Question

Consider the following projects:

Cash Flows ($)
Project	C0	C1	C2	C3	C4	C5
A	−2,500	2,500	0	0	0	0
B	−5,000	2,500	2,500	5,500	2,500	2,500
C	−6,250	2,500	2,500	0	2,500	2,500

a. If the opportunity cost of capital is 9%, which project(s) have a positive NPV?

Positive NPV project(s)

	Project A
	Project B
	Project C
	Projects A and B
	Projects A and C
	Projects B and C
	Projects A, B, and C
	No project

b. Calculate the payback period for each project: (Round your answers to 2 decimal places. If a project never pays back, enter "0".)

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

c. Which project(s) would a firm using the payback rule accept if the cutoff period were three years?

Project(s) accepted                  (Click to select)Project AProject BProject CProjects A and BProjects A and CProjects B and CProjects A, B, and CNo project

d. Calculate the discounted payback for each project. (Do not round intermediate calculations. Round your answers to 2 decimal places. If a project never pays back, enter "0".)

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

e. Which project(s) would a firm using the discounted payback rule accept if the cutoff period were three years?

Project(s) accepted                (Click to select)Project A Project B Project C Projects A and B Projects A and C Projects B and C Projects A, B, and C No project

Answer 1

Part a:
Project B and project C have positive NPV.

9% shown in the NPV formula (in excel) is the cost of capital.

Part b:

Payback period for project A:

Cash flows for project A:

Net cash flow:
C0:-$2,500
C1:$2,500
C2:0
C3:0
C4:0
C5:0

Cumulative net cash flow:
C0:-$2,500
C1:$2,500-$2,500=$0
C2:0
C3:0
C4:0
C5:0

Payback Period=Full years until recovery+(Unrecovered cost at the beginning of last year)/(Cash flow during the last year)

Payback Period=1+0=1 years

Cash flow for project B:
Project B
C0:-$5,000
C1:$2,500
C2:$2,500
C3:$5,500
C4:$2,500
C5:$2,500

Cumulative net cash flow:
C0:-$5,000
C1:$2,500-$5,000=-$2,500
C2:$2,500-$2,500=$0
C3:$5,500
C4:$2,500
C5:$2,500
Payback Period=2

Cash flow for project C:
C0:-$6,250
C1:$2,500
C2:$2,500
C3:$0
C4:$2,500
C5:$2,500

Cumulative cash flow for project C
C0:-$6,250
C1:$2,500-$6,250=-$3750
C2:$2,500-$3750=-$1250
C3:$0-$1250=-$1250
C4:$2,500-$1250=$1250
C5:$2,500

Payback period=3+$1250/$2,500=3.5 years

Part c:
The firm would accept project A and project B if the cutoff payback period were three years.

Part d:

Discounted payback period for project A at a cost of capital of 9%:

Cash flows for project A:
Net cash flow:
C0:-$2,500
C1:$2,500
C2:0
C3:0
C4:0
C5:0

Discounted net cash flow:
C0:-$2,500
C1:$2,500/(1+9%)^1=$2,500/(1.09)^1=$2293.577982
C2:0
C3:0
C4:0
C5:0

Cumulative discounted net cash flow:
C0:-$2,500
C1:$2293.577982-$2,500=$-206.422018
C2:0
C3:0
C4:0
C5:0

Payback period=0

Cash flow for project B:
Project B
C0:-$5,000
C1:$2,500
C2:$2,500
C3:$5,500
C4:$2,500
C5:$2,500

Discounted net cash flow:
Project B
C0:-$5,000
C1:$2,500/(1+9%)=$2,500/(1.09)^1=$2293.577982
C2:$2,500/(1+9%)^2=$2,500/(1.09)^2=$2104.199983
C3:$5,500/(1+9%)^3=$5,500/(1.09)^3=$4247.00914
C4:$2,500/(1+9%)^4
C5:$2,500/(1+9%)^5

Cumulative discounted net cash flow:
C0:-$5,000
C1:$2293.577982-$5,000=-$2706.422018
C2:$2104.199983-$2706.422018=-$602.222035
C3:$4247.00914-$602.222035=$3644.787105

Payback Period=Full years until recovery+(Unrecovered cost at the beginning of last year)/(Cash flow during the last year)
=2+$602.222035/$4247.00914=2+0.141799091 or 2.14 years (Rounded to 2 decimal places)

Cash flow for project C:
C0:-$6,250
C1:$2,500
C2:$2,500
C3:$0
C4:$2,500
C5:$2,500

Discounted cash flow for project C at a cost of capital of 9%:
C0:-$6,250
C1:$2,500/(1+9%)^1=$2,500/(1.09)^1=$2293.577982
C2:$2,500/(1+9%)^2=$2,500/(1.09)^2=$2104.199983
C3:$0/(1+9%)^3=$0
C4:$2,500/(1+9%)^4=$2,500/(1.09)^4=$1771.063028
C5:$2,500/(1+9%)^5=$2,500/(1.09)^5=$1624.828466

Cumulative discounted net cash flow:

C0:-$6,250
C1:$2293.577982-$6,250=-$3956.422018
C2:$2104.199983-$3956.422018=-$1852.222035
C3:$0-$1852.222035=-$1852.222035
C4:$1771.063028-$1852.222035=-$81.159007
C5:$1624.828466-$81.159007=$1543.669459
Payback Period=Full years until recovery+(Unrecovered cost at the beginning of last year)/(Cash flow during the last year)
=4+$81.159007/$1624.828466=4+0.049949277=4.049949277 or 4.05 Years (Rounded to 2 decimal places)

Part e:
Only project B can be selected as the discounted payback period is less than 3 years and the whole amount is paid back.