Question

Dinklage Corp. has 4 million shares of common stock outstanding. The current share price is $70, and the book value per share is $9. The company also has two bond issues outstanding. The first bond issue has a face value of $75 million, a coupon rate of 7 percent, and sells for 95 percent of par. The second issue has a face value of $60 million, a coupon rate of 6 percent, and sells for 107 percent of par. The first issue matures in 25 years, the second in 8 years.

Suppose the most recent dividend was $4.30 and the dividend growth rate is 4.5 percent. Assume that the overall cost of debt is the weighted average of that implied by the two outstanding debt issues. Both bonds make semiannual payments. The tax rate is 21 percent. What is the company’s WACC? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Market Value of Shares = No. of Shares * Market price per share

= 4 M * $ 70

= $ 270 M

Market Value of Bond 1:

= Face Vale * % of Price

= $ 75 M * 95%

= $ 71.25 M

Market Value of Bond 2:

= Face Vale * % of Price

= $ 60 M * 107%

= $ 64.20 M

YTM is the rate at which PV of Cash inflows are equal to PV of cash outflows.

YTM of Bond 1:

Year	Cash Flow	PVF/ PVAF @ 7 %	PV of Cash Flows	PVF/ PVAF @ 8 %	PV of Cash Flows
1-25	$                    5.25	11.6536	$                          61.18	10.6748	$                       56.04
25	$                  75.00	0.1842	$                          13.82	0.1460	$                       10.95
PV of Cash Inflows			$                          75.00		$                       66.99
PV of Cash Oiutflows			$                          71.25		$                       71.25
NPV			$                            3.75		$                        -4.26

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 7 % + [ 3.75 / 8.01 ] * 1%
= 7 % + [ 0.47 ] * 1%
= 7 % + [ 0.4684 % ]
= 7.47 %

PVAF = Sum [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r )^n
r - Int Rate per period
n - No. of Periods

How to calculate PVAF using Excel?
+PV(Rate,NPER,-1)
Rate = Disc rate
NPER - No. of Periods

After Tax cost of Bond 1:

= YTM ( 1 - Tax Rate )

= 7.47% ( 1 - 0.21 )

= 7.47% * 0.79

= 5.90%

YTM of Bond2 :

Year	Cash Flow	PVF/ PVAF @ 4 %	PV of Cash Flows	PVF/ PVAF @ 5 %	PV of Cash Flows
1-8	$                    3.60	6.7327	$                          24.24	6.4632	$                       23.27
8	$                  60.00	0.7307	$                          43.84	0.6768	$                       40.61
PV of Cash Inflows			$                          68.08		$                       63.88
PV of Cash Oiutflows			$                          64.20		$                       64.20
NPV			$                            3.88		$                        -0.32

YTM = Rate at which least +ve NPV + [ NPV at that rate / Change in NPV due to Inc of 1% in Int Rate ] * 1%
= 4 % + [ 3.88 / 4.2 ] * 1%
= 4 % + [ 0.92 ] * 1%
= 4 % + [ 0.9233 % ]
= 4.92 %

PVAF = Sum [ PVF(r%, n) ]
PVF(r%, n) = 1 / ( 1 + r )^n
r - Int Rate per period
n - No. of Periods

How to calculate PVAF using Excel?
+PV(Rate,NPER,-1)
Rate = Disc rate
NPER - No. of Periods

After Tax cost of Bond 2:

= YTM ( 1 - Tax Rate )

= 4.92% ( 1 - 0.21 )

= 4.92% * 0.79

= 3.89%

COst of Capita:

Particulars	Amount
D0	$      4.30
Growth rate	4.5%
Price	$   70.00

Ke = [ D1 / P0 ] + g
D1 = D0 ( 1 + g )
= 4.3 * ( 1 + 0.045 )
= 4.3 * ( 1.045 )
= 4.49

Ke = [ D1 / P0 ] + g
= [ 4.49 / 70 ] + 0.045
= 0.0642 + 0.045
= 0.1092
I.e 10.92 %

Where
D0 = Just Paid Div
D1 = Expected Div after 1 Year
P0 = Price Today
Ke = Required Ret
g = Growth Rate
WACC:

WACC is weighted Average cost of securities in that portfolio

Source	Qty	Price	Value	Weight	Cost after Tax	Weighted Cost
Debt1	75	$         0.95	$                           71.25	0.1715	5.90%	1.01%
Debt2	60	$         1.07	$                           64.20	0.1545	3.89%	0.60%
Equity Stock	4	$       70.00	$                         280.00	0.6740	10.92%	7.36%
WACC						8.97%