Question

Barron Chemical uses a thermoplastic polymer to enhance the appearance of certain RV panels. The initial cost of one process was $124,000 with annual costs of $47.000. Revenues are $77,000 in year 1, increasing by $1000 per year. A salvage value of $22.000 was realized when the process was discontinued after 8 years. What rate of return did the company make on the process? 16.66 points The rate of return made by the company is %. eBook

Answer 1

Here we are required to calculate the IRR of the investment made by the firm.

Given, Initial cost = $ 124,000

Annual cost = $ 47,000

Revenue = $ 77,000 per year increases by $ 1,000 every year.

Net cash flow = $ 77,000 - 47,000 = $ 30,000 increases by $ 1,000 every year

Salvage value = $ 22,000

Useful life = 8 years

Here we can determine the IRR using trial and error method. As we know when we discount the cash flow at IRR the NPW= 0.  

$\large NPW = - 124,000 + 30,000(P/A,i\%,8) + 1000(P/G,i\%,8) + 22,000(P/F,i\%,8)$

Assume rate = 22%

$\large NPW = - 124,000 + 30,000(P/A,22\%,8) + 1000(P/G,22\%,8) + 22,000(P/F,22\%,8)$

$\large \implies NPW = - 124,000 + 30,000\times \frac{1-1.22^{-8}}{0.22}+ 1000\times \frac{1.22^8-0.22\times 8-1}{0.22^2\times 1.22^8}+ 22,000\times 1.22^{-8}$

On solving the equation we get

NPW (22%) = - $ 1897.50787

Therefore, 22% is not the required rate of return. The required rate must be less than 22% assume rate = 21%

$\large NPW = - 124,000 + 30,000\times \frac{1-1.21^{-8}}{0.21}+ 1000\times \frac{1.21^8-0.21\times 8-1}{0.21^2\times 1.21^8}+ 22,000\times 1.21^{-8}$

Solve the above equation we will get

NPW(21%) = $ 2005.309482

Now, apply linear interpolation to determine the IRR

$\large IRR = 21 + (22 -21)\times \frac{NPW_{21\%}}{NPW_{21\%}-NPW_{22\%}}$

$\large \implies IRR = 21 + \frac{2,005.309482}{2,005.309482 - (- 1,897.50787)}$

$\large \implies IRR = 21 + 0.5138$

$\large \implies IRR \approx 21.51\%$

Solved it using excel too got the same value kindly refer the attached picture.

=IRR( AZ7:AZ15 ) AY - AZ BA BB BC Year 0 10 11 Cash Flow -124000 30000 31000 32000 33000 34000 35000 36000 59000 IRR Y 21.51% 12 13 14

Please contact if having any query will be obliged to you for your generous support. Your help mean a lot to me, please help. Thank you.