Question

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

Years		Cash Flows
1		$	9,240
2			15,800
3			21,200
4			25,400
5			33,200

The coefficient of variation for the project is 1.025.

Coefficient of Variation				Discount Rate
0	−	0.25			6	%
0.26	−	0.50			8	%
0.51	−	0.75			12	%
0.76	−	1.00			16	%
1.01	−	1.25			20	%

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.

• 6%

• 8%

• 12%

• 20%

• 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.)

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

• Yes

• No

B.)

Allison’s Dresswear Manufacturers is preparing a strategy for the fall season. One alternative is to expand its traditional ensemble of wool sweaters. A second option would be to enter the cashmere sweater market with a new line of high-quality designer label products. The marketing department has determined that the wool and cashmere sweater lines offer the following probability of outcomes and related cash flows.
  

	Expand Wool Sweaters Line							Enter Cashmere Sweaters Line
Expected Sales	Probability			Present Value of Cash Flows from Sales				Probability			Present Value of Cash Flows from Sales
Fantastic		0.4		$	226,000				0.3		$	366,000
Moderate		0.4			184,000				0.3			327,000
Low		0.2			93,300				0.4			0

The initial cost to expand the wool sweater line is $155,000. To enter the cashmere sweater line, the initial cost in designs, inventory, and equipment is $173,000.
  
a. Calculate net present value if, Allison’s Dresswear Manufacturers decides to: (Negative amounts should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to the nearest whole dollar.)
  

Answer 1

Requirement (a) – Appropriate Discount Rate

The coefficient of variation for the project of 1.025 is lies in between the slab of 1.01 – 1.25, therefore, the appropriate discount rate for the Project = 20%

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

Period	Annual Cash Flow ($)	Present Value factor at 20%	Present Value of Cash Flow ($)
1	9,240	0.833333	7,700.00
2	15,800	0.694444	10,972.22
3	21,200	0.578704	12,268.52
4	25,400	0.482253	12,249.23
5	33,200	0.401878	13,342.34
TOTAL			56,532.30

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

= $56,532.30 - $56,900

= -$367.70 (Negative NPV)

“The Net Present Value (NPV) of the Project will be -$367.70 (Negative NPV)“

Requirement (c) – DECISION

“NO”. 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 Negative $367.70 and therefore, the Project should be rejected.

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.