An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,

Question

An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,700, and a discount rate of 13 percent.

1.)

What is the discounted payback period for these cash flows if the initial cost is $6,100? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

2.) What is the discounted payback period for these cash flows if the initial cost is $8,200?

3.) What is the discounted payback period for these cash flows if the initial cost is $11,200?

An investment project has annual cash inflows of $3,400, $4,300, $5,500, and $4,700, and a discount rate of 13 percent.

Explanation / Answer

Payback period of a project is number of years required to recover the initial cost of a project. Discounted pay back period is calculated on discount cash flows with PV factor.

Calculate cumulative cash flow to find the number of years required to recover initial cost.

1. Initial cost = $6,100

So, the payback period is between 1 and 2 year.

Payback period = full years until recovery + [remaining cost at the begining of last year / cash flow during last year]

= 1 + [3091 /3368]

= 1.92 years

2. Initial cost = $8,200

So, the payback period is between 2 and 3 year.

Payback period = full years until recovery + [remaining cost at the begining of last year / cash flow during last year]

= 2 + [1824 /3812]

= 2.47 years

3. Initial cost = $11,200

So, the payback period is between 3 and 4 year.

Payback period = full years until recovery + [remaining cost at the begining of last year / cash flow during last year]

= 3 + [1012 /2883]

= 3.35 years

Years Cash Flows Discount Factor (13%) PV of Cash flows Cumulative cash flows 0 ($6,100) 1 ($6,100) ($6,100) 1 $3,400 0.8849558 $3,009 ($3,091) 2 $4,300 0.7831467 $3,368 $276 3 $5,500 0.6930502 $3,812 $4,088 4 $4,700 0.6133187 $2,883 $6,971

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