Question

The stock of Pace Inc. has a beta of 1.25 and a market value of equity of $13 million. The expected return on the market is 8% and the Treasury bill rate is 2%. If the company's cost of capital is 8.25%, what is the market value of the company's risk-free debt?

Answer 1

Cost of Equity =

= 2% + 1.25(8% - 2%)

= 9.5%

Let the Value of Debt be X Mn  

Total Capital = 13Mn + X

Cost of Capital = (Cost of Equity * Weight of Equity) + (Cost of Debt * Weight of Debt)

8.25% = 9.5% * 13 / 13+X + 2% * X / 13 + X

8.25% = 123.5% / 13+X + 2% * X / 13 + X

8.25% = (123.5% + 2% * X) / 13+X

8.25% * 13 + 8.25% * X = 123.5% + 2% * X

107.25% + 8.25% * X = 123.5% + 2% * X

8.25% * X - 2% * X = 123.5% - 107.25%

6.25% * X = 16.25%

X = 16.25% / 6.25%

X = 2.6

Value of Debt is 2.6 MN

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