Question

Consider the following information:

	Cash Flows ($)
Project	C0	C1	C2	C3	C4
A	–6,200	2,200	2,200	2,900	0
B	–1,500	0	1,000	3,200	4,200
C	–3,800	2,200	1,300	1,700	1,200

a. What is the payback period on each of the above projects? (Round your answers to 2 decimal places.)

Project	Payback Period
A	year(s)
B	year(s)
C	year(s)

b. Given that you wish to use the payback rule with a cutoff period of two years, which projects would you accept?

	Project A, Project B, and Project C
	None
	Project A and Project C
	Project B and Project C
	Project A
	Project C
	Project B
	Project A and Project B

c. If you use a cutoff period of three years, which projects would you accept?

	Project A
	Project B
	Project A and Project C
	Project A, Project B, and Project C
	Project A and Project B
	Project C
	Project B and Project C

d. If the opportunity cost of capital is 12%, which projects have positive NPVs?

	Project A and Project B
	Project A and Project C
	Project A
	Project B
	Project A, Project B, and Project C
	Project C
	Project B and Project C

e. “If a firm uses a single cutoff period for all projects, it is likely to accept too many short-lived projects.” True or false?

	True
	False

f-1. If the firm uses the discounted-payback rule, will it accept any negative-NPV projects?

	Yes
	No

f-2. Will it turn down positive-NPV projects?

	Yes
	No

Answer 1

a.

Project	Payback Period
A	2.62 Years
B	2.16 Years
C	2.18 Years

Explanation:

Payback Period = A +B/C

Where,

A = Last period with a negative cumulative cash flow

B = Absolute value of cumulative cash flow at the end of the period A

C = Total cash flow during the period after A

	Project A		Project B		Project C
Year	Cash Flow	‘CUM Cash Flow	Cash Flow	‘CUM Cash Flow	Cash Flow	‘CUM Cash Flow
0	($6,200)	($6,200)	($1,500)	($1,500)	($3,800)	($3,800)
1	$2,200	($4,000)	$0	($1,500)	$2,200	($1,600)
2	$2,200	($1,800)	$1,000	($500)	$1,300	($300)
3	$2,900	$1,100	$3,200	$2,700	$1,700	$1,400
4	$0	$1,100	$4,200	$6,900	$1,200	$2,600

Payback period for Project A = 2 + $ 1,800/$ 2,900 = 2 + 0.6206896552 = 2.6206896552 or 2.62 years

Payback period for Project B = 2 + $ 500/$ 3,200 = 2 + 0.15625 = 2.15625 or 2.16 years

Payback period for Project C = 2 + $ 300/$ 1,700 = 2 + 0.1764705882 = 2.1764705882 or 2.18 years

b.

If cut-off period is of 2 years, none of the project is acceptable as all the projects have payback period more than 2 years.

c.

If cut-off period is of 3 years, all of the three projects are acceptable as all the projects have payback period less than 3 years. So Project A, Project B, Project C is acceptable.

d.

If opportunity cost of capital is 12 %, Project B and Project C have positive NPVs.

Explanation:

			Project A		Project B		Project C
Year	PV Factor Computation	PV Factor @ 12 % (F)	Cash Flow (CA)	PV (F x CA)	Cash Flow (CB)	PV (F x CB)	Cash Flow (CC)	PV (F x CC)
0	1/(1+0.12)0	1	($6,200)	($6,200.00)	($1,500)	($1,500)	($3,800)	($3,800)
1	1/(1+0.12)1	0.892857142857143	$2,200	$1,964.2857	$0	$0	$2,200	$1,964
2	1/(1+0.12) 2	0.797193877551020	$2,200	$1,753.8265	$1,000	$797	$1,300	$1,036
3	1/(1+0.12)3	0.711780247813411	$2,900	$2,064.1627	$3,200	$2,278	$1,700	$1,210
4	1/(1+0.12)4	0.635518078404831	$0	$0.0000	$4,200	$2,669	$1,200	$763
			NPV	($417.7250)	NPV	$4,244.0666	NPV	$1,173.2859

e.

“If a firm uses a single cutoff period for all projects, it is likely to accept too many short-lived Projects.”

True.

f-1.

No, the firm will not accept any project with negative NPV. Discounted payback period cannot be computed for such negative NPV projects.

f-2.

The firm may turn-down positive NPV project, if discounted payback period is higher than cut-off period.