Homework Answers

Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate

each of the following:

a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091

b. f(-1/3) if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750,

f (0) = 1.10100000

c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) =

0.24842440

d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) =

0.65809197

The following information relating to this investment proposal has now been prepared: If production remained at 5,100 units, the current selling price would be expected to continue throughout the remainder of the life of the product. However, if production is increased, it is expected that the selling price will fall to $45 per unit for all units sold. Again, this will last for the remainder of the life of the product. No terminal value or machinery scrap value is expected at the end of four years, when production of NEW AGE is planned to end. For investment appraisal purposes, Good Hope uses a nominal discount rate of 10% per year and a target return on capital employed of 20% per year. Ignore taxation. Required: (a)Calculate the following values for the investment proposal: (14 marks) (i)net present value; (ii) internal rate of return; (iii)return on capital employed (accounting rate of return) based on initial investment; and. (iv)discounted payback period