Question

Please don't provide the answer by excel calculation. I need to understand the formula and step by step.Thank you.

5. Compare the following two alternatives by the IRR method, given MARR of 8%/year. Is the incement in cost form A to B justified? Construction cost $ Benefits $/yr Salvage $ Service Life (yrs) 510,000 145,000 10,000 11 775,000 155,000 20,000 12

Answer 1

Here we are required to calculate the IRR of the two alternatives.

First of all you are required to write the equation for NPW of the alternatives. Alternative A NPW can be written as

NPWA = -510,000+145,000(P/A, 1%, 11)+10,000(P/F,2%, 11)

$\large \implies NPW_A = - 510,000 + 145,000\times \frac{1-(1+i)^{-11}}{i} + 10,000\times (1+i)^{-11}$

No, we can determine the IRR using trial and error method. Assume rate = 25%

$\large \implies NPW_A = - 510,000 + 145,000\times \frac{1-1.25^{-11}}{0.25} + 10,000\times 1.25^{-11}$

On solving this we get

NPW = $ 21,037.37

Now assume rate = 27%

= NPWA = -510,000+145,000 x — 1-1.27-11 0.27 T10,000 X 1.27-11

Solve the above equation we get

NPW = - $ 10,982

Through linear interpolation we can determine the IRR

NPW 25% IRRA = 25+ (27 – 25) - N PW25% - N PW27%

$\large IRR_A = 25 + 2\times \frac{21,037.37}{21,037.37- (-10,982)}$

$\large IRR_A = 25 + 2\times 0.657$

$\large IRR_A = 26.31\%$

Solved it using excel got the same answer refer picture below

yr L A -510000 145000 145000 145000 145000 145000 145000 145000 145000 145000 145000 155000 26%

Now calculating IRR of alternative B

$\large NPW_B= - 775,000 + 155,000(P/A,i\%,12) + 20,000(P/F,i\%,12)$

Like we have calculated IRR for alternative A we can calculate for B

Assume rate = 15%

$\large NPW_B= - 775,000 + 155,000(P/A,15\%,12) + 20,000(P/F,15\%,12)$

On solving using the annuity table we get

NPW (15%) = $ 68,934.087

Now assume rate = 18%

$\large NPW_B= - 775,000 + 155,000(P/A,18\%,12) + 20,000(P/F,18\%,12)$

NPW(18%) = - $ 29,305.7562

Apply linear interpolation

$\large IRR_B = 15 + (18 - 15)\times \frac{NPW_{15\%}}{NPW_{15\%}- NPW_{18\%}}$

$\large IRR_B = 15 + 3\times \frac{68,934.0878}{68,934.0878- (-29,305.7562)}$

$\large IRR_B = 15 + 3\times 0.70$

$\large IRR_B = 15 + 2.1$

$\large IRR_B = 17.1\%$

Solved it using excel got the same answer refer attached picture below

fx A =IRR( BJ7:BJ19 ) BI BJ B K BL BM BN 6 | Yr 7 10 B -775000 155000 155000 10 155000 11 155000 12 155000 13 155000 14 155000 15 155000 16 17 155000 155000 155000 18 19 | 120175000 17% 20 |

IRR of Alternative A is higher than alternative B thus select A.

Select A.

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