Chapter 17, Problem 1E

A firm has the opportunity to invest in a project having an initial outlay of $20,000. Net cash inflows (before depreciation and taxes) are expected to be $5,000 per year for five years. The firm uses the straight-line depreciation method with a zero salvage value and has a (marginal) income tax rate of 40 percent. The firm’s cost of capital is 12 percent.

1. Compute the IRR and the NPV.
2. Should the firm accept or reject the project?

To determine

To compute: The IRR (Internal Rate of Return) and NPV (Net Present Value).

Answer to Problem 1E

IRR (Internal Rate of Return) value is 0.217

NPV (Net Present Value) is 4500

Explanation of Solution

Given:

Firm having the initial outlay =$20,000

Expected Net cash inflows=$5,000

Firm’s cost capital=12 percent

Explain:

It will be calculated internal rate of return (IRR):

  $\frac{{\displaystyle {\sum }_{t=1}^{5}NCF}}{{\left(1+r\right)}^t}$

  $=NNIV$

  $‘r’$ stands for internal rate of return, NCF stands for Net cash Flow and NNIV stands for initial outlay

  $\frac{{\displaystyle {\sum }_{t=1}^{5}7000}}{{\left(1+r\right)}^t}$

  $=20000$

  $\frac{{\displaystyle {\sum }_{t=1}^{5}1}}{{\left(1+r\right)}^t}$

  $=2.86$

In the table of annuity, 2.86 lies between 30.5 and 2.49, therefore r lies between $0.0-0.25$

  $r=0.2+\frac{\left\{\frac{\left(3.05-2.86\right)}{\left(3.05-2.49\right)}\right\}}{\left(0.25-0.2\right)}$

  $r=0.2+\frac{\left(0.19\right)\left(0.05\right)}{0.56}$

  $=0.217$

Now calculate net present value (NPV):

  $NVP=\frac{{\displaystyle {\sum }_{t=1}^{5}NCF}}{{\left(1+k\right)}^t-NINV}$

k stands for cost of equity, NCF stands for Net cash Flow and NNIV stands for initial outlay.

  $NVP=\frac{{\displaystyle {\sum }_{t=1}^{5}7000}}{{\left(1.12\right)}^t-20000}$

  $=7000\left\{\frac{1}{1.12}+\frac{1}{{\left(1.12\right)}^2}+\frac{1}{{\left(1.12\right)}^3}+\frac{1}{{\left(1.12\right)}^4}+\frac{1}{{\left(1.12\right)}^5}\right\}-20000$

  $=7000\left(0.9+0.8+0.7+0.6+0.5\right)-20000$

  $=7000\left(35\right)-20000$

  $=24500-20000$

  $=4500$

To determine

To describe: Whether the firm will accept or reject the project.

Answer to Problem 1E

Yes, the firm should accept the project.

Explanation of Solution

Firm having the initial outlay is $20,000

Expected Net cash inflows are $5,000

Firm’s cost capital is 12 percent and also the firm uses the straight-line depreciation method with a zero-salvage value.

Since, Internal Rate of Return (IRR) is greater than the cost of capital and Net Present Value (NPV) is greater than zero.

Hence, the firm should accept the project.