8. Suppose that the net earnings of a company at time t are being generated at the rate of 25 + 5t million dollars per year, and the general formula for present value of a continuous stream of income is: PV =| K(t)e¬rt dt K(t) is the amount per year of the annual rate of income at time t; r is the annual interest rate of invested money; and T, to T, (years) is the time period of the income stream. (a)Write a definite integral that gives the present value of the company's earnings over the next 2 years using 10% interest rate. (b) Compute the present value from part (a). (c) If a potential buyer of this company offers 50 million dollars to buy the company outright, determine if the owner of the company should sell now, or should keep the company for two years. Explain your reasoning.

8. Suppose that the net earnings of a company at time t are being generated at the rate of 25 + 5t million dollars per year, and the general formula for present value of a continuous stream of income is: PV =| K(t)e¬rt dt K(t) is the amount per year of the annual rate of income at time t; r is the annual interest rate of invested money; and T, to T, (years) is the time period of the income stream. (a)Write a definite integral that gives the present value of the company's earnings over the next 2 years using 10% interest rate. (b) Compute the present value from part (a). (c) If a potential buyer of this company offers 50 million dollars to buy the company outright, determine if the owner of the company should sell now, or should keep the company for two years. Explain your reasoning.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

8. Suppose that the net earnings of a
company at time t are being
generated at the rate of 25 + 5t million
dollars per year, and the general
formula for present value of a
continuous stream of income is:
T2
PV =
K(t)e¬rtdt
K(t) is the amount per year of the
annual rate of income at time t; r is
the annual interest rate of invested
money; and T, to T2 (years) is the time
period of the income stream.
(a)Write a definite integral that gives
the present value of the company's
earnings over the next 2 years
using 10% interest rate.
(b) Compute the present value from
part (a).
(c) If a potential buyer of this company
offers 50 million dollars to buy the
company outright, determine if the
owner of the company should sell
now, or should keep the company
for two years. Explain your
reasoning.

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