If a project costs $150,000 and is expected to return $30,000 annually, how long

Question

If a project costs $150,000 and is expected to return $30,000 annually, how long does it take to recover the initial investment? What would be the discounted payback period at i =10%? Assume that the cash flows occur continuously throughout the year.

The payback period is ______ years. (Round to one decimal place.)

The discounted payback period at i=10% would be ______ years. (Round to one decimal place.)

Please help, detailed answer and discription appreciated. I believe the first answer is 5 years. Not sure how about part 2. Thanks

Explanation / Answer

Payback period = Initial Investment / Annual cash flows

= 150,000 / 30,000

= 5 years

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Discounted payback

Discounted payback period = 7 + (150,000-146,010) / 14,010

= 7 + 0.3

= 7.3 years

The payback period is 5 years.

The discounted payback period at i=10% would be 7.3 years.

Year Discounted cash flow Cumulative cash flow 1 27,270 (30,000*0.909) 27,270 2 24,780 (30,000*0.826) 52,050 3 22,530 (30,000*0.751) 74,580 4 20,490 (30,000*0.683) 95,070 5 18,630 (30,000*0.621) 113,700 6 16,920 (30,000*0.564) 130,620 7 15,390 (30,000*0.513) 146,010 8 14,010 (30,000*0.467) 160,020

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