Question

11:55 Consider an investment that costs $100,000 and has a cash inflow of $25,000 every year for 5 years. The required return is 9%, and required payback is 4 years. What is the IRR? 7.93 QUESTI 0.2 points Save Answer What is the classic profitability index? QUESTION 0.2 points Saved What decision (accept or reject) would you make based on classic PI? accept QUESTION 0.2 points Saved What is the discounted profitability index? 0.97 QUESTION 0.2 points Saved What decision (accept or reject) would you make based on discounted PI? reiect

Answer 1

The IRR given by you is 7.93%.

Note: At the discount rate of 7.93% the NPW is zero.

$\large NPW = -100,000 + 25,000(P/A,7.93\%,5)$

$\large \implies NPW = -100,000 + 25,000\times \frac{1-1.0783^{-5}}{0.0793}$

$\large \implies NPW = -100,000 + 25,000 \times 4.00$

$\large \implies NPW = -100,000 + 100,000$

$\large \implies NPW = 0$

Therefore, IRR = 7.93%

Profitability index, $\large PI = \frac{PW_{Inflow}}{Initial \ Investment}$

PW_Inflow = 25,000(P/A,9%,5) = 25,000 × 3.8896

PW_Inflow = $ 97,241.28

$\large PI = \frac{97,241.28}{100,000} = 0.9724$

Since Profitability index is less than 1. Hence, reject the project.

Discounted profitability index

$\large DPI = \frac{PW_{Inflow}}{PW_{Cost}}$

Here the cost has incurred only in 0 years. Thus the PW of cost is $ 100,000

$\large DPI = \frac{97,241}{100,000} (\because <1, reject)$

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