Question

You must analyze two projects, X and Y. Each project costs $10,000, and the firm’s WACC is 12%. The expected net cash flows are as follows:
Project X Project Y
0 -$10,000 -$10,000
1 $6,500 $3,500
2 $3,000 $3,500
3 $3,000 $3,500
4 $1,000 $3,500

a. Calculate each project’s NPV, IRR, MIRR, payback, and discounted payback.
b. Which project(s) should be accepted if they are independent?
c. Which project(s) should be accepted if they are mutually exclusive?

Hint: (Project-X IRR = 17%, 18% : MIRR = 14.61%) (Project-Y IRR = 15%, 16% : MIRR = 13.73%)

solve the question step by step in proper format

Answer 1

Based on the given data, pls find below steps, workings and answers:

a. Calculate each project’s NPV, IRR, MIRR, payback, and discounted payback.

NPV of Project X is $ 966.01 and Project Y is $ 630.72

IRR of Project X is $ 18.03% and Project Y is $ 14.96% IRR of Project X is $ 14.61% and Project Y is $ 13.73%

Payback Period of Project X is 2.17 years and Project Y is 2.86 years Discounted Payback period of Proejct X is 2.85 years and Project Y is 3.72 years

b. Which project(s) should be accepted if they are independent?

If the projects are independent, both these projects can be accepted as both give Positive NPV and other positive factors like IRR, lower Payback periods.

c. Which project(s) should be accepted if they are mutually exclusive?

If the projects are mutually exclusive, Project X shoudl be accepted as the NPV of Proejct X is higher than Project Y; Also, Project X has lower payback period than Project Y and other factors like IRR, MIRR as well more healthier than Project Y.

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

Computation of MIRR: This can be computed using formula in Excel = MIRR("range of cashflows", discounting factor%, reinvestment factor%); Here, both discounting factor % and reinvestment factor% are considered same.

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 Normal / Discounted Pay Back Period: Here, the period is computed for each project, based on cumulative normal /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.