a.A relatively quick method for finding the before-tax cost of debt is to observe the yield to maturity (YTM) on thefirm's existing bonds or bonds of similar risk issued by other companies. This approach finds the before-tax cost of debt by calculating the YTM generated by the bond cash flows. From the issuer's point of view, this value is the cost to maturity of the cash flows associated with the debt. The cost to maturity can be calculated by using a financial calculator or an electronic spreadsheet. It represents the annual before-tax percentage cost of the debt.

Alternatively,

the

before-tax cost of debt,

r Subscript drd,

for a bond with a $1,000 par value can be approximated by using the following equation:

r Subscript d equals StartStartFraction Upper I plus StartFraction $ 1 comma 000 minus Upper N Subscript d Over n EndFraction OverOver StartFraction Upper N Subscript d plus $ 1 comma 000 Over 2 EndFraction EndEndFractionrd=I+$1,000NdnNd+$1,0002,

where

Iequals=annual

interest in dollars

Upper N Subscript dNdequals=net

proceeds from the sale of debt (bond)

nequals=number

of years to the bond's maturity

The after-tax cost of debt,

r Subscript iri,

can be found by multiplying the before-tax cost of debt,

r Subscript drd,

by 1 minus the tax rate,

T,

as stated in the following equation:

r Subscript i equals r Subscript d Baseline times left parenthesis 1 minus Upper T right parenthesisri=rd(1T).

Calculator Use

When solving for the YTM using a financial calculator, you will need to input the number of years to maturity for N, the bond's par value for FV, the periodic coupon payment for PMT, and the net proceeds from sale of the bond forPV, and then compute I/Y to find the YTM. Remember to set P/Y and C/Y to the number of payments per year for different compounding methods and enter a negative number for PV.

Input Function

2525 N

minus895895 PV

150150 PMT

1 comma 0001,000 FV

CPT

I

Solution

16.8016.80

Spreadsheet Use

When solving for the yield to maturity of a bond using an Excel spreadsheet, you will need to enter the values ofNper, Pv, Fv, Pmt, and Type into the Excel's RATE function.

A B

1 FINDING THE YTM ON A

2525-YEAR

BOND

2 Net proceeds from sale of bond $895895

3 Coupon payment $150150

4 Years to maturity 2525

5 Par value (principal)

$1 comma 0001,000

6 Before-tax cost of debt

16.8016.80%

Entry in Cell B6

isequals=RATE(B4,minusB3,B2,minusB5,0)

A minus sign appears before B3 and B5 because coupon payment

and par value are treated as cash outflows.

Since we will be calculating two different before-tax costs of debt (using the YTM and formula methods), we must select only one to calculate the after-tax cost of debt. We will use the more accurate YTM derived by the calculator.

The company is taxed at a rate of

3838%.

The after-tax cost of debt,

r Subscript iri,

can be found by multiplying the before-tax cost of debt,

r Subscript drd,

by 1 minus the tax rate,

T,

as stated in the following equation:

r Subscript i Baseline equals r Subscript d times left parenthesis 1 minus Upper T right parenthesis equals 16.80 % times left parenthesis 1 minus 0.38 right parenthesis equals 0.1042 equals 10.42 %ri=rd(1T)=16.80%(10.38)=0.1042=10.42%.

The company's after-tax cost of debt is

10.4210.42%.

Formula Use

The firm can sell for

$940940

a

2525-year,

$1 comma 0001,000-par-value

bond paying annual interest at a

15.0015.00%

coupon rate.

The

annual interest payment is equal to the annual coupon rate times the bond's par value:

0.150.15times$1 comma 0001,000equals=$150150.

To sell the new issue, A flotation cost of

4.54.5%

of the par value is required in addition to the discount of

$6060

per bond.The flotation cost is

4.54.5%

of the par value, or

$1 comma 0001,000times0.0450.045equals=$4545.

Thus, the net proceeds from sale of the bond equal the bond's par value minus the dollar amount of discount and the flotation costs:

$1 comma 0001,000minus$6060minus$4545equals=$895895.

Thebefore-tax cost of debt can be computed as follows:

r Subscript d equals StartStartFraction Upper I plus StartFraction $ 1 comma 000 minus Upper N Subscript d Over n EndFraction OverOver StartFraction Upper N Subscript d plus $ 1 comma 000 Over 2 EndFraction EndEndFraction equals StartStartFraction $ 150 plus StartFraction $ 1 comma 000 minus $ 895 Over 25 EndFraction OverOver StartFraction $ 895 plus $ 1 comma 000 Over 2 EndFraction EndEndFraction equals 0.16274 equals 16.27 %rd=I+$1,000NdnNd+$1,0002=$150+$1,000$89525$895+$1,0002=0.16274=16.27%.

