This will be a timed exam with 5 detailed questions and the expert will have 3 hours total to complete it.
Caiden
fin508solutionweek5.pdf
FIN 508 Assignment Week 5 _____________________________________________________________________________
1
5.1. Ontario Corporation may raise new capital in one of the following three ways. It has
tax rate of 35%. Find the after-tax cost of new capital.
(A) It can sell common stock at $27 a share, which will pay a dividend of $2.25 next year.
The expected rate of growth of dividends is 5% per annum forever.
Use Gordon's growth model, P0 = D1
R − g (3.6)
27 = 2.25
R − .05 , R = ke = 2.25/27 + .05 = .1333 = 13.33% ♥
(B) It can sell 8.5% bonds at $850 each, which will mature in 10 years. Assume that the
bonds pay interest twice a year and the company pays taxes once a year.
Find the cost of debt by calculating the yield to maturity of the bonds.
YTM 850 + (1000 – 850)/10
925 = .1081
After-tax cost of debt = (1 − .35)(.1081) = 7.027% ♥
Include the original issue discount and set up the equation as
NPV = 850 − i=1
20
42.5
(1 + r/2) i +
i=1
10
(85 + 15)(.35)
(1 + r) i −
1000
(1 + r) 10 = 0
PV of
sale
PV of interest
payments
PV of tax
benefits
PV of final
payment
To do it at WolframAlpha, send the following instruction.
850-sum(42.5/(1+r/2)^i,i=1..20)+sum(100*.35/(1+r)^i,i=1..10)-1000/(1+r)^10=0
The result is , or about 7.264% ♥
(C) By selling $7 preferred stock at $60 a share, redeemable at par after 5 years.
A preferred stock is similar to the ordinary stock, except that its dividend remains
constant. That is, its growth potential g is zero. Use Gordon’s growth model again to see
kp = 7/60 = .1167 = 11.67% ♥
There is no tax benefit in issuing the preferred stock.
FIN 508 Assignment Week 5 _____________________________________________________________________________
2
5.2. Quebec Company wants to issue discount bonds with a market value equal to 70% of
their face value. The bonds will carry 4% coupon, paying interest semiannually, and they
will mature after 15 years. The income tax rate of Quebec is 25%.
(A) Calculate the approximate yield-to-maturity of the bonds, and then the after-tax cost
of debt for Quebec.
YTM 40 + (1000 – 700)/15
850 = .07059 = 7.059% ♥
After-tax cost of debt (1 − .25)(.07059) = .05294 = 5.294% ♥
(B) Using the concept of original issue discount, write an equation that would give the
after-tax cost of debt for Quebec. Solve this equation by using WolframAlpha, Maple, or
Excel to find the after-tax cost of debt for Quebec.
The company issues the bonds for 70% of face value, or $700 each but redeems for
$1000 each. The difference, $300, is the original issue discount. This is the cost to the
company and it can spread it over 15 years, which gives it an additional tax deduction of
300/15 = $20 per year. The company pays $40 annually in interest, or $20 semiannually.
From the company’s perspective, the present value of all after-tax cash flows from the
bond, positive and negative, should be equal to zero. Thus
NPV = 700 − i=1
30
20
(1 + r/2) i +
i=1
15
(40 + 300/15)(.25)
(1 + r) i −
1000
(1 + r) 10 = 0
The unknown r will be the after-tax cost of debt for the company. To solve it at
WolframAlpha, send the following instruction.
700-sum(20/(1+r/2)^i,i=1..30)+sum((40+300/15)*.25/(1+r)^i,i=1..15)-1000/(1+r)^15=0
If you click on more roots several times, it eventually gives the answer. The result is
, or 5.529% ♥
You can use the following Excel table to find the after-tax cost of debt. Adjust the
number in cell B1 until the value in B9 becomes very small.
A B
1 After-tax cost of debt = .055294
2 Sale price of the bond = $ 700
3 Time to maturity = years 15
4 Coupon rate = % 4%
5 Income tax rate = % 25%
6 PV of interest payments = =-B4*1000*(1-1/(1+B1/2)^(2*B3))/B1
7 PV of tax benefits = =(B4*1000+(1000-B2)/B3)*B5*(1-1/(1+B1)^B3)/B1
8 PV of final payment = =-1000/(1+B1)^B3
9 NPV of bond = 0 =B2+B6+B7+B8
FIN 508 Assignment Week 5 _____________________________________________________________________________
3
5.3. Nova Scotia Company has the following capital structure: 4.5 million shares of stock, selling at $25 each, with β = 1.1; zero-coupon bonds with face amount $60 million,
maturing in 10 years, with yield to maturity 7.5%; and 500,000 shares of preferred stock
selling at $12 per share, paying a dividend of 30¢ per quarter. The income tax rate of
Nova Scotia is 33%. The risk-free rate is 4%, and the expected return on the market 13%.
