Question

Rana Company has $300,000 to invest and wishes to evaluate the following three projects.

Years	X ($)	Y ($)	Z ($)
0	(150,000)	(150,000)	(100,000)
1	55,000	80,000	70,000
2	55,000	40,000	30,000
3	55,000	40,000	20,000
4	55,000	70,000
cost of capital	10%	10%	10%

Required:

Which project(s) would you recommend using:

1. Payback Period (PP) in nominal and discounted values.
2. Net Present Value (NPV)
3. Profitability Index (PI)
4. The internal rate of return (IRR) (hint: use 30%)

kindly note that i need the answer with full steps and clear and detials

Answer 1

Based on the given data, pls find below workings:

Based on the below workings, Project Z is having lower Payback (normal and discounted) period; However, since the payback method does not consider the cash flows post the payback period, the decision of investment should be chosen based on the other methods - IRR, NPV and NPV;

Based on all these three methods, Project Y is the top priority option for investment followed by Project X and then Project;

Considering the investment value of $ 300000, it is recommended to invest in Project Y and Project X to gain maximum benefits.

Computation of IRR: This can be computed using formula in Excel = IRR("range of cashflows", discounting factor%);

Computation of PI: Profitabliity index is computed as NPV / Initial Investment.

Computation of Net Present Value (NPV) based on the Discounted Cash flows; The Discounting factor is computed based on the formula: For year 0, the discounting factor is 1; For Year 1, it is computed as = Year 0 factor /(1+discounting factor%) ; Year 2 = Year 1 factor/(1+discounting factor %) and so on;

Next, the cashflows need to be multiplied with the respective years' discounting factor, to arrive at the discounting cash flows;

The total of all the discounted cash flows is equal to its respective Project NPV of the Cash Flows;

Computation of Pay Back Period: Here, the period is computed for each project, based on cumulative discounted cash flows: If the cumulative value is less than or equal to zero, the period is considered as 12 months (it means that the net cumulative cash flow has not yet paid back the initial investment); Once the value turns positive in a particular year, the period for such year is observed at a proportion of actual discounted cash flow to the cumulative CF; This gives the period less than 12 months in such year; Once this is computed, total of all the years is taken and divided by 12, to arrive at the Payback period in no.of years.