E9-5. Weighted average cost of capital Answer: ra (0.55 0.067) (0.10 0.092)

Solutions to Problems

P9-1. Concept of cost of capital LG 1; Basic a. The firm is basing its decision on the cost to finance a particular project rather than the firm’s combined cost of capital. This decision-making method may lead to erroneous accept/reject decisions. ra wd rd we re ra 0.40 (7%) 0.60(16%) ra 2.8% 9.6% ra 12.4% Reject project 263. Accept project 264. Opposite conclusions were drawn using the two decision criteria. The overall cost of capital as a criterion provides better decisions because it takes into consideration the long-run interrelationship of financing decisions.

b.

c. d.

P9-2.

Cost of debt using both methods LG 3; Intermediate a. Net proceeds: Nd $1,010 Nd $980 $30

b.

Cash flows:

T 0 1–15 15

CF $ 980 120 1,000

c.

Cost to maturity: N 15, P 980, PMT 120, FV 1,000 Solve for I: 12.30% After-tax cost: 12.30% (1 0.4) 7.38% d. Approximate before-tax cost of debt

$120 rd

($1,000 $980) 15 ($980 $1,000) 2

rd $121.33 $990,000 rd 12.26% Approximate after-tax cost of debt e.

12.26%

(1

0.4)

7.36%

The advantages of the calculator method are evident. There are fewer keypunching strokes and one gets the actual cost of debt financing. However, the approximation formula is fairly accurate and expedient in the absence of a financial calculator.

P9-3.

Before-tax cost of debt and after-tax cost of debt LG 3; Easy a. N 10, PV 930 (an expenditure), PMT 0.6(1,000) 60, FV 1,000 Solving for I 7.00% b. Use the model: After-tax cost of debt before-tax cost of debt (1 tax bracket) 7.0% (1 0.2) 5.6%

P9-4.

Cost of debt using the approximation formula: LG 3; Basic

I rd

$1,000 N d n N d $1,000 2

ri

rd

(1

T)

Bond A

$90 rd

$1,000 $955 20 $955 $1,000 2

(1 0.40)

$92.25 $977.50

5.66%

9.44%

ri 9.44% Bond B

$100 rd

$1,000 $970 16 $970 $1,000 2

(1 0.40)

$101.88 10.34% $985

6.20%

ri 10.34% Bond C

$120 rd

$1,000 $955 15 $955 $1,000 2

(1 0.40)

$123 12.58% $977.50

7.55%

ri 12.58% Bond D

$90 rd

$1,000 $985 25 $985 $1,000 2

(1 0.40)

$90.60 $992.50

5.48%

9.13%

ri 9.13% Bond E

$110 rd

$1,000 $920 22 $920 $1,000 2

(1 0.40)

$113.64 11.84% $960

7.10%

ri P9-5.

11.84%

Cost of debt using the approximation formula LG 3; Intermediate

I rd

$1,000 N d n N d $1,000 2

ri

rd

(1

T)

Alternative A

$90 rd

$1,000 $1,220 16 $1,220 $1,000 2

$76.25 $1,110

6.87%

ri 6.87% (1 0.40) 4.12% Calculator: N 16, PV $1,220, PMT Solve for I: 6.71% After-tax cost of debt: 4.03% Alternative B

$90, FV

$1,000

$70 rd

$1,000 $1,020 5 $1,020 $1,000 2

$66.00 $1,010

6.54%

ri 6.54% (1 0.40) 3.92% Calculator: N 5, PV $1,020, PMT Solve for I: 6.52% After-tax cost of debt: 3.91% Alternative C

$70, FV

$1,000

$60 rd

$1,000 $970 7 $970 $1,000 2

$64.29 $985

6.53%

ri 6.53% (1 0.40) 3.92% Calculator: N 7, PV $970, PMT Solve for I: 6.55% After-tax cost of debt: 3.93% Alternative D

$60, FV

$1,000

$50 rd

$1,000 $895 10 $895 $1,000 2

$60.50 $947.50

6.39%

ri 6.39% (1 0.40) 3.83% Calculator: N 10, PV...

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