Question

McCann Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $900 2 1,040 3 1,280 4 1,110 a. If the discount rate is 12 percent, what is the present value of these cash flows? b. What is the present value at 19 percent?

Consider the following two mutually exclusive projects: Year Cash Flow (A) Cash Flow (B) 0 –$272,703 –$15,035 1 27,800 4,583 2 52,000 8,185 3 58,000 13,305 4 389,000 9,509 Whichever project you choose, if any, you require a 6 percent return on your investment.

a. What is the payback period for Project A?

b. What is the payback period for Project B?

Answer 1

1. Net Present Value = NPV = ΣCF_n/(1+r)ⁿ

where, CF_n is the cash flow in period and r is the discount rate

(a) r = 12%

Given, CF₁ = 900
CF₂ = 1040
CF₃ = 1280
CF₄ = 1110

=> NPV = 900/(1+0.12) + 1040/(1+0.12)² + 1280/(1+0.12)³ + 1110/(1+0.12)⁴ = $3249.16

(b) r = 19%

CF₁ = 900
CF₂ = 1040
CF₃ = 1280
CF₄ = 1110

=> NPV = 900/(1+0.19) + 1040/(1+0.19)² + 1280/(1+0.19)³ + 1110/(1+0.19)⁴ = $2803.81

2.

To find Payback period, we need to find the cumulative cash flow

(a) Project A

Year	Cash Flow	Cumulative Cash Flow
0	-272703	-272703
1	27800	-244903
2	52000	-192903
3	58000	-134903
4	389000	254097

Payback period is the period when the cumulative cash flow becomes positive

=> Payback Period = 3 + 134903/389000 = 3.35 years

(b) Project B

Year	Cash Flow	Cumulative Cash Flow
0	-15035	-15035
1	4583	-10452
2	8185	-2267
3	13305	11038
4	9509	20547

Payback period = 2 + 2267/13305 =  2.17 years