The following table gives the information about two companies, where the debt an
ID: 2624055 • Letter: T
Question
The following table gives the information about two companies, where the debt and equity are in millions of dollars.
Company
Debt
Equity
?
Cost of debt
Tax rate
Business
Lorentz Airline
$117
$351
1.65
9%
33%
Airline
Zeeman Hotels
$ 15
$ 60
1.55
8%
32%
Hotels
The risk-free rate is 4.4% and the expected return on the market 12%. Lorentz Airline wants to buy a hotel using its existing capital. Find the required rate of return on the acquisition.
Please show all work
Company
Debt
Equity
?
Cost of debt
Tax rate
Business
Lorentz Airline
$117
$351
1.65
9%
33%
Airline
Zeeman Hotels
$ 15
$ 60
1.55
8%
32%
Hotels
Explanation / Answer
For hotel
?L = 1.55
we need to find beta for zeeman hotels at airline leverage level
the beta of equity alone can be written as a
function of the unlevered beta and the debt-equity ratio
?L = ?u (1+ ((1-t)D/E))
?u = 1.55/(1+ ((1-32%)*15/60)) = 1.32
Levered beta at airlien's level of debt = 1.32* (1+ ((1-32%)*117/351)) = 1.625
This is the beta that Lorentz airline will use to assess cost of capital
re = 4.4% + 1.625*(12%-4.4%)= 16.75%
required rate of return on the acquisition = 117/(117+351)*9%*(1-33%) + 351/(117+351)*16.75%= 14.07%
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