Chapter 7, Problem 1P

Your brother wants to borrow $10,000 from you. He has offered to pay you back $12,000 in a year. If the cost of capital of this investment opportunity is 10%, what is its NPV? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

Summary Introduction

To calculate: The net present value and internal rate of return

Introduction:

NPV and IRR help to make capital-budget decisions. It would choose an alternative or an investment to increase the value of an enterprise.

Answer to Problem 1P

The NPV is 909.09 and IRR is 20%.

Explanation of Solution

Given information: Person X’s brother wishes to borrow $10,000 from Person X and offered to pay back $12,000 per year. The cost of capital for the investment opportunity is 10%.

Formula to compute the NPV:

$\begin{array}{c}\text{NPV}=\text{Cash inflow}-\text{Cash outflow}\\ \text{=}\left(\frac{\text{Cash inflow}}{{\left(1+r\right)}^1}\right)-\text{Cash outflow}\end{array}$

Compute the NPV:

$\begin{array}{c}\text{NPV}=\left(\frac{\text{Cash inflow}}{{\left(1+r\right)}^1}\right)-\text{Cash outflow}\\ \text{=}\frac{\$12,000}{{\left(1+0.1\right)}^1}-\$10,000\\ =\$10,909.09-\$10,000\\ =\$909.09\end{array}$

Hence, the NPV is $909.09.

Formula to compute IRR:

$\text{IRR}=\frac{\text{Cash inflow}}{\text{Cash outflow}}-1$

Compute the IRR:

$\begin{array}{l}\text{IRR}={\left(\frac{\text{Cash inflow}}{\text{Cash outflow}}\right)}^{\frac{1}{n}}-1\\ ={\left(\frac{\$12,000}{\$10,000}\right)}^{\frac{1}{1}}-1\\ =\$1.2-1\\ =20\%\end{array}$

Hence, the IRR is 20%.

Determine the maximum deviation allowable in the cost of capital without making any changes to the decision:

The calculated internal rate of return is 20%. Hence, the cost of capital can be increased up to 10% leaving the decision unchanged.