Do not use the original issue discount. Find the weighted average cost of capital for Nova
Scotia.
Total market value of stock, S = 4.5*25 = $112.5 million
Suppose the current value of the bonds is $B million. Growing in value at the rate of
7.5% per year, they will reach their face value, $60 million, in ten years. Thus
60 = B(1.075) 10
Solve for B, B = 60/1.075 10
= $29.11163570 million. This is the present value of debt.
The value of preferred stock, P is .5*12 = $6 million
The total value of the company, V = 112.5 + 29.11163570 + 6 = $147.612 million
Cost of debt = YTM = .075
Cost of equity = ke = r + β[E(Rm) – r] = .04 + 1.1(.13 − .04) = .139
Cost of preferred stock, kp = D1/P0 = 1.20/12 = .1
Use the equation
WACC = (1 − t) kd B
V + ke
S
V + kp
P
V
to get
WACC = (1 − .33)(.075)
29.112
147.612 + (.139)
112.5
147.612 + (.1)
12
147.612 = .1199 = 11.99%♥
FIN 508 Assignment Week 5 _____________________________________________________________________________
4
5.4. New Brunswick Corporation has 35% debt and 65% equity (market values) in its capital structure. The pretax cost of debt is 9%, and that of equity 14%. The total value of
the company is $225 million and its income tax rate is 30%. New Brunswick has to raise
$25 million in new capital, which will make the expected EBIT of the company to be $20
million, with a standard deviation of $10 million. The company has decided to raise the
new capital half with debt and half with equity at the existing rates. Calculate New
Brunswick's new WACC, and the probability that its interest coverage ratio will be less
than one.
Before new financing,
35% debt means B/V = .35, and thus S/V = .65
Cost of debt, kd = .09
Cost of equity ke = .14
Total value of the company, V = $225 million
Income tax rate, t = .3
Market value of debt, B = .35(225) = $78.75 million, and equity, S = .65(225) = $146.25
million
The company will raise $25 million in new capital, with $12.5 million each from debt
and equity. After new financing,
B = 78.75 + 12.5 = $91.25 million
S = 146.25 + 12.5 = $158.75 million
V = 225 + 25 = $250 million
Use the equation
WACC = (1 − t) kd B
V + ke
S
V
to get
WACC = (1 − .3)(.09)(91.25)/250 + .14(158.75)/250 = .111895 = 11.19% ♥
Total interest due = .09(91.25) = $8.2125 million. By definition,
Interest coverage ratio = Earnings before interest and taxes (EBIT)
Interest due
The interest coverage ratio is less than 1 if EBIT is less than $8.2125 million. The
expected EBIT of the company is $20 million, so it can easily pay $8.2125 million in
interest. The probability of default is quite small. To get a numerical answer, first find
z = (8.2125 − 20)/10 = − 1.17875.
Draw a normal probability curve, with z = 0 at the center. The point z = − 1.17875 will
appear well to the left of the center. The required probability is the small area under the
tail of the curve.
FIN 508 Assignment Week 5 _____________________________________________________________________________
5
To find the yellow area, check the tables,
P(ICR < 1) = .5 − (.3790 + .875*(.3810 − .3790)) = .11925 = 11.925% ♥
You can verify the result by using the following instruction at Excel.
EXCEL =NORMDIST(8.2125,20,10,TRUE)
5.5. Manitoba Corporation stockholders expect a growth rate of 5% in the company, and a dividend of $2.00 next year. The WACC of Manitoba is 11.5%. There are 4 million
shares of the common stock, selling at $20 per share. The company also has $70 million
face value zero-coupon bonds, which will be due after 8 years. The bondholders have a
required rate of return of 7%. Find the tax rate of Manitoba.
This problem is slightly different because the income-tax rate is unknown. We can
arrange the information in the following way:
Number of shares of common stock, given, N = 4 million
Price per share of common stock, given, P0 = $20
Total value of equity, S = NP0 = 4(20) = $80 million
Dividend per share of common stock next year, D1 = $2
Growth rate of dividends, given, g = .05
Using Gordon’s growth model, cost of equity, ke = D1/P0 + g = 2/20 + .05 = .15
Face value of the bonds, given, F = $70 million
Number of years to maturity, given, T = 8 years
Required rate return by bondholders = Discount rate of the bonds = .07
Present value of bonds, B = F/(1 + r) T = 70/1.07
8 = 40.74063732 $40.74 million
Required rate return by bondholders, given = Cost of debt, kd = .07
Total value of company, V = S + B = 80 + 40.74 = 120.74 $120.74 million
Since WACC is given as 11.5%, we can write equation (9.5) as
FIN 508 Assignment Week 5 _____________________________________________________________________________
6
.115 = (1 − t)(.07)
40.74
120.74 + (.15)
80
120.74
To solve the equation, go the WolframAlpha and insert the following
.115=(1-t)*.07*40.74/120.74+.15*80/120.74
The result is , or 33.90% ♥
5.6. British Columbia Co has the following capital structure. It has 12 million shares of common stock selling for $20 each. The stock will pay a dividend of $2 next year and
this dividend is expected to grow at the rate of 5% annually. British Columbia has just
raised $120 million by selling 10% coupon bonds at par. British Columbia also has 10
million shares of preferred stock, which pays a dividend of $1.50 annually, and the
preferred shareholders have a required rate of return of 12%. British Columbia has 33%
income tax rate. Find the WACC of British Columbia.
