Question

For short-answer questions, provide your answers and explanations. For numerical questions, it is important to show your work.

Canada Telecom, a telephone company, is contemplating investing in a project in multimedia applications. The company is currently 30% debt financed. The company’s analysts have estimated the project’s cash flows but need to determine the project cost of capital. Canada Telecom analysts assess that their new multimedia division has a target debt-equity ratio of 0.6, and a cost of debt of 6.5%. In addition, the risk-free rate is 3%, and market risk premium is 5%.

XYZ Co. is a pure play in the multimedia business and is 35% debt financed. Its current equity beta is 1.05. Assume that both Canada Telecom and XYZ have a tax rate of 35%, and a debt beta of 0.

1. Is Canada Telecom’s WACC the right discount rate for its new project? Why or why not?
2. Explain why you cannot use XYZ’s equity beta (1.05) as a proxy for the equity beta of Canada Telecom’s new project. Estimate the new project’s equity beta.
3. What is the new project’s cost of capital?

Answer 1

Solution:

a) Is Canada Telecom’s WACC the right discount rate for its new project? Why or why not?

No, Canada Telecom's WACC is not the right discount rate for its new project. The reason is the difference between the capital structure of the Canada telecom and this project. The company is currently 30% debt financed i.e. debt to equity ratio of 30/70 = 0.43. The new multimedia division has a target debt-equity ratio of 0.6. So, the new project has higher debt in its capital structure. The cashflow characteristics of new project also might be different than the overall firm. So, the relevant discount rate for the new project should be based upon its overall riskiness.

b) Explain why you cannot use XYZ’s equity beta (1.05) as a proxy for the equity beta of Canada Telecom’s new project. Estimate the new project’s equity beta.

XYZ's equity beta of 1.05 can not be used as a proxy for the equity beta of Canada Telecom’s new project because their is difference between the capital structure of XYZ and new project.

Its given that XYZ Co. is a pure play in the multimedia business and is 35% debt financed.
So, the share of XYZ's equity financing = 100 - 35 =65%.
Therefore its debt to equity ratio = 35/65 = 0.5385

The new multimedia division of Canada Telecom has a target debt-equity ratio of 0.6.

Both Canada Telecom and XYZ have a tax rate of 35%, and a debt beta of 0

Using pure play method to calculate the new project’s equity beta:

Beta of XYZ = 1.05

Unlevered beta = Beta of XYZ / [1 + {debt to equity ratio of XYZ * (1-tax rate)}]
= 1.05 / [1+(0.5385*(1-0.35))]
= 1.05 / [1+(0.5385*0.65)]
= 0.7778

Levered beta = Unlevered beta * [1 + {debt to equity ratio of the new project * (1-tax rate)}]
= 0.7778 * [1+(0.6*(1-0.35))]
= 0.7778 * [1+(0.6*(0.65))]
= 1.0811

So, the new project’s equity beta = 1.08

c) What is the new project’s cost of capital?

The new project's cost of capital = It's WACC = Weight of debt * Cost of debt * (1-tax rate) + Weight of equity * Cost of equity

Target debt-equity ratio of new project = 0.6
or Debt/ Equity = 0.6
or Debt = 0.6Equity
We know, debt + equity = 1
So, Putting debt = 0.6 equity in above equation
0.6 equity + equity = 1
Equity = 1/1.6 = 0.625
and Debt = 1-0.625 = 0.375

So, weight of debt = 0.375 and weight of equity = 0.625

By CAPM,
Cost of equity = Risk free rate + Beta of the project * Market risk premium
=3 + 1.08*5
=8.4%

Also given that cost of debt = 6.5% and tax rate = 35%

Using WACC formula:
=Weight of debt * Cost of debt * (1-tax rate) + Weight of equity * Cost of equity
=0.375*6.5*(1-0.35) + 0.625*8.4
=0.375*6.5*0.65 + 0.625*8.4
= 6.834

The new project’s cost of capital = 6.83%.