Answer and Explanation:
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Ordinary shares: $5,500,000 book value of outstanding ordinary shares. Nominal value of each share is $100. The firm plan just paid a $8.50 dividend per share. The firm is maintaining 4% annual growth rate in dividends, which is expected to continue indefinitely.
Preferred shares: 45,000 outstanding preferred shares with face value of $100, paying fixed dividend rate of 12%
The firm's marginal tax rate is 30%.
Required:
a) Calculate the current price of the corporate bond?
b)Calculate the current price of the ordinary share if the average return of the shares in the same industry is 9%?
c) Calculate the current price of the preferred share if the average return of the shares in the same industry is 10%
The computation is shown below:
a. For the current price of the corporate bond
Before that first we have to determine the after tax yield to maturity i.e
After tax YTM = Before tax YTM × (1 - tax rate)
= 12% × ( 1 - 30%)
= 12% × (1 - 0.3)
= 12% × (0.7)
= 8.4%
Now
Price of bond = Interest × PVIFA(YTM%,n) + Redemption value × PVIF(YTM%,n)
Interest = 1000 × 10% = $100
YTM% = 8.4%
n = 20
PVIFA(YTM%,n) = [1 - (1 ÷ (1 + r)^n ÷ r ]
PVIFA(8.4%,20) = [1 - (1 ÷ (1 + 8.4%)^20 ÷ 8.4%]
= [1 - (1 ÷ (1 + 0.084)^20 ÷ 0.084]
= [1-(1 ÷ (1.084)^20 ÷ 0.084]
= [1 - 0.1993 ÷ 0.084]
= 0.8007 ÷ 0.084
= 9.5327
PVIF(8.4%,20) = 1 ÷ (1 + 8.4%)^20
= 1 ÷ (1.084)^20
= 0.19926
So, the price of bond is
= $100 × 9.5327 + $1000 × 0.19926
= $953.27 + $199.26
= $1,152.52
b)Price of stock = Dividend of next year ÷ (Required rate of return - growth rate )
where,
Growth rate = 4%
Required rate of return = 9%
The Dividend of next year = Dividend paid × (1 + growth rate)
= 8.50 × (1 + 4%)
= 8.50 × (1 + 0.04)
= 8.50 × (1.04)
= $8.84
Thus the price of the stock is
= $8.84 ÷ (9% - 4%)
= $8.84 ÷ 5%
= $176.80
c) Price of preference shares is
= Dividend ÷ Required rate of return
where,
Dividend = 100 × 12% = $12
And, the Required rate of return = 10%
So, the price of preference shares is
= 12 ÷ 10%
= $120