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# Horizon value, value of operations, common stock price

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1 Akyol Corporation is undergoing a restructuring, and its free cash flows are expected to be unstable
during the next few years. However, FCF is expected to be \$95 million in Year 5, i.e., FCF at t = 5 equals
\$95 million, and the FCF growth is expected to be constant at 8% beyond that point. If the weighted
average cost of capital is 12%, what is the horizon value (in millions) at t = 5?

2. Suppose Yon Sun Corporation's free cash flow during the just-ended (t = 0) year was \$80 million, and
FCF is expected to grow at a constant rate of 8% in the future. If the weighted average cost of capital is
14%, what is the firm's value of operations, in millions?

3. Zhdanov, Inc. forecasts that its free cash flow in the coming year, i.e., at t = 1, will be -\$15 million
(negative), but its FCF at t = 2 will be \$22 million. After Year 2, FCF is expected to grow at a constant
rate of 6% forever. If the weighted average cost of capital is 16%, what is the firm's value of operations,
in millions?

4. Based on the corporate valuation model, the value of a company's operations is \$1,400 million. The
company's balance sheet shows \$80 million in accounts receivable, \$60 million in inventory, and \$150
million in short-term investments that are unrelated to operations. The balance sheet also shows \$90
million in accounts payable, \$120 million in notes payable, \$300 million in long-term debt, \$50 million in
preferred stock, \$180 million in retained earnings, and \$800 million in total common equity. If the company
has 40 million shares of common stock outstanding, what is the best estimate of the common stock's
price per share?

5. Vasudevan, Inc. forecasts the free cash flows (in millions) shown below. If the weighted average cost
of capital is 12% and the free cash flows are expected to continue growing at the same rate after Year 3
as from Year 2 to Year 3, what is the Year 0 value of operations, in millions?
Year Free Cash Flow
1 \$(20.00)
2 \$42.00
3 \$48.00

6. In problem 5, if the growth rate in free cash flows after Year 3 was lower than what you calculated for
the growth from Year 2 to Year 3, and all other information remained the same as problem 7, then the
Year 0 value of operations, in millions, as compared to your answer to problem 7, would:
a. Increase.
b. Decrease.
c. Stay the same.
e. Shrink by half.

7. Your company, CSUS Inc., is considering a new project whose data are shown below. The required
equipment has a 3 year class life and will be depreciated by the MACRS depreciation system over the
project's next 4 years. Revenues and other cash operating costs are expected to be constant over the
project's 10 year expected operating life. What is the project's Year 4 cash flow?
Equipment cost (depreciable basis) \$80,000.00
Sales revenues, each year \$45,000.00
Cash operating costs \$20,000.00
Marginal tax rate 25.00%

8. Liberty Services is now at the end of the final year of a project. The equipment originally cost
\$28,500, of which 70% has been depreciated. The firm can sell the used equipment today for \$12,000,
and its tax rate is 40%. What is the equipment's after-tax salvage value for use in a capital budgeting
analysis?

9. Marshall-Miller & Company is considering the purchase of a new machine for \$60,000, installed. The
machine has a 5 year class life and will be depreciated by the MACRS depreciation system over the
project's next 6 years. The firm expects to operate the machine for 4 years and then to sell it for \$14,500.
If the marginal tax rate is 34%, what will the after-tax salvage value be when the machine is sold at the
end of Year 4?

