Question

Waste Industries is evaluating a $56,900 project with the following cash flows.

Years		Cash Flows
1		$	9,710
2			19,200
3			26,500
4			19,800
5			27,300

The coefficient of variation for the project is 0.443.

Coefficient of Variation				Discount Rate
0	−	0.25			7	%
0.26	−	0.50			9	%
0.51	−	0.75			13	%
0.76	−	1.00			16	%
1.01	−	1.25			19	%

Use Appendix B for an approximate answer but calculate your final answer using the formula and financial calculator methods.

a. Select the appropriate discount rate.

• 7%

• 19%

• 13%

• 9%

• 16%

b. Compute the net present value. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations and round your answer to 2 decimal places.) Net present value: ________

c. Based on the net present value should the project be undertaken?

• No

• Yes

Answer 1

Requirement (a) – Appropriate Discount Rate

The coefficient of variation for the project of 0.443 is lies in between the slab of 0.26-0.50, therefore, the appropriate discount rate for the Project = 9%

Requirement (b) – Net Present Value (NPV) of the Project

Period	Annual Cash Flow ($)	Present Value factor at 9.00%	Present Value of Cash Flow ($)
1	9,710	0.917431	8,908.26
2	19,200	0.841680	16,160.26
3	26,500	0.772183	20,462.86
4	19,800	0.708425	14,026.82
5	27,300	0.649931	17,743.13
TOTAL			77,301.32

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $77,301.32 - $56,900

= $20,401.32

“The Net Present Value (NPV) of the Project will be $20,401.32”

Requirement (c) – DECISION

“YES”. As per NPV Decision Rule, the Project should be accepted only if the NPV is Positive, else, Reject the Project. Here, the NPV of the Project is Positive $20,401.32 and therefore, the Project should be raccepted.

NOTE

The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Discount Rate/Cost of capital and “n” is the number of years.