You will receive annual benefit $129.5 for 10 years if you invest $1,000 today.

Question

You will receive annual benefit $129.5 for 10 years if you invest $1,000 today. Calculate the internal rate of return for this investment. For the above a, you can get an increase of annual benefit $25 if you increase the investment by $141.25 today. Calculate the internal rate of return for this incremental cash flow. When your MARR is 4%, decide if this increment of investment is acceptable or not. For the above a, you can get the annual benefit $90 for an infinite period. Calculate the internal rate of return and decide if it is acceptable or not acceptable. MARR 4%.

Explanation / Answer

(a) Present Worth (PW)

(i) Optimistic scenario:

PW ($) = - 250,000 + 25,000 x PVIFA (6%, 30 years)

= - 250,000 + 25,000 x 13.7648 [From PVIFA table]

= - 250,000 + 344,120

= 94,120

(ii) Most likely scenario

PW ($) = - 250,000 + 20,000 x PVIFA (6%, 30 years)

= - 250,000 + 20,000 x 13.7648 [From PVIFA table]

= - 250,000 + 275,296

= 25,296

(iii) Pessimistic scenario

PW ($) = - 250,000 + 13,000 x PVIFA (6%, 30 years)

= - 250,000 + 13,000 x 13.7648 [From PVIFA table]

= - 250,000 + 178,942.4

= - 71,057.6

(b)

Mean annual savings = $(25,000 + 20,000 + 13,000) / 3 = $58,000 / 3 = $19,333.33

(c)

PW ($) = - 250,000 + 19,333.33 x PVIFA (6%, 30 years)

- 250,000 + 19,333.33 x 13.7648 [From PVIFA table]

= - 250,000 + 266,119.42

= 16,119.42

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