Number of shares of common stock, given, N = 12 million
Price per share of common stock, given, P0 = $20
Total value of common stock, S = NP0 = 12(20) = $240 million
Dividend per share next year, given, D1 = $2
Dividend growth rate, given, g = .05
Cost of equity from Gordon’s growth model, ke = D1/P0 + g = 2/20 + .05 = .15
Total value of bonds, given, B = $120 million
Cost of debt, given, kd = .1
Dividend of preferred stock, per share, given, Dp = $1.50
Cost of capital for preferred stock, given, kp = .12
Price per share of preferred stock, from Gordon’s growth model, zero growth,
Pp = Dp/kp = 1.5/.12 = $12.50
Number of shares of preferred stock, given, Np = 10 million
Total value of preferred stock, P = NpPp = 10,000,000*12.5 = $125 million
Total value of company, V = 240 + 120 +125 = $485 million
Putting all these numbers (9.2), we find
WACC = (1 − .33)(.1)
120
485 + (.15)
240
485 + (.12)
125
485 = 12.17% ♥
FIN 508 Assignment Week 5 _____________________________________________________________________________
7
5.7. Prince Edward Island Corporation has the following capital structure: $60 million (face value) of 8% bonds, which are selling at 95 and maturing after 10 years; 10 million
shares of common stock selling at $10 each; and one million shares of preferred stock
selling at $10 each and paying an annual dividend of $1.25. The β of the stock is 1.63
whereas the expected return on the market is 12%. The risk-free rate is 4% and the
company's tax rate is 32%. Find the WACC of Prince Edward Island.
Number of shares of common stock, given, N = 10 million
Price per share of common stock, given, P0 = $10
Market value of stock, NP0 = 10*10 = $100 million
Given β = 1.63, r = .04, and E(Rm) = .12, we find the cost of equity as
ke = .04 + 1.63(.12 − .04) = .1704
Face value of the bonds, given, F = $60 million
Bonds sell at 95, meaning 95% of their face value, given
Market value of debt = .95F = .95(60) = $57 million
Cost of debt = YTM = 80 + (1000 – 950)/10
975 = .08718
Number of shares of preferred stock, given = 1 million
Price per share of preferred stock, given, Pp = $10
Market value of preferred stock = 1*10 = $10 million
Dividend per share of preferred stock, given, Dp = $1.25
Cost of preferred stock (Gordon’s growth model, no growth) = Dp/Pp = 1.25/10 = .125
Total value of the company = 100 + 57 + 10 = $167 million
Income tax rate = .32
Thus
WACC = (1 – .32)(.08718)(57/167) + .1704(100/167) + .125(10/167) = .1298 ♥
FIN 508 Assignment Week 5 _____________________________________________________________________________
8
5.8. Saskatchewan Corporation has debt/assets ratio of .3, its cost of debt is 8% and that of equity 13%. The tax rate of Saskatchewan is 30%. The company is not growing and it
has a dividend payout ratio of 100%. Its dividend per share is $2. Saskatchewan has 2
million shares of common stock. Find the total value of Saskatchewan, and its WACC.
First, find price per share by using Gordon’s growth model.
Cost of equity (given), ke = R = .13
Growth rate of the company and its dividends (given), g = 0
The dividend per share next year (given), D1 = $2
Thus, current price by Gordon’s growth model,
P0 = D1/(R − g) = 2/(.13 − 0) = $15.38 per share
Number of shares of stock (given), N = 2 million
Total value of stock, S = NP0 = 2*15.38 = $30.77 million,
Debt-to-Assets ratio (given), B/V = .3
Which gives, (V − S)/V = .3, or (V − 30.77)/V = .3
Or, V − 30.77 = .3 V, or (1 − .3)V = 30.77, or V = 30.77/.7
Or, V = $43.96 million ♥
The value of debt, B = V − S = 43.96 − 30.77 = $13.19 million
Cost of debt (given), kd = .08
WACC = (1 − .3)(.08)
13.19
43.96 + .13
30.77
43.96 = .1078 = 10.78% ♥
