Question

1. Trucks R' Us has a market capitalization of $142 billion, $78 billion in BB rated debt, and $10 billion in cash. If Trucks R' Us' equity beta is 1.68, then their underlying asset beta is closest to:

A) 1.00

B) 1.20

C) 1.32

D) 1.48

E) 2.13

2. Alpha Industries is considering a project with an initial cost of $7.4 million. The project will produce cash inflows of $1.54 million a year for 7 years. The firm has a pre-tax cost of debt of 8.6 percent and a cost of equity of 13.7 percent. The debt-equity ratio is 0.65 and the tax rate is 35 percent. What is the net present value of the project?

Hint: WACC is the discount rate to calculate NPV. If debt-equity ratio is 0.65, Wd is 0.65/1.65

A) -$372,951

B) -$187,016

C) $-25,700

D) $133,333

E) $269,480

3. Temporary Housing Services Incorporated (THSI) is considering a project that involves setting up a temporary housing facility in an area recently damaged by a hurricane. THSI will lease space in this facility to various agencies and groups providing relief services to the area. THSI estimates that this project will initially cost $5 million to set up and will generate $20 million in revenues during its first and only year in operation (paid in one year). Operating expenses are expected to total $12 million during this year and depreciation expense will be another $3 million. THSI will require no working capital for this investment. THSI's marginal tax rate is 35%. Ignoring the original investment of $5 million, what is THSI's free cash flow for the first and only year of operation?

A) $5.0 million

B) $3.75 million

C) $8.0 million

D) $6.25 million

E) $7.00 million

4. In September 2008, the IRS changed tax laws to allow banks to utilize the tax loss carryforwards of banks they acquire to shield their future income from taxes (prior law restricted the ability of acquirers to use these credits). Suppose Fargo Bank acquires Covia Bank and with it acquires $74 billion in tax loss carryforwards. If Fargo Bank is expected to generate taxable income of 10 billion per year in the future, and its tax rate is 30%, what is the present value of these acquired tax loss carryforwards given a cost of capital of 8%?

NOTE: Assume that the firm can use tax loss carryforwards to write-off 100% of its earnings

Please post with worked out solutions

Answer 1

Answer - 1

Trucks R' Us is a levered firm with $78 billion BB rated debt in its capital structure, hence the equity beta and asset beta would not be the same. The equity beta for a levered firm is given as follows:

E = A [1 + (Debt / Equity)]

Where -

E is equity beta given as 1.68

A is asset beta which is required in the question

Debt is given as $78 billion

Equity is given as $142 billion

On putting these figures in the above formula, we get-

E = A [1 + (Debt / Equity)]

1.68 = A [1 + ($78 B/ $142 B)]

1.68 = A [1 + 0.5493]

A = 1.68 / 1.5493

A = 1.08

Hence, asset beta is 1.08 which is closest to option (A) 1.00 from the available options.

Answer - 2

Following information is given of Alpha Industries -

1. Project initial cost is $7.4 million.
2. Cash inflows of $1.54 million a year for 7 years.
3. Pre-tax cost of debt of 8.6% and a cost of equity of 13.7%.
4. Debt-equity ratio is 0.65
5. Tax rate is 35%

For calculating net present value of the project we have to discount the cash inflows with the weighted average cost of capital (WACC) rate, which is calculated as below.

WACC = Ke * We + Kd * Wd

Where -

Ke is cost of equity given as 13.7%

Kd is post-tax cost of debt

Kd = Pre-tax cost of debt (1 - Tax rate)

Kd = 8.6 (1 - 0.35)

Kd = 5.59%

Wd is the weight of debt and We is the weight of equity which can be calculated using debt-equity ratio of 0.65

Hence, Wd = 0.65/1.65 = 0.3939 and We = 1/1.65 = 0.6061

On putting these figures in the above formula, we get-

WACC = Ke * We + Kd * Wd

WACC = 13.7 * 0.6061 + 5.59 * 0.3939

WACC = 8.3036 + 2.2019

WACC = 10.5055%

Now, let us calculate the net present value of the project

Statement showing net present value

Amount ($)

Year	Particulars	Amount (A)	Discount Factor @ 10.5055% (B)	Present Value (A * B)
0	Project initial cost	-7,400,000	1	-7,400,000
1 to 7	Cash Flows	1,540,000	4.7884436	7,374,203
	Net Present Value	-25,797

Hence, net present value is -$25,797 (approx) which is closest to option (C) -$25,700 from the available options.

Answer - 3

Following information is given of Temporary Housing Services Incorporated (THSI) -

1. Project initial cost is $5 million.
2. Revenue of $20 million in a year.
3. Operating expenses of $12 million.
4. Depreciation expense of $3 million.
5. Tax rate is 35%

Statement showing THSI's free cash flow

Particulars	Working	Amount       (in million $)
Revenues	Given	20.00
Operating expenses	Given	-12.00
Depreciation expense	Given	-3.00
Profit before tax		5.00
Tax	35% of Profit before tax	-1.75
Profit after tax		3.25
Depreciation expense	Add back	3.00
Free Cash Flow		6.25

Hence, the THSI's free cash flow is -$6.25 million which is option (D) -$25,700 from the available options.

Answer - 4

In the given case where Fargo Bank acquires Covia Bank and with the acquisition it also acquires $74 billion in tax loss carryforwards which can be used to shield the future income of Fargo Bank from taxes in consequence of the new tax law. The Fargo Bank is expected to generate taxable income of $10 billion per year in the future and having a cost of capital of 8%.

Now, for calculating the present value of these acquired tax loss carryforwards we need to assume that the firm can use tax loss carryforwards to write-off 100% of its earnings and the discount rate of 8% can be used for the present value calculations.

Present value of acquired tax loss carryforwards = Taxable income * Discount factor

Where -

Taxable income is given as $10 billion

Discount factor needs to be calculated using the discount rate of 8%

Discount factor =

where -

r = 0.08 (8% discount rate)

t = 7.4 (period in which losses can be written off = $74 billion / $10 billion)

Discount factor =

Discount factor =

Discount factor = 5.7722

On putting these figures in the above formula, we get-

Present value of acquired tax loss carryforwards = Taxable income * Discount factor

Present value of acquired tax loss carryforwards = $10 billion * 5.7722

Present value of acquired tax loss carryforwards = $57.72 billion