Question

Quantitative Problem: Bellinger Industries is considering two projects for inclusion in its capital budget, and you have been asked to do the analysis. Both projects' after-tax cash flows are shown on the time line below. Depreciation, salvage values, net operating working capital requirements, and tax effects are all included in these cash flows. Both projects have 4-year lives, and they have risk characteristics similar to the firm's average project. Bellinger's WACC is 7%.

0 1 2 3 4

Project A -1,200 650 355 270 320

Project B -1,200 250 290 420 770

What is Project A's payback? Do not round intermediate calculations. Round your answer to four decimal places. years

What is Project A's discounted payback? Do not round intermediate calculations. Round your answer to four decimal places. years

What is Project B's payback? Do not round intermediate calculations. Round your answer to four decimal places. years

What is Project B's discounted payback? Do not round intermediate calculations. Round your answer to four decimal places. years

Answer 1

1) Payback period for project A :

Initial investment in Year 0 = 1200

The calculations for payback period are shown below:

Project A
Years	Cash Flow	Cumulative Cash flow
1	650	650
2	355	1005
3	270	1275
4	320	1595

We can see from the above table that the cumulative cash flow is 1005 in year 2 and 1275 in year3

So the payback period will be between year 2 & 3

Payback period = 2 + (Unrecovered amount in the 3rd year) / (Cash flow in year 3)

= 2 + (1200 - 1005 ) / 270

= 2.7222 years (Answer)

2)Discounted Payback period for project A :

Initial investment in Year 0 = 1200

The calculations for Discounted payback period are shown below:

Years	Cash Flow(CF)	PV Factor@ 7% (pv)	CF *pv	Cumulative (CF *pv)
1	650	0.934579439	607.4766	607.4766355
2	355	0.873438728	310.0707	917.5473841
3	270	0.816297877	220.4004	1137.947811
4	320	0.762895212	244.1265	1382.074279

We can see from the above table that the cumulative cash flow is 1137.947811 in year 3 and 1382.074279 in year4

So the discounted payback period will be between year 3 & 4

Discounted Payback period = 3 + (Unrecovered amount in the 4th year) / (Discounted Cash flow in year 4)

= 3 + (1200 - 1137.947811 ) / 244.1265

= 3.2542 years (Answer)

3)  Payback period for project B :

Initial investment in Year 0 = 1200

The calculations for payback period are shown below:

Project B
Years	Cash Flow	Cumulative Cash flow
1	250	250
2	290	540
3	420	960
4	770	1730

We can see from the above table that the cumulative cash flow is 960 year 3 and 1730 in year 4

So the payback period will be between year 3 & 4

Payback period = 3 + (Unrecovered amount in the 4th year) / (Cash flow in year 4)

= 3 + (1200 -960/ 770)

= 3.3117 years (Answer)

4)

Discounted Payback period for project B :

Initial investment in Year 0 = 1200

The calculations for Discounted payback period are shown below:

Years	Cash Flow(CF)	PV Factor@ 7% (pv)	CF *pv	Cumulative (CF *pv)
1	250	0.934579439	233.6448598	233.6448598
2	290	0.873438728	253.2972312	486.942091
3	420	0.816297877	342.8451083	829.7871993
4	770	0.762895212	587.4293133	1417.216513

We can see from the above table that the cumulative cash flow is 829.787199 in year 3 and 1417.21651 in year4

So the discounted payback period will be between year 3 & 4

Discounted Payback period = 3 + (Unrecovered amount in the 4th year) / (Discounted Cash flow in year 4)

= 3 + (1200 - 829.7871993) / 587.4293133

= 3.6302 Years(answer)