Question

You are a consultant to a firm evaluating an expansion of its current business. The cash-flow forecasts (in millions of dollars) for the project are as follows:

Years	Cash Flow
0	−260
1–10	+60

a.

On the basis of the behavior of the firm’s stock, you believe that the beta of the firm is 1.3. Assuming that the rate of return available on risk-free investments is 6% and that the expected rate of return on the market portfolio is 14%, what is the net present value of the project? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

NPV

$

b.	Should the project be accepted?
	Yes No

Answer 1

Step-1, The Calculation of the required rate of return on the stock

As per Capital Asset Pricing Model [CAPM], the required rate of return for the stock is calculated by using the following equation

The required rate of return = Risk-free Rate + Beta[Market rate of return – risk-free rate]

= 6.00% + 1.30[14.00% - 6.00%]

= 6.00% + [1.30 x 8.00%]

= 6.00% + 10.40%

= 16.40%

Step-2, The Net Present Value (NPV) of the Project

Year	Annual Cash flow ($ in millions)	Present Value factor at 16.40%	Present Value of Annual Cash flows ($ in millions)
1	60.00	0.85911	51.55
2	60.00	0.73806	44.28
3	60.00	0.63408	38.04
4	60.00	0.54474	32.68
5	60.00	0.46799	28.08
6	60.00	0.40205	24.12
7	60.00	0.34541	20.72
8	60.00	0.29674	17.80
9	60.00	0.25493	15.30
10	60.00	0.21901	13.14
TOTAL			285.73

Net Present Value (NPV) of the Project = Present value of annual cash inflows – Initial investment costs

= $285.73 Million - $260 Million

= $25.73 Million

“The Net Present Value (NPV) of the Project will be $25.73 Million“

DECISION

“YES”. The project should be accepted, since the Net Present Value (NPV) of the Project is Positive $25.73 Million”

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.