Question

1. Gutweed Co. is considering a project with an initial cost of $4 million. The project will produce cash inflows of $1.5 million a year for five years. The firm has a weighted average cost of capital of 9%. Assume that the project has an average risk level as the whole firm. What is the net present value of the project?

   		$1.83 million
   		$3.22 million
   		$0.92 million
   		$2.41 million

Given the following data for a stock: beta = 1.2; risk-free rate = 3%; market rate of return = 13%; and expected rate of return on the stock = 17%. Then the stock is:

		overpriced
		correctly priced
		underpriced
		cannot be determined

Answer 1

1. Calculation of NPV (Net Present Value)

Answer: NPV = 1.83449 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 @ 9% (WACC)	Present Value of cash flow
(I)	(II)	(III)	(II) * (III)
1	$1.5	0.91743	$1.37615
2	$1.5	0.84168	$1.26252
3	$1.5	0.77218	$1.15827
4	$1.5	0.70843	$1.06265
5	$1.5	0.64993	$0.97490
Present Value of the Cash flows inflows			$ 5.83449

Initial Investment =$ 4 million/- (provided in the question)

NPV = Present Value of future cash inflows – Initial Investment

NPV = $5.83449 million - $ 4 million

= 1.83449 Million

Calculation of Discounting Factor (Present Value Factor)

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

R = Discount Rate (i.e. = 9%)

N = No of years

E.g. for year 2 Discount Factor = 1/ (1.09)²

                                                                ⁼ 1/ (1.09) (1.09)

                                                =   0.84168

2. Given the following data for a stock: beta = 1.2; risk-free rate = 3%; market rate of return = 13%; and expected rate of return on the stock = 17%. Then the stock is:

Answer: Underpriced

A stock is said to be

1. Underpriced when excepted return of the stock is more than the required rate of return.
2. Overpriced when excepted return of the stock is less than the required rate of return.
3. Correctly priced excepted return of the stock is equal to the required rate of return.

In order to find out stock is overpriced or underpriced we need to compare expected return and required rate of return.

Expected return = 17%

Required rate of return is not provided in the question so we need to find the same using CAPM

Required rate of return as per CAPM = R_f + β (Rm _- R_f)

Where,

R_{f =}Risk free rate of return = 3%

β = Beta of stock B = 1.2

Rm = Market return = 13%

Required rate of return = 3% + 1.2 (13 % - 3%)

                                      =3% +12%

                                      =15%

Comparison of Stock

Expected return = 17%

Required rate of return = 15%

Since excepted return of the stock is more than the required rate of return, stock is said to be underpriced.