Question

I am trying to determine the weight of long-term debt but don't know where to begin.

I know the answer is 22.58% but I don't know how to get there.  

This is the problem:

Problem 9-17
WACC Estimation

The following table gives the balance sheet for Travellers Inn Inc. (TII), a company that was formed by merging a number of regional motel chains.

Travellers Inn: (Millions of Dollars)
Cash		$10		Accounts payable		$10
Accounts receivable		20		Accruals		10
Inventories		20		Short-term debt		5
Current assets		$50		Current liabilities		$25
Net fixed assets		50		Long-term debt		30
				Preferred stock		5
				Common equity
				Common stock		$10
				Retained earnings		30
				Total common equity		$40
Total assets		$100		Total liabilities and equity		$100

The following facts also apply to TII:

1. Short-term debt consists of bank loans that currently cost 11%, with interest payable quarterly. These loans are used to finance receivables and inventories on a seasonal basis, so bank loans are zero in the off-season.
2. The long-term debt consists of 30-year, semiannual payment mortgage bonds with a coupon rate of 10%. Currently, these bonds provide a yield to investors of r_d = 12%. If new bonds were sold, they would have a 12% yield to maturity.
3. TII's perpetual preferred stock has a $100 par value, pays a quarterly dividend of $2.50, and has a yield to investors of 8%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 4% flotation cost to sell it.
4. The company has 4 million shares of common stock outstanding. P₀ = $20, but the stock has recently traded in price the range from $17 to $23. D₀ = $1 and EPS₀ = $2. ROE based on average equity was 24% in the most recent year, but management expects to increase this return on equity to 31%; however, security analysts and investors generally are not aware of management's optimism in this regard.
5. Betas, as reported by security analysts, range from 1.3 to 1.7; the T-bond rate is 10%; and RP_M is estimated by various brokerage houses to be in the range from 4.5% to 5.5%. Some brokerage house analysts reports forecasted dividend growth rates in the range of 10% to 15% over the foreseeable future.
6. TII's financial vice president recently polled some pension fund investment managers who hold TII's securities regarding what minimum rate of return on TII's common would make them willing to buy the common rather than TII bonds, given that the bonds yielded 12%. The responses suggested a risk premium over TII bonds of 4 to 6 percentage points.
7. TII is in the 40% federal-plus-state tax bracket.
8. TII's principal investment banker predicts a decline in interest rates, with r_d falling to 10% and the T-bond rate to 7%, although the bank acknowledges that an increase in the expected inflation rate could lead to an increase rather than a decrease in interest rates.

I know the answer is 22.58% but I don't know how to get there.  

Answer 1

We will calculate the market value of each of the three components:

Long term Debt

Market value can be calculated using the PV function in excel. Inouts are:

Rate = YTM = 12%; Nper = 30 years, FV = Par value = $ 30 million (this figure appears on the balance sheet against long term debt); PMT = anual coupon = 10% of par value = 10% x 30 = $ 3 million

Hence, Market value of long term debt = D = - PV (Rate, Nper, PMT, FV) = - PV (12%, 30, 3, 30) = $ $25.17

Preferred Stock

Current market price = Annual dividend / yield = 4 x quarterly dividend / 8% = (4 x 2.50 x Par value) / 8% = (4 x 2.50 x 100) / 8% = $ 125 / share

Book value of preferred stock = $ 5 million ((this figure appears on the balance sheet against preferred stock)

Number of preferred stock = Ns = Book value / Par value = 5 million / 100 = 5,000,000 / 100 = 50,000

Market value of preferred stock, S = Current market price x Number of preferred stock = 125 x 50,000 = $ 6.25 million

Common Equity

Market value, E = Price x Number = P0 x N = 20 x 4 million = $ 80 million

Hence, the weight of long-term debt = D / (D + S + E) =  25.17 / (25.17 + 6.25 + 80.00) = 22.58%

I sincerely hope that you now got a much needed headstart.