Chapter 17, Problem 5E

a)

To determine

To describe: The internal rate of return and the net present value.

Answer to Problem 5E

The internal rate of return is approximately 15% and the NPV is close to zero.

Explanation of Solution

To purchase the contract of Bobcats, the net investment (NINV) is $\$800,000$

The rate of return after tax is $k=12\%$

Income tax rate is $t=40\%$

The investment depreciates over the four year period.

So, the depreciation per year is $\frac{\$800,000}{4}=\$200,000$

The net cash flow in each of the year calculated as,

Year	Incremental Returns	Depreciation	Net Cash Flow
1	$\$450,000$	$\$200,000$	$\left(\$450,000-\$200,000\right)\left(1-0.6\right)+\$200,000=\$350,000$
2	$\$350,000$	$\$200,000$	$\left(\$350,000-\$200,000\right)\left(1-0.6\right)+\$200,000=\$290,000$
3	$\$275,000$	$\$200,000$	$\left(\$275,000-\$200,000\right)\left(1-0.6\right)+\$200,000=\$245,000$
4	$\$200,000$	$\$200,000$	$\left(\$200,000-\$200,000\right)\left(1-0.6\right)+\$200,000=\$200,000$

The net present value (NPV) of the investment is,

  $NPV={\displaystyle \sum _{t=1}^n\frac{NFC}{{\left(1+k\right)}^t}-NINV}$

So, the net present value (NPV) of the investment is,

  $\begin{array}{l}NPV=\frac{\$350,000}{{\left(1+0.12\right)}^1}+\frac{\$290,000}{{\left(1+0.12\right)}^2}+\frac{\$245,000}{{\left(1+0.12\right)}^3}+\frac{\$200,000}{{\left(1+0.12\right)}^4}-\$800,000\\ =\$312,000+\$231,186+\$174,377+\$127,065-\$800,000\\ =\$45,128\end{array}$

Bcats should sign the superstars, as $NPV>0$

The internal rate of return $(r)$ makes the net present value zero.

Let’s assume that $r=13\%$

The net present value (NPV) of the investment is,

  $\begin{array}{l}NPV=\frac{\$350,000}{{\left(1+0.13\right)}^1}+\frac{\$290,000}{{\left(1+0.13\right)}^2}+\frac{\$245,000}{{\left(1+0.13\right)}^3}+\frac{\$200,000}{{\left(1+0.13\right)}^4}-\$800,000\\ =\$309,735+\$227,113+\$169,785+\$122,699-\$800,000\\ =\$29,332\end{array}$

Now, let’s assume that $r=14\%$

The net present value (NPV) of the investment is,

  $\begin{array}{l}NPV=\frac{\$350,000}{{\left(1+0.14\right)}^1}+\frac{\$290,000}{{\left(1+0.14\right)}^2}+\frac{\$245,000}{{\left(1+0.14\right)}^3}+\frac{\$200,000}{{\left(1+0.14\right)}^4}-\$800,000\\ =\$307,018+\$223,146+\$165,317+\$118,413-\$800,000\\ =\$13,892\end{array}$

Now, again let’s assume that $r=15\%$

The net present value (NPV) of the investment is,

  $\begin{array}{l}NPV=\frac{\$350,000}{{\left(1+0.15\right)}^1}+\frac{\$290,000}{{\left(1+0.15\right)}^2}+\frac{\$245,000}{{\left(1+0.15\right)}^3}+\frac{\$200,000}{{\left(1+0.15\right)}^4}-\$800,000\\ =\$304,348+\$219,282+\$161,078+\$114,351-\$800,000\\ =-\$941\end{array}$

At $r=15\%$ , the NPV is close to zero. So, the internal rate of return is approximately 15%

Economics Concept Introduction

Introduction:

The internal return rate (IRR) describes a metric used to estimate the return on potential investments for the purpose of capital budgeting. The internal rate of return is a discount rate equal to zero for a given project, the net present value (NPV) of all the cash flows.

b)

To determine

To describe: That Bcats should sign the superstars.

Answer to Problem 5E

Bcats should sign the superstars.

Explanation of Solution

Since the internal rate of return exceeds the required rate of return $\left(r>k\right)$ , Bcats should sign the superstars.

Economics Concept Introduction

Introduction:

The internal return rate (IRR) describes a metric used to estimate the return on potential investments for the purpose of capital budgeting. The internal rate of return is a discount rate equal to zero for a given project, the net present value (NPV) of all the cash flows.