Chapter 10, Problem 1OR

a)

Summary Introduction

To determine: The cost of capital of the project.

Introduction:

The difference between the present value of cash inflows and the present value of cash outflows over a period of time is known as the Net Present value.

Explanation of Solution

Given information:

The initial investment for the project is $83,600,000 and it creates an annual cash inflow of $18,800,000 for 12 years. The project NPV is $66,000,000 and the IRR is 20%.

It is given that the IRR must be less than 20%. However, it is given as 20%. Thus, the NPV will become zero.

Hence, Company S should discount the cash flows at less than 20%, as the NPV is positive.

b)

Summary Introduction

To determine: The cost of capital of the firm.

Introduction:

The difference between the present value of cash inflows and the present value of cash outflows for a particular period is known as the Net Present value. Cost of capital is the cost of long term financing of the firm.

Explanation of Solution

Given information:

The initial investment for the project is $83,600,000 and it generates an annual cash inflow of $18,800,000 for 12 years. The project NPV is $66,000,000 and the IRR is 20%.

 Explanation:

When the initial investment I₀, annual cash flow (AC), rate of interest r, and the time period n is given NPV can be calculated using the below equation:

$\text{NPV}=\text{AC}\frac{\left({\left(1+r\right)}^n-1\right)}{\text{r}{\left(1+r\right)}^n}-{\text{I}}_0$

By trial and error method let us assume the cost of capital to be 0.07.

$\begin{array}{c}\text{NPV}=18,800,000\left(\frac{\left({\left(1+0.07\right)}^{12}-1\right)}{0.07{\left(1+0.07\right)}^{12}}\right)-83,600,000\\ =\left(18,800,000\times 7.942686\right)-83,600,000\\ =149,322,502.4-83,600,000\\ =65,722,502.38\end{array}$

When substituting 11%, NPV is $65,722,502.38. The NPV is nearly equal to the given NPV $66,000,000. Thus, cost of capital of the firm is 7% (approximately).