Question

P10-4 Long-term investment​ decision, payback method Personal Finance Problem   Bill Williams has the opportunity to invest in project A that costs $ $8,200 today and promises to pay $2,300​, $2,600​, $2,600​, $2,000 and $1,800 over the next 5 years. ​ Or, Bill can invest $8,200 in project B that promises to pay $1,400​, $1,400​, $1,400​, $3,500 and $4,100 over the next 5 years.  ​(​Hint: For mixed stream cash​ inflows, calculate cumulative cash inflows on a​ year-to-year basis until the initial investment is

recovered.​)

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

a.Cumulative cash flow in year 1= $2,300

Cumulative cash flow in year 2= $4,900

Cumulative cash flow in year 3= $7,500

Payback period= full years until recovery + unrecovered cost at the start of the year/ cash flow during the year

= 3 years + ($8,200 - $7,500)/ $2,000

= 3 years + $700/ $2,000

= 3 years + 0.35

= 3.35 years.

b.Cumulative cash flow in year 1= $1,400

Cumulative cash flow in year 2= $2,800

Cumulative cash flow in year 3= $4,200

Cumulative cash flow in year 4= $7,700

Payback period= full years until recovery + unrecovered cost at the start of the year/ cash flow during the year

= 4 years + ($8,200 - $7,700)/ $4,100

= 4 years + $500/ $4,100

= 4 years + 0.12

= 4.12 years.

c.Using the payback period decision rule, Bill should choose project A since it has the shortest payback period.

d.The problem with his choice is that the payback method suffers from the limitation that the payback method does not take the time value of money into account and that it does not take into account the cash flows after the payback method.

In case of any query, kindly comment on the solution.