# Suppose that company you work for purchased a textile for $25 million 4 years ago. It's current...

## Question:

Suppose that company you work for purchased a textile for $25 million 4 years ago. It's current market value is $20 million, and is estimated to decline exponentially for the foreseeable future following this exponential friction: {eq}MV_N = MV_0e^{-0.2 N} {/eq}, where N is the year and {eq}MV_0 {/eq} is the present market value. The mill's estimated revenue is expected to be $5 million by the end of this year and is then forecast to decline by 20% per year due to raising energy and material costs. When should the company abandon the mill? Assume a MARR of 6%.

## Required Rate of Return:

The required rate of return is the minimum return on investment that is investor seeks on his investment. The required rate of return is also used while evaluating long term investment opportunities to discounted cash flow generator from it.

## Answer and Explanation:

**Values given:**

Textile purchased = $25 million

Market value = $20 million

Estimated revenue = $5 million

Forecast = -20%

MARR = 6%

**Solving:**

{eq}PV \ = \ \dfrac{Estimated \ revenue}{MARR \ - \ Forecast}\left [ 1 \ - \ \left ( \dfrac{1 \ + \ Forecast}{1 \ + \ MARR} \right )^N \right ] \\ PV \ = \ \dfrac{5}{6\% \ + \ 20\%}\left [ 1 \ - \ \left ( \dfrac{1 \ - \ 20\%}{1 \ + \ 6\%} \right )^N \right ] \\ PV \ = \ \dfrac{5}{0.06 \ + \ 0.20}\left [ 1 \ - \ \left ( \dfrac{1 \ - \ 0.20}{1 \ + \ 0.06} \right )^N \right ] \\ PV \ = \ \dfrac{5}{0.26}\left [ 1 \ - \ \left ( \dfrac{0.80}{1.06} \right )^N \right ] \\ PV \ = \ 20 \ \left [ 1 \ - \ \left ( \dfrac{0.80}{1.06} \right )^N \right ] \\ PV \ = \ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} {/eq}

{eq}NPV \ = \ \left ( \dfrac{Estimated \ revenue}{MARR \ - \ Forecast}\left [ 1 \ - \ \left ( \dfrac{1 \ + \ Forecast}{1 \ + \ MARR} \right )^N \right ] \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ \left ( \dfrac{5}{6\% \ + \ 20\%}\left [ 1 \ - \ \left ( \dfrac{1 \ - \ 20\%}{1 \ + \ 6\%} \right )^N \right ] \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ \left ( \dfrac{5}{0.06 \ + \ 0.20}\left [ 1 \ - \ \left ( \dfrac{1 \ - \ 0.20}{1 \ + \ 0.06} \right )^N \right ] \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ \left ( \dfrac{5}{0.26}\left [ 1 \ - \ \left ( \dfrac{0.80}{1.06} \right )^N \right ] \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ \left ( 20 \ \left [ 1 \ - \ \left ( \dfrac{0.80}{1.06} \right )^N \right ] \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ \left ( 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ) \ - \ \left [ 20 \ - \ \dfrac{20e^{-0.2N}}{1.06^{N}} \right ] \\ NPV \ = \ 0 {/eq}

N | PV of revenue (A) | Difference in PV market value of mill (B) | NPV ((C) = (A) - (B)) |
---|---|---|---|

3 | 10.963749 | 10.78414335 | 0.179605246 |

4 | 12.991508 | 12.8817875 | 0.109720879 |

5.208 | 14.78961 | 14.78954179 | 0.00006821 |

5.209636667 | 14.791665 | 14.79174379 | -0.00008879 |

So, N is 5.208 years

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from Financial Accounting: Help and Review

Chapter 1 / Lesson 29