chapter 1 #17 10/14 The head of the accounting department at a major software ma

Question

chapter 1 #17 10/14 The head of the accounting department at a major software manufacturer has asked you to put together a pro forma statement of the company's value under several possible growth scenarios and the assumption that the company's many divisions will remain a single entity forever. The manager is concerned that, despite the fact that the firm's competitors are comparatively small, collectively their annual revenue growth has exceeded 50 percent over each of the last five years. She has requested that the value projections be based on the firm's current profits of $3.2 billion (which have yet to be paid out to stockholders) and the average interest rate over the past 20 years (6 percent in each of the following profit growth scenarios: Profits grow at an annual rate of 9 percent. (This one is tricky ) Profits grow at an annual rate of 2 percent. Profits grow at an annual rate of 0 percent. Profits decline at an annual rate of 4 percent.

Explanation / Answer

Present value of profits will be = P(1+r)/(1+i) + P((1+r)/(1+i))^2 + P((1+r)/(1+i))^3 + P((1+r)/(1+i))^4---------------------------------------------------- + P((1+r)/(1+i))^4 So we can see that this is a geometric progression so Sgp = A(1-R^n)/(1-R)

here Sgp is present value

r is annual growth rate

P is profits

n is no of years

i is interest rate

A is first term of GP P(1+r)/(1+i)

R is (1+r)/(1+i)

P in billions r in decimal i in decimal n A R Sgp in billions a) 3.2 0.09 0.06 20 3.29 1.03 86.9072 b) 3.2 0.02 0.06 20 3.08 0.96 43.7926 c) 3.2 0 0.06 20 3.02 0.94 36.7037 d) 3.2 -0.04 0.06 20 2.90 0.91 26.4862

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