# Henry is offered an investment with the following conditions: The cost of the investment is 1,000...

## Question:

Henry is offered an investment with the following conditions:

The cost of the investment is 1,000

The investment pays out a sum X at the end of the first year; this payout grows at the rate of 10% per year for 11 years.

If his discount rate is 15%, calculate the smallest X which would entice him to purchase the asset.

## Net Present Value:

Net present value is often used in capital budgeting to evaluate and select projects. Based on this method, a project is considered financially viable if the net present value calculated at the required rate of return is positive.

The minimum amount is \$129.28.

The smallest X that would entice him to purchase such that the net present value of the project is exactly. The payments from the investment here are growing annuity. We can use the following formula to compute the present value of an annuity with first payment {eq}M {/eq} for {eq}T{/eq} periods, periodic growth rate {eq}g{/eq}, and periodic return {eq}r{/eq}:

• {eq}\displaystyle \frac{M}{r - g}\left(1 - \left(\frac{1 + g}{1 + r}\right)^N\right) {/eq}

Applying the formula, the net present value of the project is zero when:

• {eq}\displaystyle \frac{X}{15\% - 10\%}\left(1 - \left(\frac{1 + 10\%}{1 + 15\%}\right)^{11}\right) = 1,000 {/eq}
• {eq}7.734838008 * M = 1,000 {/eq}
• {eq}M = 129.28 {/eq} 