Question

Company ABC received a contract from company XYZ, worth $460 million to build a product. XYZ will pay $50 million when the contract is signed, another $360 million at the end of the first year, and the $50 million balance at the end of second year. The expected cash outflows required to produce the product are estimated to be $150 million now, $95 million the first year, and $218 million the second year. The firm’s MARR is 27% for this project.

a) Compute the values of i* for this project. (30 points)

b) Calculate IRR. Is the project acceptable? (70 points)

Answer 1

Cash flow Diagram

a) i value for outflow

150 + 95 (1+i)^-1 + 208 (1+i)^-2 = 460

Let (1 / 1+i) = x

150 + 95 X + 208 X^2 = 460

208 X^2 + 95 X - 310 = 0

X = 1.015

(1 / 1+i) = x = 1.015

i = -0.0147 (Negetive i value means the firm is spending less than what it has won for the contract)

i value for inflow

50 + 360 (1/ 1+i)^1 + 50 (1/ 1+i)^ = 460

Let (1 / 1+i) = x

50 + 360 X + 50 X^2 = 460

X = 1

(1 / 1+i) = x = 1

i = 0 (Which means the PW of inflows are exactly equal to $460 Million)

b)In order to estimate the IRR, we need to equate the Present worth of Inflows to present worth of outflows

Present worth of Outflows = Present worth of Inflows.

150 + 95 (1+i)^-1 + 208 (1+i)^-2 = 50 + 360 (1+i)^-1 + 50 (1+i)^-2

150 + 95 (1/ 1+i)^1 + 208 (1/ 1+i)^2 = 50 + 360 (1/ 1+i)^1 + 50 (1/ 1+i)^2

Let (1 / 1+i) = x

150 + 95 X + 208 X^2 = 50 + 360 X + 50 X^2

Solving the equation

158X^2 - 265X + 100 = 0

Solving the equation by trial and error method

X = 0.58

(1 / 1+i) = x = 0.58

i = 0.724 = 72.4%

Since IRR is mor than MARR the project can be accepted