Question

Discounted payback: Nugent Communication Corp. is investing $9,365,000 in new technologies. The company’s management expects significant benefits in the first three years after installation (as can be seen by the following cash flows), and smaller constant benefits in each of the next four years. What is the discounted payback period for the project assuming a discount rate of 10 percent?

Answer 1

Answer:

4 Years and 3 months

Explanation:

The present value for the project are calculated as below:

Present Value = Future Value / (1+r)^n

PV1 = $2,265,433 / (1+10%)^1 = $2,059,484

PV2 = $4,558,721 / (1+10%)^2 = $3,767,538

PV3 = $3,378,911 / (1+10%)^3 = $2,538,626

PV4 =  $1,250,000 / (1+10%)^4 = $853,767

PV5 = $1,250,000 / (1+10%)^5 = $776,152

PV6 = $1,250,000 / (1+10%)^6 = $705,592

PV7 = $1,250,000 / (1+10%)^7 = $641,448

NOW

YR    DISCOUNTED CASH FLOW       ACC. CASH FLOW

0                 ($9,365,000)                          ($9,365,000)

1                   $2,059,484                             ($7,305,516)

2                  $3,767,538                              ($3,537,978)

3                  $2,538,626                              ($999,352)

4                   $853,767                                 ($145,585)

5                   $776,152                                  $630,567

The accumulated cash flow in the year 5 is postive because the project takes complete 4 years and some month of the year 5. The months of year 5 can be calculated by the following formula:

Years = Last negative Acc. cash flow / Cash inflow in the year of first positive accumulated cash flow

Now by putting values, we have:

Years = $145,585 / $630,567 = 0.23 years

We can convert this answer into number of months by simply multiplying by 12.

So

Number of Months = 0.23 years * 12 = 2.77 which is almost 3 months

So the payback period is 4 years and 3 months.