Chapter 18, Problem 39P

To determine

Calculate the present worth.

Explanation of Solution

Time period is denoted by ‘n’ and MARR is denoted by ‘i’. The present worth (PW) for the option ‘invest now’ can be calculated as follows:

$\begin{array}{c}\text{PW}=-\text{First cost}+\left(\left(\begin{array}{l}{\text{Revenue}}_{\text{Pessimistic}}\\ \times \left({\text{P}}_{\text{Pessimistic}}\right)\end{array}\right)+\left(\begin{array}{l}{\text{Revenue}}_{\text{Most likely}}\\ \times \left({\text{P}}_{\text{Most likely}}\right)\end{array}\right)+\left(\begin{array}{l}{\text{Revenue}}_{\text{Optimistic}}\\ \times \left({\text{P}}_{\text{Optimistic}}\right)\end{array}\right)\right)\left(\frac{{\left(\text{1}+\text{i}\right)}^{\text{n}}-1}{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{n}}}\right)\\ =-\text{80,000,000}+\left(\left(\text{35,000,000}\times \left(\frac{1}{3}\right)\right)+\left(\text{25,000,000}\times \left(\frac{1}{3}\right)\right)+\left(\text{10,000,000}\times \left(\frac{1}{3}\right)\right)\right)\left(\frac{{\left(\text{1}+\text{0}\text{.12}\right)}^{\text{5}}-1}{\text{0}\text{.12}{\left(\text{1}+\text{0}\text{.12}\right)}^{\text{5}}}\right)\\ =-\text{80,000,000}+\left(11,666,667+8,333,333+3,333,333\right)\left(3.6048\right)\\ =4,111,999\end{array}$

The present worth is $4,111,999.

The present worth (PW) for option ‘invest later’ can be calculated as follows.

$\begin{array}{c}\text{PW}=\left(\begin{array}{l}-\text{Cost}+\text{Revenue}\left(\frac{1}{{\left(1+\text{i}\right)}^1}\right)-\text{First cost}\left(\frac{1}{{\left(1+\text{i}\right)}^1}\right)\\ +\left(\left(\begin{array}{l}{\text{Revenue}}_{\text{Pessimistic}}\\ \times \left({\text{P}}_{\text{Pessimistic}}\right)\end{array}\right)+\left(\begin{array}{l}{\text{Revenue}}_{\text{Most likely}}\\ \times \left({\text{P}}_{\text{Most likely}}\right)\end{array}\right)\right)\left(\frac{{\left(\text{1}+\text{i}\right)}^{\text{4}}-1}{\text{i}{\left(\text{1}+\text{i}\right)}^{\text{4}}}\right)\left(\frac{1}{{\left(1+\text{i}\right)}^1}\right)\end{array}\right)\\ =\left(\begin{array}{l}-\text{4,000,000}+900,000\left(\frac{1}{{\left(1+0.12\right)}^1}\right)-800,000,000\left(\frac{1}{{\left(1+0.12\right)}^1}\right)\\ +\left(\left(\text{35,000,000}\times \left(\frac{1}{2}\right)\right)+\left(\text{25,000,000}\times \left(\frac{1}{2}\right)\right)\right)\left(\frac{{\left(\text{1}+\text{0}\text{.12}\right)}^{\text{4}}-1}{\text{0}\text{.12}{\left(\text{1}+\text{0}\text{.12}\right)}^{\text{4}}}\right)\left(\frac{1}{{\left(1+\text{0}\text{.12}\right)}^1}\right)\end{array}\right)\\ =\left(\begin{array}{l}-\text{4,000,000}+900,000\left(0.8929\right)-80,000,000\left(0.8929\right)\\ +\left(17,500,000+12,500,000\right)\left(3.0373\right)\left(0.8929\right)\end{array}\right)\\ =6,731.675\end{array}$

The present worth is $6,731,675. Since the present worth for the ‘invest later’ option is greater, select option ‘invest later’.