Using the approximation formula, the after-tax cost of debt is found to be:

r Subscript i Baseline equals r Subscript d times left parenthesis 1 minus Upper T right parenthesis equals 16.27 % times left parenthesis 1 minus 0.38 right parenthesis equals 0.1009 equals 10.09 %ri=rd(1T)=16.27%(10.38)=0.1009=10.09%.

b. The cost of preferred stock,

r Subscript prp,

is the ratio of the preferred stock dividend,

Upper D Subscript pDp,

to the firm's net proceeds,

Upper N Subscript pNp,

from the sale of the preferred stock:

r Subscript p Baseline equals StartFraction Upper D Subscript Upper P Over Upper N Subscript Upper P EndFractionrp=DPNP.

The net proceeds represent the amount of money to be received minus any flotation costs.

The

6.006.00%

(annual dividend) preferred stock having a par value of

$100100

can be sold for

$9090.

An additional fee of

$44

per share must be paid to the underwriters. Therefore, the preferred dividend is equal to

$100100times0.0600.060equals=$6.006.00

and

the

net proceeds is equal to

$9090minus$44equals=$8686.

The cost of preferred stock can be computed as follows:

r Subscript p equals StartFraction Upper D Subscript Upper P Over Upper N Subscript Upper P EndFraction equals StartFraction $ 6.00 Over $ 86 EndFraction equals 0.0698 equals 6.98 %rp=DPNP=$6.00$86=0.0698=6.98%.

The company's cost of preferred stock financing is

6.986.98%.

c. The cost of retained earnings to the firm is the same as the cost of an equivalent fully subscribed issue of additional common stock. The cost of common stock equity,

r Subscript srs,

can be expressed as follows:

r Subscript s Baseline equals StartFraction Upper D 1 Over Upper P 0 EndFraction plus grs=D1P0+g,

where

Upper D 1D1equals=per-share

dividend expected at the end of year 1

Upper P 0P0equals=value

of common stock

ggequals=constant

rate of growth in dividends

Given the dividends paid in the past five years, the annual dividend growth rate,

g,

can be found using the followingequation:

g equals left parenthesis StartFraction Upper D 2012 Over Upper D 2008 EndFraction right parenthesis Superscript one fourth Baseline minus 1 equals left parenthesis StartFraction $ 5.12 Over $ 3.50 EndFraction right parenthesis Superscript 0.25 Baseline minus 1 equals 0.100 equals 10.0 %g=D2012D2008141=$5.12$3.500.251=0.100=10.0%.

The firm's common stock is currently selling for

$8282

per share. The firm expects to pay cash dividends of

$5.645.64

per share next year. The firm's dividends have been growing at an annual rate of

10.010.0%,

and this growth is expected to continue into the future. The cost of retained earnings to the firm can be computed as follows:

r Subscript s equals StartFraction Upper D 1 Over Upper P 0 EndFraction plus g equals StartFraction $ 5.64 Over $ 82 EndFraction plus 0.100 equals 0.1688 equals 16.88 %rs=D1P0+g=$5.64$82+0.100=0.1688=16.88%.

Thus, the company's cost of retained earnings financing is

16.8816.88%.

If we let

Upper N Subscript nNn

represent the net proceeds from the sale of new common stock after subtracting underpricing and flotation costs, the cost of the new issue,

r Subscript nrn,

can be expressed as follows:

r Subscript n Baseline equals StartFraction Upper D 1 Over Upper N Subscript n EndFraction plus grn=D1Nn+g.

Since the stock must be underpriced by

$33

per share, and flotation costs are expected to amount to

$4.504.50

per share, the net proceeds from the sale of new common stock can be found by subtracting underpricing and flotation costs from the price of the stock:

$8282minus$33minus$4.504.50equals=$74.5074.50.

The cost of the new issue of common stock is specified as:

r Subscript n Baseline equals StartFraction Upper D 1 Over Upper N Subscript n EndFraction plus g equals StartFraction $ 5.64 Over $ 74.50 EndFraction plus 0.100 equals 0.1757 equals 17.57 %rn=D1Nn+g=$5.64$74.50+0.100=0.1757=17.57%.

