Question

Carr Company is considering two capital investment proposals. Estimates regarding each project are provided below:Project Soup Project NutsInitial investment $400,000 $600,000 Annual net income 30,000 46,000 Net annual cash inflow 110,000 146,000 Estimated useful life 5 years 6 years Salvage value -0- -0- The company requires a 10% rate of return on all new investments.Present Value of an Annuity of 1Periods 9% 10% 11% 12% 5 3.890 3.791 3.696 3.6056 4.486 4.355 4.231 4.111The annual rate of return for Project Soup is

Answer 1

Answer:

IRR = 11.65%

Explanation:

Period  Cash Flow

0    -400,000

1     110,000

2     110,000

3     110,000

4     110,000

5     110,000

We could list the annual cash inflow and solve using the excel formula

IRR               0.11649

Or if we aren't allowed to do so, use maths

The way to obtain the present value would be:

Annuity x factor = PV

If we know know the rate we can look into the table doing:

factor = PV/annuity

We know Project Soup is 5 year so we look into this row:

400,000/110,000 = 3.6363

The rate wold be between 11% 3.696 and 12%  3.605

Those rate are close to our goal of 3.6363

We could solve an approximation doing excel or working with math:

$\left[\begin{array}{cc}X&Y&\\x_0 = 3.696&y_0 = 0.11&x=3.6363&?&x_1=3.605&y_1 =0.12\end{array}\right]$

$y = y_0 +\frac{y_1-y_0}{x_1-x_0} (x-x_0)$

We got from the table, the 2 rates which are close to our goal, and thetwo factor close to our goal. we post each value into the formula and solve:

$y = 0.11 +\frac{.12-.11}{3.696-3.605} (3.6363-3.605)$

$y = 0.11 +\frac{0.01}{0.091} (0.0313)$

y= 0.1165 = 11.65%