Question from \"Understanding Analysis\" Exercise 4.5.2. Decide on the validity of the following conjectures. (a) Continuous functions take bounded open intervals to bounded open intervals. (b) Continuous functions take bounded open intervals to open sets. (c) Continuous functions take bounded closed intervals to bounded closed intervals. Solution (a)False. The function f(x)=x2 takes (-1,1) to [0,1). (b) False,Same example.[0,1) is not open (c) True. Let f(x) be continuous on [a,b]. By the Extreme Value Theorem., there are points x0,x1? [a,b] such that f(x0) and f(x1) are the minimum and maximum of f(x), respectively, on [a,b]. Hence f([a,b])? [f(x0),f(x1)]. By the Intermediate Value Theorem, we have equality..

1. Question Garage, Inc., has identified the following two mutually exclusive projects: Year Cash
Flow (A) Cash Flow (B) 0 –$ 28,000 –$ 28,000 1 13,400 3,800 2 11,300 9,300 3 8,700 14,200 4
4,600 15,800
a-1 What is the IRR for each of these projects? (Do not round intermediate calculations. Enter
your answers as a percent rounded to 2 decimal places, e.g., 32.16.) IRR Project A % Project B
%
b-1 If the required return is 10 percent, what is the NPV for each of these projects? (Do not
round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) NPV
Project A $ Project B $
c. At what discount rate would the company be indifferent between these two projects? (Do not
round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places,
e.g., 32.16.) Discount rate %????
Solution
The NPV and IRR of Project A is as follows:
The NPV and IRR of project B is as shown below:
a. IRR of project A : 16.13%
IRR of project B : 16.02%
b. NPV of project A :$3,198.96
NPV of project B: $4,600.78.
c. For identifying the rate at which both project become indifferent is obtained by find the IRR of
the differnce between the cash flows of the two projects. This is shown as below:
The discount rate at which the company would be indifferent between these two projects is
15.75%Project AYearCash flow0-280001134002113003870044600IRR16.134%NPV$
3,198.96