The company's cost of new common stock financing is

17.5717.57%.

d. The weighted average cost of capital (WACC),

r Subscript ara,

can be specified as follows:

r Subscript a equals left parenthesis w Subscript i times r Subscript i right parenthesis plus left parenthesis w Subscript p Baseline times r Subscript p right parenthesis plus left parenthesis w Subscript s Baseline times r Subscript r or n right parenthesisra=wiri+wprp+wsrr or n,

where

w Subscript iwiequals=proportion

of long-term debt in capital structure

w Subscript pwpequals=proportion

of preferred stock in capital structure

w Subscript swsequals=proportion

of common stock equity in capital structure

r Subscript iriequals=after-tax

cost of debt

r Subscript prpequals=cost

of preferred stock

r Subscript rrrequals=cost

of retained earnings

r Subscript nrnequals=cost

of new common stock

The capital structure of the company includes

2525%

debt,

3030%

preferred stock, and

4545%

common stock. Using the cost of retained earnings,

r Subscript rrr,

the weighted average cost of capital (WACC),

r Subscript ara,

can be computed as follows:

r Subscript a equals left parenthesis w Subscript i times r Subscript i right parenthesis plus left parenthesis w Subscript p Baseline times r Subscript p right parenthesis plus left parenthesis w Subscript s Baseline times r Subscript r right parenthesisra=wiri+wprp+wsrr,

equals left parenthesis 0.25 times 10.42 % right parenthesis plus left parenthesis 0.30 times 6.98 % right parenthesis plus left parenthesis 0.45 times 16.88 % right parenthesis=(0.2510.42%)+(0.306.98%)+(0.4516.88%),

equals 0.1230 equals 12.30 %=0.1230=12.30%.

Using the cost of retained earnings, the company's WACC is

12.3012.30%.

Note that if the after-tax cost of debt using the approximation formula is used here, the firm's WACC would be

12.2112.21%

instead.

Using the cost of new common stock,

r Subscript nrn,

the weighted average cost of capital (WACC),

r Subscript ara,

can be computed asfollows:

r Subscript a equals left parenthesis w Subscript i times r Subscript i right parenthesis plus left parenthesis w Subscript p Baseline times r Subscript p right parenthesis plus left parenthesis w Subscript s Baseline times r Subscript n right parenthesisra=wiri+wprp+wsrn,

equals left parenthesis 0.25 times 10.42 % right parenthesis plus left parenthesis 0.30 times 6.98 % right parenthesis plus left parenthesis 0.45 times 17.57 % right parenthesis=(0.2510.42%)+(0.306.98%)+(0.4517.57%),

equals 0.1261 equals 12.61 %=0.1261=12.61%.

Using the cost of new common stock, the company's WACC is

12.6112.61%.

Note that if the after-tax cost of debt using the approximation formula is used here, the firm's WACC would be

12.5212.52%

instead.

Question is complete.

Calculation of individual costs and WACC Dillon Labs has asked its financial manager to measure the cost of each specific type of capital as well as the weighted average cost of capital. The weighted average cost is to be measured by using the following weights: 5050% long-term debt, 2525% preferred stock, and 2525% common stock equity (retained earnings, new common stock, or both). The firm's tax rate is 3030%.

Debt The firm can sell for $960 a 14-year, 1,000-par-value bond paying annual interest at a11.00% coupon rate. A flotation cost of 4% of the par value is required in addition to the discount of $40 per bond.

Preferred stock10.00% (annual dividend) preferred stock having a par value of $100100 can be sold for $80. An additional fee of $5 per share must be paid to the underwriters.

Common stock - The firm's common stock is currently selling for $60 per share. The dividend expected to be paid at the end of the coming year (2016) is $3.08. Its dividend payments, which have been approximately 70% of earnings per share in the past 5 years, were as shown in the following table:

Year Dividend

2015 $2.89

2014 $2.72

2013 $2.55

2012 $2.40

2011 $2.25

It is expected that to attract buyers, new common stock must be underpriced $77 per share, and the firm must also pay $3.00 per share in flotation costs. Dividend payments are expected to continue at 70% of earnings. (Assume that rr=rs

a.Calculate the after-tax cost of debt.

b.Calculate the cost of preferred stock.

c.Calculate the cost of common stock

d.Calculate the WACC for Dillon Labs.