Question

Your division is considering two investment projects, each of which requires an up-front expenditure of $35 million. You estimate that the cost of capital is 10% and the the investment will produce the following after-tax- cash flows (in millions of dollars):

Year	Project A	Project B
1	$25	$15
2	$25	$25
3	$25	$35
4	$25	$45

a.What is the payback Period for each of the projects (assume cash flows occur evenly during the year, 1/365th each day)?

b. Computer the net present value (NPV) for each project. c. if the two projects are independent, which projects should the firm undertake?

d. If the two projects are mutually exclusive, which project or projects the firm undertake?

Answer 1

1. What is the payback period for the investment?

Payback period for project - A

Answer: 1.4 years OR 1 year and 146 days

Total Initial Capital Investment = $35 Million   

Annual Expected after tax cash flow = $25 Million

Payback period = $35 Million ÷ $25 Million

                      = 1.4 years OR 1 year and 146 days (i.e. 365 days * .4)

Payback period for Project – B

Answer: 1.8 years or 1 year and 292 days

When the annual cash flows are not uniform, the cumulative cash inflows from operations must be calculated for each year. The payback period shall be corresponding period when total of cumulative cash inflows is equal to the initial capital investment. However, if exact sum does not match then the period in which it lies should be identified. After that we need to compute the fraction of the year.

Initial capital investment = $35 Million

Cash flows

Year	Cash flow (in Millions)	Cumulative cash flow (In Millions)
1	$15	$15
2	$25	$40
3	$35	$75
4	$45	$120

Payback period in this case will lie between year 1 and year 2. Since up to year 1 a sum of $15 million shall be recovered, balance of $20 shall be recovered in the part (Fraction) of 2^ndyear, Computation is as follows

            = (Balance recoverable ÷ Cash flow of year 4)

= ($20 million ÷ $ 25 million)

            =.80 years

               

Payback period = 1.8 years or 1 year and 292 days (i.e. 365 *.80)

$15 million will be received in year1 and cash flow of balance $20 million will be received in 0.8 years (292 days) . So Total payback period will be 1.8 years (1year and 292 days)

2. Calculation of NPV (Net Present Value)

Project A NPV

Answer: NPV =$44.24650 Million

NPV = Present Value of future cash inflows – Initial Investment

Calculation of Present value of cash inflows for project

Year	Cash Flow (In Millions)	Present Value Factor @ 10% (Cost of Capital)	Present Value of cash flow
(I)	(II)	(III)	(II) * (III)
1	$25	0.90909	$ 22.72725
2	$25	0.82645	$ 20.66125
3	$25	0.75131	$ 18.78275
4	$25	0.68301	$ 17.07525
Present Value of the Cash flows inflows			$ 79.24650

Initial Investment =$35 million/- (provided in the question)

NPV = Present Value of future cash inflows – Initial Investment

NPV = $79. 24650 million – $35 million

                 

                   = $ 44.24650 Million

Project B NPV

Answer: NPV =$56.32890 Million

NPV = Present Value of future cash inflows – Initial Investment

Calculation of Present value of cash inflows for project

Year	Cash Flow (In Millions)	Present Value Factor @ 10% (Cost of Capital)	Present Value of cash flow
(I)	(II)	(III)	(II) * (III)
1	$15	0.90909	$13.63635
2	$25	0.82645	$20.66125
3	$35	0.75131	$26.29585
4	$45	0.68301	$30.73545
Present Value of the Cash flows inflows			$91.32890

Initial Investment =$35 million/- (provided in the question)

NPV = Present Value of future cash inflows – Initial Investment

NPV = $91.32890 million – $35 million

                 

                   = $ 56.32890 Million

Notes

Calculation of Discounting Factor (Present Value Factor)

Discount Factor = 1/ (1+R) ^N

R = Discount Rate (i.e. = 10%)

N = No of years

E.g. for year 2 Discount Factor = 1/ (1.10)²

                                                                ⁼ 1/ (1.10) (1.10)

                                                =0.82645

3. If two projects are independent which project should the firm undertake?

Answer: firm can undertake both projects A & B

A project is said to be independent, when project whose acceptance or rejection is independent of the acceptance or rejection of other projects.

In case of independent projects firm can invest in all projects which are profitable

In the given case both projects are having positive NPV and Payback period is within the maximum acceptable payback period of 5 years

(Please refer the decision rule provided at the end)

4. If the 2 projects are mutually exclusive, which project or projects the firm undertake?

Mutually Exclusive project refer to a set of projects out of which only one project can be selected for investment. If one project is selected other projects are rejected. We can only select one project.

Answer

As per NPV method: project B (project with highest positive NPV)

As per Payback method: Project A (project with shortest payback period)

Decision Rule for NPV

For Independent Projects	For Mutually Exclusive Projects
When NPV>0 Accept the project When NPV< 0 Reject the project	Project with Highest positive NPV should be selected.

Decision rule for Payback period

For Independent Projects	For Mutually Exclusive Projects
When payback period less than or equal to Maximum Acceptable payback period = Accept the project. When payback period more than or equal to Maximum Acceptable payback period = Reject the project.	Project with least payback period should be selected.

Project	Payback period	NPV
A	1.4 years	$44.2465
B	1.8 years	$56.3289