# Net Present Value: Probability, Tax, Debt, Capital, and Equity

1. Possible net present values and associated probabilities for a new investment are as follows:

NPV -1020 -800 80 450 550 800

Probability .15 .30 .20 .10 .10 .15

What is the expected value______________, median,______________ and mode _________________?

2. You have been given the job of evaluating the following merger candidate. You have collected the following cash flow for the acquisition candidate for the proposed merger (in millions):

Year 1 2 3 4 5

Cash flows now 80 85 105 145 180

Additional cash flows with merger 40 90 100 125 150

Total cash flows with merger 120 175 205 270 330

Risk free rate of return 3.5%

Beta for this project (the company after merging) 1.6

Market risk premium 5%

Pre-tax cost of debt 7.5%

Marginal tax rate 30%

Number of shares outstanding for the target company (millions) 55

Current market price per share for the target company $60

Percentage of the acquisition financed with debt 50%

Percentage of the acquisition financed with common equity 50%

What is the after tax cost of debt?

What is the after tax cost of common equity

What is the weighted average cost of capital for this acquisition candidate?

What is the maximum price per share you are willing to pay for this candidate?

Based on the numbers above, would you pursue this candidate?

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#### Solution Summary

This solution illustrates how to compute the expected value, median and mode of a project based upon its net present values and the probability of each. It also illustrates how to compute the after-tax cost of debt, cost of common equity, weighted-average cost of capital, net present value, and maximum price to pay for a merger candidate.

Capital Budgeting and Long-Term Financing Decisions

See the attached file.

Capital Budgeting and Long-Term Financing Decisions

1. We will open a business that requires the following three steps; we will need to find a viable location, market the product, and borrow money from the local bank. All three steps must be successful and the probability of success for the location is 70 percent, the probability of success for the successful marketing of the product is 60 percent, and the probability of success for obtaining the loan is 40 percent. The probability of joint success in all three steps is ___________.

2. Based on history, there is an .60 probability of a positive net present value when competitors do not respond to our introduction of a new product. Based on this same history, if competitors do respond, there is a .20 probability of a positive net present value. After studying history, and the financial capabilities of our competitors going forward, we determine that there is a .60 probability that competitors will respond. The total probability of a positive net present value is ______.

3. Possible net present values and associated probabilities for a new investment are as follows:

NPV -1000 -500 60 450 650 900

Probability .15 .10 .20 .10 .30 .15

What is the expected value______________, median,______________ and mode _________________?

4. Doug's Doughnuts is considering a new store location. For accounting purposes, fixed annual operating costs for a store are $85,000 a year, and variable costs are 40 percent of sales. The average sale for a customer is a doughnut and coffee which cost $5.25. The annual break-even sales level (in number of customers) for this store location is _______.

5. Teresa's Tanning Salon expects annual sales of $225,000, annual fixed cash outlays are $67,000 a year at each location, variable cash outlays are 20 percent of sales, depreciation is $15,000 per year, and taxes are 30% (of pretax income). Initial outlay for the building is $140,000. The company does its analysis based on a 10-year store life. We believe the business can be sold for $100,000 after taxes (disposal value) at the end of its 10 year lifer. Using an 14% required return, what is the net present value of this venture?

6. Please rework the prior problem to determine what annual sales volume is needed to generate a net present value of $0? To do this you will need to review the problem in the book and its excel answer. I will repeat the instructions here. You will need to calculate the net present value in the traditional wayfirst. When you do this you need to make sure that the second year sales references the first year ( plus first year in the formula) You will then do a goal seek to solve this problem The goal seek function is accessed by clicking on the data tab then the analysis tab then clicking on the what if box and then clicking on the goal seek box. To use this function, you will set the npv cell to zero by changing the sales cell.

7. As chief financial officer (CFO) of Madison Corp. you observed the price at which your bonds are selling in the market, the coupon on your bonds, and the credit rating on your debt. From this information you determine that your pretax cost of debt in 6.70%, the coupon rate is 10.5%, and the credit rating has improved from an A rating to a AA rating. In addition, Madison is in the 34% tax bracket. What is Madison's after tax cost of debt (round at 2 decimal places such as 1.45%)

8. As CFO of Mayknn Corporation you observe the preferred stock that Mayknn issued 75 years ago at a par value of $100 is now selling for $62. In addition this preferred stock now pays a dividend of $2.75. Mayknn is in the 25% tax bracket and has a credit rating of BBB. What is the after tax cost of existing preferred stock for Mayknn? (round at 2 decimal places)

9. As a young corporate financial analyst for Marshall Corporation you observe that Moody's has assigned Marshall an equity rating of AAA. In addition, Marshall's common equity is trading at $148, is expected to pay a$4.76 dividend, and is expected to grow at 6% a year. Marshall has a 15% profit margin and is expected to be in the 25% tax bracket? What is Marshall's cost of common equity? (round at 2 decimal places)

10. Using the same information as in the previous problem. If Marshall Corp. expects to pay a $3.58 in flotation cost to issue new common stock, what is the after tax cost of new common stock for Marshall? (round at 2 decimal places)

11. As a senior corporate financial analyst you were approached by the Matthew Corp.'s CFO and asked to determine the cost of common equity. You read about the Nobel prize-winning mean variance capital asset pricing model and decided to give it a try. You found the beta for Marshall is 1.40, the rate of return on long term US government bonds to be 5%, the return on short term government bonds is 2.5%, and the market risk premium over the past 70 years has averaged 5.5%. Using this data, what is Matthew's cost of equity? (round at 2 decimal places)

12. As president of Madison Corp. your finance people tell you that Madison is 25% debt and 75% common stock. In addition they tell you the cost of the common stock is 10% and the cost of the debt is 4.4%. What is Madison's weighted average cost of capital? (round at 2 decimal places)

13. Using the information is the previous problem, the president suggest that Madison take on more debt in the future to finance additional positive net present value projects. She estimates that a 60% debt and 40% equity mixture for the entire corporation is better. If Madison adopts this new debt oriented structure the cost of equity will increase to 14% and the cost of debt will increase to 7.5%. Please recalculate and report the new weighted average cost of capital and determine if Madison should stay where it is or adopt the higher debt oriented capital structure? (round at 2 decimal places)

14. TNT Corporation is considering the acquisition of BRM Corporation. TNT has 220,000 shares of stock, with earnings per share of $2 and a market price per share of $30. BRM has 250,000 shares outstanding with earnings per share of $1.20 and a market price of $10. The merger is expected to increase net income of the combined companies by $150,000. What is the maximum exchange ratio TNT can offer and what is the minimum exchange ratio BRM could accept?

15. You have been given the job of evaluating the following merger candidate. You have collected the following cash flow for the acquisition candidate for the proposed merger (in millions):

Year 1 2 3 4 5__

Cash flows now 80 85 105 145 180

Additional cash flows with merger 40 90 100 125 150

Total cash flows with merger 120 175 205 270 330

Risk free rate of return 4.5%

Beta for this project (the company after merging) 1.6

Market risk premium 5.5%

Pre-tax cost of debt 6.5%

Marginal tax rate 25%

Number of shares outstanding for the target company (millions) 20

Current market price per share for the target company $60

Percentage of the acquisition financed with debt 50%

Percentage of the acquisition financed with common equity 50%

What is the after tax cost of debt?

What is the after tax cost of common equity

What is the weighted average cost of capital for this acquisition candidate?

What is the maximum price per share you are willing to pay for this candidate?

Based on the numbers above, would you pursue this candidate?

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