Question

Bea Kerr is an analyst in the​ treasurer's office at MupetLabs Inc. Mr. Kerr needs your help to estimate the market value weights for​ MupetLabs' cost of capital. MupetLabs has​ long-term bonds​ outstanding, preferred shares outstanding and common shares. Selected information for each of the securities is provided in the table below. ​Long-term Debt Preferred Shares Common Shares ​$20 million face value 1.5 million shares outstanding 5.3 million shares outstanding Coupon rateequals5.5​% Face valueequals​$8 per share Market price of shareequals​$23 Annual coupons Dividend rate ​(annual)equals10​% Time to maturityequals7 years Equivalent preferred shares yield 6​% YTMequals9​%

a.  What is the market value of​ long-term debt?

b.  What is the market value of preferred​ shares?

c.  What are the capital structure weights for MupetLabs​ Inc.?

Answer 1

Answer a.

Long-term Debt:

Face Value = $20,000,000

Annual Coupon Rate = 5.50%
Annual Coupon = 5.50% * $20,000,000
Annual Coupon = $1,100,000

Time to Maturity = 7 years
Annual YTM = 9.00%

Market Value = $1,100,000 * PVIFA(9.00%, 7) + $20,000,000 * PVIF(9.00%, 7)
Market Value = $1,100,000 * (1 - (1/1.09)^7) / 0.09 + $20,000,000 * (1/1.09)^7
Market Value = $1,100,000 * 5.032953 + $20,000,000 * 0.547034
Market Value = $16,476,928

Answer b.

Preferred Shares:

Number of Shares = 1,500,000
Face Value per share = $8.00
Dividend Rate = 10.00%
Equivalent Yield = 6.00%

Annual Dividend = Dividend Rate * Face Value per share
Annual Dividend = 10.00% * $8.00
Annual Dividend = $0.80

Price per share = Annual Dividend / Equivalent Yield
Price per share = $0.80 / 0.06
Price per share = $13.333333

Market Value = Number of Shares * Price per share
Market Value = 1,500,000 * $13.333333
Market Value = $20,000,000

Answer c.

Common Shares:

Number of Shares = 5,300,000
Market Price per share = $23.00

Market Value = Number of Shares * Market Price per share
Market Value = 5,300,000 * $23.00
Market Value = $121,900,000

Market Value of Firm = Market Value of Long-term Debt + Market Value of Preferred Shares + Market Value of Common Shares
Market Value of Firm = $16,476,928 + $20,000,000 + $121,900,000
Market Value of Firm = $158,376,928

Weight of Long-term Debt = Market Value of Long-term Debt / Market Value of Firm
Weight of Long-term Debt = $16,476,928 / $158,376,928
Weight of Long-term Debt = 0.1040

Weight of Preferred Shares = Market Value of Preferred Shares / Market Value of Firm
Weight of Preferred Shares = $20,000,000 / $158,376,928
Weight of Preferred Shares = 0.1263

Weight of Common Shares = Market Value of Common Shares / Market Value of Firm
Weight of Common Shares = $121,900,000 / $158,376,928
Weight of Common Shares = 0.7697