# Finance: MIRR, IRR, NPV and cost of instruments.

1 . John and Larry's, Inc. does not pay dividends at this time. You overhear the CFO tell the CEO that the plan is to begin paying dividends in 4 years. The first dividend will be $2.00 and the dividends are expected to grow at a 5% rate

thereafter. Given required rate of return of 15.5%, what should be the price of the stock today? (3 points)

2 . The Suretype Typewriter Company is facing decreased sales due to the continual trend toward the use of computers for word processing tasks. Based on the most recent long-term earnings forecasts, it is anticipated that dividends will decline at

a rate of 9% annually, forever. If the firm just paid a dividend of $1.75 and the required return on the stock is 14%, at what price should the stock sell for? (3 points)

3 . What is the value of 2,000 shares of Creative Crafts, Inc. stock? Creative Crafts, Inc. just paid a $2.00 dividend (D0). You expect dividends to grow by 20% per year in years 1 and 2, by 12% in year 3, and by 5% thereafter. The required return on the stock is 16%. (3 points)

4 . The stock of Rockstar International is selling for $28.75 per share. Rockstar's last dividend (D0) was $2.50 per share and its dividends are projected to grow at a constant rate in the future. If the required return on the stock is 13 percent, what

is the projected dividend growth rate? (3 points)

5 . What price would you be willing to pay for a stock that just paid a $4.25 dividend (D0) if the anticipated dividend growth rate is 6% and the required return on the stock is 14%? (3 points)

6 . Two investors are evaluating AT&T's stock for possible purchase. They agree on the expected value of D1 and also on the expected future dividend growth rate. Further, they agree on the riskiness of the stock, and thus, the discount rate.

Assume that the first investor would plan to sell the stock after 2 years and the 2nd investor would plan on selling the stock after 10 years. Would they agree on the price of the stock, or would they disagree on the price because of the differences

in the length of time that each plans to hold the stock? Clearly explain your answer. (3 points)

7 . A proposed new project requires an initial investment of $847,000. The expected cash flows are $172,000 per year for the first two years, and then $500,000 per year in the third and fourth years. Assume the appropriate discount rate is 15%.

a) What is the NPV? (3 points)

b) What is the IRR? (3 points)

c) What is the Modified IRR (MIRR)? (3 points)

d) What is the profitability index? (3 points)

8 . Suppose your firm is evaluating four potential new investments. You calculate that these projects, Q, X, Y, and Z, have the NPV and IRR figures given below:

Project Q: NPV = $7,000 IRR = 15%

Project X: NPV = $4,000 IRR = 16%

Project Y: NPV = -$5,000IRR = 12%

Project Z: NPV = -$800 IRR = 18%

a) Which project(s) should be accepted if they are independent? Clearly explain your reasoning. (3 points)

b) Which project(s) should be accepted if they are mutually exclusive? Clearly explain your reasoning. (3 points)

9 . Suppose an investment costs $650 and generates cash inflows of $121 per year for the next 8 years.

a) What is the payback period (undiscounted)? (3 points)

b) Calculate the discounted payback period using an 7.5% discount rate. (3 points)

c) Calculate the discounted payback period using an 17.5% discount rate. (3 points)

d) Would the payback period (undiscounted) change given a change in the discount rate? Is this a strength or a weakness of the undiscounted payback period approach? (3 points)

e) Can you identify the discount rate at which the investment would just pay off on a discounted basis at the end of its 8-year life? If so, calculate that rate. (3 points)

1 0 . A growing business is considering two mutually-exclusive projects with the following forecasted cash flows.

Time Project A Project B

0 -$100,000-$100,000

1 -15,00075,000

2 20,000 30,000

3 55,000 9,000

4 95,000 10,000

a) Calculate the IRR of each project. (3 points)

b) Calculate the NPV of each project at discount rates of 0%, 5%, 10% and 15%. (3points)

c) Calculate the incremental IRR (i.e., the crossover rate). (3 points)

d) Construct an NPV profile to illustrate how the choice between the two projects depends on the discount rate. Make sure you are explicit about the conclusions to be drawn from the NPV profile! (i.e., Do X if ...; do Y if ...; do Z if ...) (3 points)

1 1 . Suppose that you are trying to decide between two mutually exclusive projects. Project A has an IRR of 23% and project B has an IRR of 28%. If the appropriate discount rate is 11%, which project should a financial manager that is acting in the best interests of shareholders choose? Clearly explain your answer. (3 points)

1 2 . Consider a firm that currently has a market value of $320,000. The firm is considering a project with the following cash flows and a required return (hurdle rate) of 15.75%.

T = 0 -$100,000

Year 1 $30,000

Year 2 $30,000

Year 3 $30,000

Year 4 $43,000

a) Calculate the undiscounted payback period. (3 points)

b) If the firm decided to accept this project, what would the firm's new market value be? Explain your answer clearly and be sure to support your conclusion with the appropriate figures. (3 points)

#### Solution Summary

The problem set deals with issues in finance including: cost of equity, Net present value, Modified Internal rate of return, Internal rate of return etc.