Question

Consider the following cash flows:

Year 0 1 2 3 4 5 6

Cash Flow -$10,000 $2,200 $3,300 $2,500 $2,500 $2,300 $2,100

A. Payback The company requires all projects to payback within 3 years. Calculate the payback period. Should it be accepted or rejected?

B. Discounted Payback Calculate the discounted payback using a discount rate of 10%. Should it be accepted or rejected?

C. IRR Calculate the IRR for this project. Should it be accepted or rejected?

D. NPV Calculate the NPV for this project at a rate of 10%. Should it be accepted or rejected?

E. PI Calculate the Profitability Index (PI) for this project. Should it be accepted or rejected?

There are two common formulas for the profitability Index:

PV of Future Cash Flows/Initial Cost, accept if PI > 1.0 or NPV/ Initial Cost, accept if PI > 0

Answer 1

A. Payback Period = ( Last Year with a Negative Cash Flow ) + [( Absolute Value of negative Cash Flow in that year)/ Total Cash Flow in the following year)]

= 3 + (2000 / 2500)

= 3.80 Years

The payback period is 3.80 Years

Since  the company requires all projects to payback within 3 years, and the actual payback period is more than 3 years, hence the project must be rejected.

Hence the correct answer is rejected.

B.

Discounted Payback Period =

( Last Year with a Negative Cumulative Cash Flow ) + [( Absolute Value of negative Cumulative Cash Flow in that year)/ Total Present Cash Flow in the following year)]

= 4 + (908.26 / 1718.69)

= 4.53 Years

Hence the Discounted Payback Period is 4.53 years

Since  the company requires all projects to payback within 3 years, and the actual discounted payback period is more than 3 years, hence the project must be rejected.

Hence the correct answer is rejected.

C.

Let the IRR be x.

Now , Present Value of Cash Outflows=Present Value of Cash Inflows

10000= 2200/(1.0x) +3300/ (1.0x)^2 +2500/(1.0x)^3+ $ 2500/(1.0x)^4 + $ 2300/(1.0x)^5 +$ 2100/(1.0x)^6   

Or x= 13.20%

Hence the IRR is 13.20%

Since the IRR is more than the cost of capital, the project must be accepted.

D.  NPV of Project = Present Value of Cash Inflow - Present Value of cash Outflow

= [ $2200 * 1/(1.10) ^ 1 + 3300* 1/(1.10) ^2+2500* 1/(1.10) ^3+2500* 1/(1.10) ^4+ 2300* 1/(1.10) ^5+2100* 1/(1.10) ^6] - $ 10,000

= $ 926.61

Hence the NPV is $ 926.61

Since the NPV is positive, the project must be accepted.