Question

Long-term investment decision, payback method Bill Williams has the opportunity to invest in project A that costs $9,000 today and promises to pay annual end-ofyear payments of $2,200, $2,500, $2,500, $2,000, and $1,800 over the next 5 years. Or, Bill can invest $9,000 in project B that promises to pay annual end-of-year payments of $1,500, $1,500, $1,500, $3,500, and $4,000 over the next 5 years. a. How long will it take for Bill to recoup his initial investment in project A? b. How long will it take for Bill to recoup his initial investment in project B? c. Using the payback period, which project should Bill choose? d. Do you see any problems with his choice?

Answer 1

Answer:

a.- PA 3.9

b.- PB 4.22

c.- It would seems a better investment using the payback period the project A.

d.- However, the project B net 3,500 while project A net 2,000

It would be better to apply and interest rate to discount the diferent cashflow and not decide only using this method

Explanation:

The payback represent the point during the life of the project at which you redeem the initial investment.

Usually

investment/cashflow(per years) = payback

Because the cash flow are not the same each period we are going to add the cash flow until we got a positive return

PROJECT A  

cash flow                -9000

YEAR 1  2200 -6800

YEAR 2 2500 -4300

YEAR 3 2500 -1800

YEAR 4 2000   200

YEAR 5  1800 2000

At the end of year 3 (beginning of year 4) the project is -1800 end of the year 4 we are 200 positive

So during this fourth year the project achieve the payback.

assuming the 2000 revenue are generated at a linear rate we calculate the payback, We divide the beginning balance by the cash flow of the year

1800/2000 = 0.9

3 complete years + 0.9 of 4th year = 3.9 years

Same procedure for PROJECT B

cash flow  -9000

year 1 1500 -7500

year 2 1500 -6000

year 3 1500 -4500

year 4 3500 -1000

year 5 4500 3500

Durgin the 5th year the compay achieve the payback.

we divide the beginning balance by the cash flow

1000/4500 = 2/9 = 0.2222222222

4 complete year + 0.222222 = 4.222222 years