Question

Kay Construction has the following mutually exclusive projects available. The company has historically used a three year cutoff for projects. The required return is 12 percent.

Year. Project A Project B

0. -$126,000. -$196,000

1. 64500. 44500

2. 45500. 59500

3. 55500. 85500

4. 50500. 115500

5. 45500. 130500

a. Calculate the payback period for both projects.

b. Calculate the NPV for both projects.

c. Which project, if any, should the company accept?

Answer 1

a
Project A
Year	Cash flow stream	Cumulative cash flow
0	-126000	-126000
1	64500	-61500
2	45500	-16000
3	55500	39500
4	50500	90000
5	45500	135500
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 2 and 3
therefore by interpolation payback period = 2 + (0-(-16000))/(39500-(-16000))
2.29 Years
Accept project as payback period is less than 3 years
Project B
Year	Cash flow stream	Cumulative cash flow
0	-196000	-196000
1	44500	-151500
2	59500	-92000
3	85500	-6500
4	115500	109000
5	130500	239500
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 3 and 4
therefore by interpolation payback period = 3 + (0-(-6500))/(109000-(-6500))
3.06 Years
Reject project as payback period is more than 3 years
b
Project A
Discount rate	0.12
Year	0	1	2	3	4	5
Cash flow stream	-126000	64500	45500	55500	50500	45500
Discounting factor	1	1.12	1.2544	1.404928	1.5735194	1.762342
Discounted cash flows project	-126000	57589.29	36272.32	39503.8	32093.663	25817.92
NPV = Sum of discounted cash flows
NPV Project A =	65277
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Accept project as NPV is positive
Project B
Discount rate	0.12
Year	0	1	2	3	4	5
Cash flow stream	-196000	44500	59500	85500	115500	130500
Discounting factor	1	1.12	1.2544	1.404928	1.5735194	1.762342
Discounted cash flows project	-196000	39732.14	47433.04	60857.21	73402.338	74049.2
NPV = Sum of discounted cash flows
NPV Project B =	99473.93
Where
Discounting factor =	(1 + discount rate)^(Corresponding period in years)
Discounted Cashflow=	Cash flow stream/discounting factor
Accept project as NPV is positive

c

Accept project A as NPV is positive and payback meets cutoff