Question

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 9%, 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 9%. 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 $2.00, and has a yield to investors of 11%. New perpetual preferred stock would have to provide the same yield to investors, and the company would incur a 7% 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 22% 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 35% 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 5%, although the bank acknowledges that an increase in the expected inflation rate could lead to an increase rather than a decrease in interest rates.

Assume that you were recently hired by TII as a financial analyst and that your boss, the treasurer, has asked you to estimate the company's WACC under the assumption that no new equity will be issued. Your cost of capital should be appropriate for use in evaluating projects that are in the same risk class as the assets TII now operates.

1. What are the market value weights for long-term debt, preferred stock, and common stock in Travellers' capital structure? Do not round intermediate calculations. Round your answers to two decimal places.

   	Weight
   Long-term debt	%
   Preferred stock	%
   Common stock	%

2. What is the required return on long-term debt? Round your answer to two decimal places.

     %

3. What is the required return on preferred stock? Do not round intermediate calculations. Round your answer to two decimal places.

     %

4. Using the DCF model and the retention growth model for g, what is the required return on stock? Do not round intermediate calculations. Round your answers to two decimal places.

   Estimate of g	Retention growth model	Lowest analyst g	Highest analyst g
   Required return on stock	%	%	%

5. Using the own-bond-yield-plus-judgemental-risk-premium approach, what is the required return on stock? Do not round intermediate calculations. Round your answers to two decimal places.

   Required return on stock (judgemental risk premium = 4%):   %

   Required return on stock (judgemental risk premium = 6%):   %

6. Using the CAPM approach, what is the required return on stock? Do not round intermediate calculations. Round your answers to two decimal places.

   Required return on stock (beta = 1.3, RP_M = 4.5%):   %

   Required return on stock (beta = 1.3, RP_M = 5.5%):   %

   Required return on stock (beta = 1.7, RP_M = 4.5%):   %

   Required return on stock (beta = 1.7, RP_M = 5.5%):   %

7. What is Travellers' WACC? Use the required returns on stock from part e. Do not round intermediate calculations. Round your answers to two decimal places.

   WACC (lowest required return on stock):   %

   WACC (highest required return on stock):   %

Answer 1

(a) Long Term Debt (Book Value) = $ 30 million

Par Value of each bond = $ 1000 (assumed)

Number of Bonds Issued = Nb = 30000000 / 1000 = 30000

Yield to Maturity = YTM =12 %, Coupon Rate = 10% (paid semi annually) and Maturity = 25 years

Semi Annual Coupon = 0.1 x 1000 x 0.5 = $ 50

Let Market Price of Bond be P

Therefore, P = 50 x (1/0.06) x [1-{1/(1.06)^(50)}] + 1000 / (1.06)^(50) = $ 842.38

Market Value of Debt = Md = Nb x P = 30000 x 842.38 = $ 25271441.81

Preferred Stock (Book Value) = $ 5 million

Dividend Per Quarter = $ 1.5 per share

Annual Dividend = 1.5 x 4 = $ 6 per share

Yield of Preferred Stock = Yp = 11%

Let Preferred Stock Market Price be PPm = Annual Dividend / Yp = $ 54.54

Number of Preferred Stock Issued = 5000000 / Par Value = 5000000 / 100 = 50000

Market Value of Preferred Stock = Mp = PPm x Number of Preferred Stock = 54.54 x 50000 = $ 2727272.73

Common Stock Market Price = $ 20 and Number of Common Stock Outstanding = 4 million

Market Value of Common Stock = 20 x 4 = $ 80 million = Me

Net Income = $ 2 per share and Dividend = $ 1 per share. Therefore, Retained Earnings = 2 - 1 = $ 1 per share

Total Retained Earnings = 1 x 4 = $ 4 million
Book Value of Retained Earnings = $ 30 million

Market Value of Retained Earnings =Mre = Increase Retained Earnings + Book Value of Retained Earnings

= 4 + 30

= $ 34 million

Total Capital Structure = Md + Me + Mp + Mre = 25271441.81 + 80000000 + 2727272.73 + 34000000 = $ 141998714.5

Long Term Debt % = [25271441.81 / 141998714.5] x 100 = 17.78 %

Preferred Stock % = [2727272.73 / 141988714.5] x 100 = 1.88%

Common Stock % = [ 80000000 / 144988714.5] x 100 = 56.34 %

NOTE: Common Stock % does not include retained earnings hence sum of these %s is less than 100%. Common Equity % includes common stock and retained earnings.

(b) Yield to Maturity of Long Term Debt Bonds = 12 %

Tax Rate = 35%

After Tax YTM = (1-0.35) x 12 = 7.8%

As the long term bond yields 7.8% after tax to bond investors, the same is the cost incurred by the issuer (which happens to be Traveller's Inc) to keep the bonds in the market.

Hence the company's long term cost of debt is the same as its long term bond's yield.

Therefore, Long Term Cost of Debt =7.8% (after tax)

(c) Preferred Stock Market Value = $ 54.54

Floatation Cost = 4% = F

Annual Dividend = $ 6

Rate of Return on Preferred Stock = 6 / [54.54 x (1-0.04)] = 0.1146 or 11.46 %

(d) D0= $ 1 , P0 = $ 20 and ROE =26 %

Retention Ratio = (EPS0 - D0) / EPS0 = (2-1) / 2 = 0.5

Growth for Upcoming Year = g = ROE x Retention Ratio = 0.5 x 0.26 = 0.13

NOTE: ROE for the year ended is used for calculating upcoming year's expected growth. The forecasted ROE of 34% is for the upcoming year and that would impact growth of the year after the upcoming one.

D1 = D0 x (1+g) = 1 x (1.13) = $ 1.13 (this in sync with the analyst's forecast of a dividend growth betweeen 10% and 15%)

Therefore, Rate of Return on Common Stock = (D1/P0) + g = (1.13/20) + 0.13 = 0.1865 or 18.65%

NOTE: Please raise separate queries for answer to the remaining subparts

This solution is provided with detailed explanation. Please discuss in case of Doubt.

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