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# Present Value

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On the first day of summer, Buford learns that his favorite nearby golf course will sell him a special voucher that allows him to play golf for \$10 in fees per game this year and every year for the next 7 years. The conditions are that Buford must commit now to paying for the same number of golf games each year, and must pay for each year's golf up front on the first day of each summer. Buford has a downward sloping demand curve for golf, reflecting his willingness to pay for the fees per game and for the use of golf equipment. That demand curve has finite intercepts on both the price and quantity axis. At \$10 in fees per game, Buford agrees to choose 18 games each summer, and he capture an amount of consumer's surplus equal to \$55 per summer. Some or all of the consumer's surplus captured when paying low fees will have to be used to access golf equipment. Buford can borrow and lend at an annual interest rate of 8%, with annual compounding of interest, and he is exempt from any tax considerations.

(a) Since Buford agrees to pay (\$10/game × 18 games/year =) \$180 now and again each year for the next 7 years, what is the present value of the fee payment obligations that Buford has made?

(b) Suppose we think of the \$55 per year of consumer's surplus as being experienced today and on the first day of summer for each of the next 7 years. In order to play golf, Buford must decide whether to lease or to purchase his equipment. This golf course is prepared to provide full rental use of all necessary golf equipment over the 8 seasons of play. Buford does not get any extra utility from owning or renting any of this equipment, he just wants to be able to play the game. Given what we know about Buford, what is the largest amount of money, expressed on a present value basis, that Buford would pay to rent golf equipment for these eight golf seasons?

(c) Alternatively, the golf shop will sell Buford the necessary equipment with a guarantee to repurchase it from him eight years from today for 20% of today's purchase price. What is the largest amount of money Buford should pay to purchase golf equipment that comes with this re-purchase guarantee?

https://brainmass.com/economics/utility-demand/present-value-tax-considerations-164879

#### Solution Preview

On the first day of summer, Buford learns that his favorite nearby golf course will sell him a special voucher that allows him to play golf for \$10 in fees per game this year and every year for the next 7 years. The conditions are that Buford must commit now to paying for the same number of golf games each year, and must pay for each year's golf up front on the first day of each summer. Buford has a downward sloping demand curve for golf, reflecting his willingness to pay for the fees per game and for the use of golf equipment. That demand curve has finite intercepts on both the price and quantity axis. At \$10 in fees per game, Buford agrees to choose 18 games each summer, and he capture an amount of consumer's surplus equal to \$55 per summer. Some or all of the consumer's surplus captured ...

#### Solution Summary

The solution calculates present value for tax considerations. Price and quantity axis for willingness is determined.

\$2.19

## Finance Review Questions

Question 1. Otel Corporation entered into an agreement with its investment banker to sell 15 million shares of the company's stock with Otel netting \$270 million dollars from the offering.

The out-of-pocket expenses incurred by the investment banker were \$5,000,000.

a. What profit or loss would the investment banker incur if the issue sold to the public at an average price of \$25 per share?
b. What profit or loss would the investment banker incur if the issue were sold to the public at an average price of \$15 per share?
c. Is this an example of a negotiated deal or best efforts? Why? Who bears the greater risk, the investment banker or the company? Why?
d. If the investment banker agrees to handle the issue on a best efforts basis, earning 7.5 percent of the proceeds, calculate the investment banker's profit or loss if all 15 million shares are sold at an average price of \$15. How much will the company receive?
e. Who bears the greater risk in a best efforts deal, the investment banker or the company? Why?

Question 2. Differentiate between each of the following and provide a specific example to illustrate each answer.

a. A golden parachute and a poison pill.
b. A friendly merger and a hostile merger.
c. A vertical merger and a horizontal merger.
d. An acquiring company and a target company
e. Purchase accounting and pooling of interest accounting

Problem 3. Campbell Company's balance sheet and income statement are shown below (in millions of dollars). The company and its creditors have agreed upon a voluntary reorganization plan. In this plan, each share of the \$4 preferred will be exchanged for one share of \$1.50 preferred with a par value of \$50 plus one 10 percent subordinated income debenture with a par value of \$50. The \$6 preferred issue will be retired with cash.

Current Current
Current Assets 250.0 Current liabilities 275.0
Net fixed assets 195.0 Advance payments 15.00
\$4 preferred stock, \$100 par value (1,000,000) shares 100.0
\$6 preferred stock, no par, callable at 10 (800,000 shares) 8.0
Common stock, \$0.50 par value (20,000,000) shares 10.0
Retained earnings 37.0
Total assets 445.0 Total claims 445.0

a. Construct the pro forma balance sheet after reorganization takes place. Show the new preferred at its par value.
b. Construct the pro forma income statement after reorganization takes place. How does the recapitalization affect net income available to common stockholders?
Income Statement
Current
Net sales 600.0
Operating expense 550.0
Net operating income 50.0
Other income 10.0

EBT 60.0
Taxes 9.0 15%
Net income 51.0
Dividends on \$4 PS 4.0
Dividends on \$6 PS 4.8
Income to Common SHs 42.2
c. What are the required pre-tax earnings before and after the reorganization?
d. Calculate the debt ratio before and after the reorganization?
e. Would the common stockholders be in favor of the reorganization? Why or why not?

Problem 4. A Treasury bond futures contract settles at 105-8.

a. What is the present value of the futures contract?
b. If the contract settles at 105-8, are current market interest rates higher or lower than the standardized rate on a futures contract? Explain.
c. What is the implied annual interest rate on the futures contract?
d. Calculate the new value of the futures contract if interest rates increase by 1 percentage point annually.
e. Calculate your profit or loss if you sold a futures contract at 105-8 and purchased an offsetting contract when rates increased by 1 percentage point annually.

Question 5. Your portfolio is diversified . It has an expected return of 11.0% and a beta of 1.10. You want to add 300 shares of Tundra Corporation at \$40 a share to your portfolio. Tundra has an expected return of 13.0% and a beta of 1.50. The total value of the investor's current portfolio is \$45,000.

a. Calculate the expected return on the portfolio after the purchase of the Tundra stock?
b. Calculate the expected beta on the portfolio after you add the new stock?
c. Is your portfolio less risky or more risky than average? Explain.
d. Will your portfolio likely outperform or underperform the market in a period when stocks are rapidly falling in value?
e. Is beta always an accurate predictor of a portfolio's performance? Explain?

Question 6. Calhoun Resorts is interested in developing a new facility in Toronto. The company estimates that the hotel would require an initial investment of \$10 million. The company expects that the facility will produce positive cash flows of \$2,710,000 a year at the end of each of the next 5 years. The project's cost of capital is 11%.

a. Calculate the expected net present value of the project.
b. The company recognizes that the cash flows could be higher or lower than 2,710,000, depending on whether the host government imposes a facility tax. The company will know in one year whether the tax will be imposed. There is a 30 percent chance that the tax will the imposed, in which case the yearly cash flows will be only \$2.5 million. At the same time, there is a 70 percent chance that the tax will not be imposed, in which case the yearly cash flows will be \$3.2 million. The company is deciding whether to proceed with the facility today or to wait 1 year to find out whether the tax will be imposed. If it waits year, the initial investment will remain at \$10 million and positive cash flows will continue for 5 years. Assume that all cash flows are discounted at 11 percent. Using decision tree analysis, calculate the value of the real option to wait a year before deciding.
c. Discuss 2-3 factors other than the value of the real option that the company should consider in making its decision.

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