A firm follows the simple growth model and can invest $1000 every year into new projects which have a rate of return of 17%. Each project generates a constant stream of earnings year after year. The firm's stock has a required rate of return of 13%. If the firm is founded today, the firm value equals ________.
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A. B. C. D.C
You should be careful in solving such a problem.
Suppose the firm invests $1,000 today in a project. This first project generates a constant stream of perpetuity with an annual payment of $1,000 * 0.17 = $170.
The present value of this stream is 170/0.13 = $1,307.6. The NPV of the project is then $1,307.6 - $1,000 = $307.6. Since the firm does this every year, it has a perpetuity of $307.6 (the NPVs of projects 2 and on, at the time the projects are started).The present value of these NPVs is $307.6/0.13 = $2,367. Thus, the total value of the firm is $2,367 + $307.6 (first project) = $2,675.