Question

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 10%.

	0		1		2		3		4
Project A	-900		700		410		220		270
Project B	-900		300		345		370		720

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

Given :

1. WACC =  10%.

2. Cash flows of Project A & Project B

Year	Project A	Project B
0	$(900)	$(900)
1	$700	$300
2	$410	$345
3	$220	$370
4	$270	$720

Part a) Calculation of Project A's payback

Year	Cash flows	Cumulative cash flows
0	$(900)	$(900)
1	$700	$(200)
2	$410	$210
3	$220	$430
4	$270	$700

Pay back period can be calculated using Cumulative cash flows

Pay back period = A + B/C

Where,
A is the last period number in which we have negative cumulative cash flow (i.e.. 1)
B is the cumulative net cash flow (ignoring negative sign) at the end of the period A (i.e.., 200)
C is the total cash inflow during the period following period A (i.e.. 410)

Pay back period = 1 + 200/410 = 1 + 0.487805 = 1.487805 or 1.4878 years

Pay back period = 1.4878 years

Part b) Calculation of Project A's discounted payback

Year	Cash flows	PVF@10%	Discounted cash flows	Cumulative Discounted cash flows
0	$(900)	1	$(900.0000)	$(900.0000)
1	$700	0.90909090	$636.3636	$(263.6364)
2	$410	0.82644628	$338.8430	$75.2066
3	$220	0.75131480	$165.2893	$240.4959
4	$270	0.68301346	$184.4136	$424.9095

Discounted Pay back period can be calculated using cumulative discounted cash flows

Discounted Cash Flow = Cash Flow / (1+r)^n
where R = WACC i.e.. 10%
And n = Period of Cash flows i.e.. 0,1,2 & so on

Discounted Pay back period = A + B/C

Where,
A is the last period number in which we have negative cumulative discounted cash flow (i.e.. 1)
B is the cumulative discounted cash flow (ignoring negative sign) at the end of the period A (i.e.., $263.6364)
C is the total discounted cash inflow during the period following period A (i.e.. $338.8430)

Discounted Pay back period = 1 + 263.6364/338.8430 = 1 + 0.778049 = 1.778049 or 1.7780 years

Discounted Pay back period = 1.7780 years

Part c) Calculation of Project B's payback

Year	Cash flows	Cumulative cash flows
0	$(900)	$(900)
1	$300	$(600)
2	$345	$(255)
3	$370	$115
4	$720	$835

Pay back period can be calculated using Cumulative cash flows

Pay back period = A + B/C

Where,
A is the last period number in which we have negative cumulative cash flow (i.e.. 2)
B is the cumulative net cash flow (ignoring negative sign) at the end of the period A (i.e.., $255)
C is the total cash inflow during the period following period A (i.e..  $370)

Pay back period = 2 + 255/370 = 1 + 0.689189 = 2.689189 or 2.6892 years

Pay back period = 2.6892 years

Part d) Calculation of Project B's discounted payback

Year	Cash flows	PVF@10%	Discounted cash flows	Cumulative Discounted cash flows
0	$(900)	1	$(900.0000)	$(900.0000)
1	$300	0.909090909	$272.7273	$(627.2727)
2	$345	0.826446281	$285.1240	$(342.1488)
3	$370	0.751314801	$277.9865	$(64.1623)
4	$720	0.683013455	$491.7697	$427.6074

Discounted Pay back period can be calculated using cumulative discounted cash flows

Discounted Cash Flow = Cash Flow / (1+r)^n
where R = WACC i.e.. 10%
And n = Period of Cash flows i.e.. 0,1,2 & so on

Discounted Pay back period = A + B/C

Where,
A is the last period number in which we have negative cumulative discounted cash flow (i.e.. 3)
B is the cumulative discounted cash flow (ignoring negative sign) at the end of the period A (i.e.., $64.1623)
C is the total discounted cash inflow during the period following period A (i.e.. $277.9865)

Discounted Pay back period = 3 + 64.1623/277.9865 = 3 + 0.130472 = 3.130472 or 3.1305 years

Discounted Pay back period = 3.1305 years