Question

B 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. B's WACC is 9%.

	0		1		2		3		4
Project A	-950		650		385		260		310
Project B	-950		250		320		410		760

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

To calculate the payback period we simply need to subtract the CF from the initial cost of investment:

Project A

Year	Opening Balance	CF	Closing Balance
1	$                  950.00	$                         650.00	$               300.00
2	$                  300.00	$                         385.00	$                -85.00

• Opening balance of year 1= Cost
• Opening balance = previous year's closing balance for all years after year 1
• Closing balance = Opening balance - CF
• When the closing balance becomes negative or 0, the CFs of the following years are not considered
• The closing balance of year 1 was 300 and the CF for year 2 was 385 so the portion of year during which the 300 is recovered is 300/385= 0.78
• So the payback period is 1.78 years

To calculate the discounted payback period, we first need to calculate the discounted CFs:

Year	CF	Discount Factor	Discounted CF
0	$-950.00	1/(1+0.09)^0=	1	1*-950=	$ -950.0000
1	$ 650.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*650=	$   596.3303
2	$ 385.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*385=	$   324.0468
3	$ 260.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*260=	$   200.7677
4	$ 310.00	1/(1+0.09)^4=	0.708425211	0.708425211065196*310=	$   219.6118

Now using the discounted CF, we can calculated the discounted payback period:

Year	Opening Balance	DCF	Closing Balance
1	$                  950.00	$                         596.33	$               353.67
2	$                  353.67	$                         324.05	$                  29.62
3	$                    29.62	$                         200.77	$              -171.14

• The closing balance of year 2 was 29.62 and the CF for year 3 was 200.77 so the portion of year during which the 29.62 is recovered is 29.62/200.77= 0.15
• So the discounted payback period is 2.15 years

Project B

Year	Opening Balance	CF	Closing Balance
1	$                  950.00	$                         250.00	$               700.00
2	$                  700.00	$                         320.00	$               380.00
3	$                  380.00	$                         410.00	$                -30.00

• The closing balance of year 2 was 380 and the CF for year 3 was 410 so the portion of year during which the 300 is recovered is 380/410= 0.93
• So the payback period is 2.93 years

Now we calculate the discounted CF of project B:

Year	CF	Discount Factor	Discounted CF
0	$-950.00	1/(1+0.09)^0=	1	1*-950=	-950.00
1	$ 250.00	1/(1+0.09)^1=	0.917431193	0.91743119266055*250=	229.36
2	$ 320.00	1/(1+0.09)^2=	0.841679993	0.84167999326656*320=	269.34
3	$ 410.00	1/(1+0.09)^3=	0.77218348	0.772183480061064*410=	316.60
4	$ 760.00	1/(1+0.09)^4=	0.708425211	0.708425211065196*760=	538.40

Year	Opening Balance	DCF	Closing Balance
1	$                  950.00	$                         229.36	$               720.64
2	$                  720.64	$                         269.34	$               451.30
3	$                  451.30	$                         316.60	$               134.71
4	$                  134.71	$                         538.40	$              -403.69

• The closing balance of year 3 was 134.71 and the CF for year 4 was 538.40 so the portion of year during which the 300 is recovered is 134.71/538.40= 0.25
• So the discounted payback period is 3.25 years