Question

1. Evaluate a 4-year project costing $25,000 and returning $8000 annually using the payback period technique and a 3- year cutoff. (5) 2. Evaluate the project above using the NPV method and a 12% required rate. (10) 3. Bonus: Evaluate the project in Problem #1 using the IRR method and a 10% required rate. (5)

Answer 1

Initial Project Cost = $25,000

Annual Cash flow = $8,000

Project life = 4

1. Payback period of Project would be:

$= \frac{\textup{Initial Cost}}{\textup{Annual cash flow}}$

$= \frac{25000}{8000}$

$\bg_green \large \textup{= 3.13 years}$

This Project should be rejected because its payback period is more than its cutoff payback period i.e 3 years.

2.

Required return (i) = 12%

$NPV = A*(P/A,i,n)-\textup{Initial Cost}$

where,

A = Annual cash flow

P/A,i,n = Present value Interest annuity factor ( To find Present value of uniform annual cash flows)

$NPV = A*\left ( \frac{(1+i)^n-1}{i*(1+i)^n} \right )-\textup{Initial Cost}$

$NPV = 8000*\left ( \frac{(1+.12)^4-1}{.12*(1+.12)^4} \right )-25000$

$NPV = 8000*3.03734934662641-25000$

$NPV = 24298.7947730113-25000$

$\bg_green \large NPV = -\$701.21$

As the NPV of Project is negative. Thus, project should be rejected.

3.

IRR is the rate at which NPV of project in nil i.e 0.

We can compute the IRR of the project with Trial and error method.

We have NPV of project at 12% = -701.21

Thus,

Compute the NPV of Project at 10%

$NPV = 8000*\left ( \frac{(1+.1)^4-1}{.1*(1+.1)^4} \right )-25000$

$NPV = 358.92$

Thus,

$IRR = \textup{lower rate} + \frac{NPV_{\textup{at lower rate}}}{NPV_{\textup{at lower rate}}-NPV_{\textup{at higher rate}}}*\textup{(higher rate - lower rate)}$

$IRR = 0.10 + \frac{358.92}{358.92+701.21}*\textup{(0.12 - 0.10)}$

$IRR = 0.10 + \frac{398.92}{1060.13}*0.02$

$IRR = 0.10 + 0.0067$

$\bg_green \large IRR = 10.67\%$

Required return = 10%

On the basis of IRR analysis, This project should be accepted because its internal rate of return is higher than its required return.

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.