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 8%.

	0		1		2		3		4
Project A	-900		700		360		250		300
Project B	-900		300		295		400		750

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

Payback period is the period in which the project initial investment is recovered by the future cash flows

a. Payback period of project A is computed as follows:

Year	Cash flows	Cumulative cash flows
0	- 900	- 900
1	700	- 200 ( -900 + 700 )
2	360	160 ( -200 + 360 )

As we can see the investment of 900 is recovered between year 1 and year 2, which means the payback period lies between them and is computed as shown below:

= 1 year + investment to be recovered / next years cash flows

= 1 year + 200 / 360

= 1.5556 years approximately

b. Discounted payback period is computed as follows:

Year	Cash flows	Discounted cash flows	Cumulative discounted cash flows
0	- 900	- 900	- 900
1	700	= 700 / 1.08 = 648.1481 Approximately	- 251.8519 ( -900 + 648.1481 )
2	360	= 360 / 1.082 = 308.6420 Approximately	56.7901 ( -251.8519 + 308.6420 )

As we can see the investment of 900 is recovered between year 1 and year 2, which means the payback period lies between them and is computed as shown below:

= 1 year + investment to be recovered / next years discounted cash flows

= 1 year + 251.8519 / 308.6420

= 1.8160 years approximately

c. Payback period of project B is computed as follows:

Year	Cash flows	Cumulative cash flows
0	- 900	- 900
1	300	- 600 ( -900 + 300 )
2	295	- 305 ( -600 + 295 )
3	400	95 ( -305 + 400 )

As we can see the investment of 900 is recovered between year 2 and year 3, which means the payback period lies between them and is computed as shown below:

= 2 years + investment to be recovered / next years cash flows

= 2 years + 305 / 400

= 2.7625 years approximately

d. Discounted payback period is computed as follows:

Year	Cash flows	Discounted cash flows	Cumulative discounted cash flows
0	- 900	- 900	- 900
1	300	= 300 / 1.08 = 277.7778 Approximately	- 622.2222 ( -900 + 277.7778 )
2	295	= 295 / 1.082 = 252.9150 Approximately	-369.3072 ( -622.2222 + 252.9150 )
3	400	= 400 / 1.083 = 317.5329 Approximately	-51.7743 ( -369.3072 + 317.5329 )
4	750	= 750 / 1.084 = 551.2724 Approximately	499.4981 ( -51.7743 + 551.2724 )

As we can see the investment of 900 is recovered between year 3 and year 4, which means the payback period lies between them and is computed as shown below:

= 3 years + investment to be recovered / next years discounted cash flows

= 3 years + 51.7743 / 551.2724

= 3.0939 years approximately

Feel free to ask in case of any query relating to this question