Question

(TCO E) A company has the opportunity to do any of the projects for which the net cash flows per year are shown below. The company has a cost of capital of 15%. Which should the company do and why? You must use at least two capital budgeting methods. Show your work.

Year	A	B	C
0	-300	-100	-300
1	100	50	100
2	100	100	100
3	100	100	100
4	100	100	100
5	100	100	100
6	100	100	100
7	100	200	0

Answer 1

Method 1-Payback period

This method refers to the period in which the proposal will generate cash to recover the initial investment made by it .It only emphasizes on the cash inflows, economic life of the project and the investment made in the project, with no consideration to time value of money. Through this method selection of a proposal is based on the earning capacity of the project .

Payback period = cash outlay (investment)/annual cash inflows

Years	0	1	2	3	4	5	6	7
Cash flows -A	-300	100	100	100	100	100	100	100
Cumulative cash flow	-300	-200	-100	0	100	200	300	400
Cash flows -B	-100	50	100	100	100	100	100	200
Cumulative cash flows	-100	-50	50	150	250	350	450	550
Cash flows -C	-300	100	100	100	100	100	100	0
Cumulative cash flows	-300	-200	-100	0	100	200	300	300

Payback period = years full recovery +unrecoverable cost at the beginning of next year /cash flows in the following year

A= 3+0= 3Years

B= 1+50/100 = 0.51years =6.12months

C= 3+0=3years

Method 2 - NPV method (Net present value method) with cost of capital 15%

NPV = Z1/1+r + Z2/(1+r)^{2 + ...} -X₀

Z1-cash flow in time 1 Z2-cash flow in time 2....

r-discounting rate (here cost of capital )

X₀-cash outflow in time

Year	1	2	3	4	5	6	7
Discount factor@15%	0.8695	0.7561	0.6575	0.5717	0.4971	0.4323	0.3759
Project A Undiscounted CF	100	100	100	100	100	100	100
Present value(Discount factor* Undiscounted CF)	86.98	75.61	65.75	57.17	49.71	43.23	37.59
Total present value	416.04
Project B Undiscounted CF	50	100	100	100	100	100	200
Present value	43.48	75.61	65.75	57.17	49.71	43.23	75.18
Total present value	410.13
Project C Undiscounted CF	100	100	100	100	100	100	0
Present value	86.98	75.61	65.75	57.17	49.71	43.23	0
Total present value	378.45

Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. NPV is used to analyze the profitability of a projected investment or project.

NPV of the projects :

A= Present value of cash inflows - outflows

= 416.04-300 =+ 116.04

B=410.13-100= + 310.13

C= 378.45-300=+ 78.45

Since Net present value of project B is greater than others, project B would be selected . Since all the 3 projects have positive NPV but project has highest NPV indicating higher profitability over and above its costs . Thus B would be selected .