10. TexMex Food Company is considering a new salsa whose data is shown below. The equipment to
be used would be depreciated by the straight-line method over its 3 year life and would have a zero
salvage value, and no new working capital would be required. Revenues and other operating costs are
expected to be constant over the project's 3 year life. However, this project would compete with other
TexMex products and would reduce their pre-tax annual cash flows. What is the project's NPV?
WACC 12.00%
Pre-tax cash flow reduction for other products (cannibalization) \$14,000.00
Investment cost (depreciable basis) \$80,000.00
Sales revenues, each year for 3 years \$67,500.00
Annual cash operating costs (excludes depreciation) \$25,000.00
Marginal tax rate 25.00%

11. Florida Car Wash is considering a new project whose data is shown below. The equipment to be
used would be depreciated by the straight-line method over the project's 3 year life and would have a zero
salvage value after Year 3. No new working capital would be required. Revenue and other operating costs
will be constant over the project's life, and this is just one of the firm's many projects, so any losses on it
can be used to offset profits in other units. If the number of cars washed declined by 40% from the
expected level, by how much would the project's NPV decline?
WACC 12.00%
Net investment cost (depreciable basis) \$60,000.00
Number of cars washed 3,000
Average price per car \$25.00
Fixed cash operating costs (excluding depreciation) \$10,000.00
Variable operating costs/unit (i.e., VC per car washed) \$5.5000
Marginal tax rate 35.00%

12. A project's base case or most likely NPV is \$45,000, and assume its probability of occurrence is 60%.
Assume the best case scenario NPV is 40% higher than the base case and assume the worst case
scenario NPV is 30% lower than the base case. Both the best case scenario and the worst case scenario
have a 20% probability of occurrence. Find the project's coefficient of variation.

13. Diplomat.com is considering a project that has an up-front cost of \$3 million and is expected to
produce a cash flow of \$575,000 at the end of each of the next 5 years. The project's cost of capital
is 16%. What is the project's net present value?

14. Refer to problem 13. If Diplomat goes ahead with this project today, it will obtain knowledge that will
give rise to additional opportunities 5 years from now (at t = 5). The company can decide at t = 5 whether
or not it wants to pursue these additional opportunities. Based on the best information available today,
there is a 40% probability that the outlook will be favorable, in which case the future investment
opportunity will have a net present value of \$6 million at t = 5. There is a 60% probability that the outlook
will be unfavorable, in which case the future opportunity will have a net present value of -\$2 million
(negative) at t = 5. Diplomat.com does not have to decide today whether it wants to pursue the additional
opportunity. Instead, it can wait to see what the outlook is. However, the company cannot pursue the
future opportunity unless it makes the \$3 million investment today. What is the estimated net present
value of the project after consideration of the potential future opportunity

15. Refer to problems 13 and 14. What is the value of the option to expand Diplomat.com's project
from the decision-tree analysis you have completed in problems 17 and 18?

16. Refer to problems 13 and 14. Next, we plan to use the Black-Scholes model to estimate the value of
this option to expand the project at t = 5. Calculate P = current stock price = PV as of t = 0 of all
expected future cash flows if the project is expanded at t = 5.

17. Refer to problem 16. Now use the Black-Scholes model to estimate the value of this option to
expand the project at t = 5. Use the P you calculated in problem 20, plus assume that the variance of
the project's rate of return is 40% and that the risk-free rate of return is 5%.

18. Oklahoma Instruments (OI) is considering a project called F-200 that has an upfront cost of \$250,000.
The project's subsequent cash flows are critically dependent on whether another of its products, F-100,
becomes an industry standard. There is a 60% chance that F-100 will become the industry standard, in
which case the F-200's expected cash flows will be \$120,000 at the end of each of the next 5 years. There
is a 40% chance that the F-100 will not become the industry standard, in which case the F-200's expected
cash flows will be \$30,000 at the end of each of the next 5 years. Assume that the cost of capital is 11%.
Based on the above information, what is the F-200's expected NPV?

19. Refer to problem 18. What is the project's coefficient of variation?

20. Refer to problem 18. Now assume that one year from now OI will know if the F-100 has become the
industry standard. Also assume that after receiving the cash flows at t = 1, OI has the option to abandon
the project, in which case it will receive an additional \$100,000 at t = 1, but no cash flows after t = 1.
Assuming that the cost of capital remains at 11%, what is the estimated value of the abandonment
option?