Chapter 18, Problem 11P

Summary Introduction

To determine: Terminal value of 401(k) plan for 3 options.

Explanation of Solution

Note: Assume all the contributions and returns are remains constant over 20 years.

Option: 1

$\begin{array}{c}\text{Terminal value}=\left(\text{Contribution and return}\times \%\text{Equity}\times \frac{{\left(1+r\right)}^n-1}{r}\right)+\left(\text{Contribution and return}\times \%Bonds\times \frac{{\left(1+r\right)}^n-1}{r}\right)\\ =16,500\left(0.6\right)\left\{\frac{\left[{\left(1+0.12\right)}^{20}-1\right]}{0.12}\right\} +16,500\left(0.4\right)\left\{\left[\frac{{\left(1+0.05\right)}^{20}-1}{0.05}\right]\right\} \\ =\$931,554\end{array}$

Option: 2

$\begin{array}{c}\text{Terminal value}=\left(\text{Contribution and return}\times \%\text{Equity}\times \frac{{\left(1+r\right)}^n-1}{r}\right)+\left(\text{Contribution and return}\times \%Bonds\times \frac{{\left(1+r\right)}^n-1}{r}\right)\\ +\left(\text{Contribution}\times \%\text{Money market securities}\times \frac{{\left(1+r\right)}^n-1}{r}\right)\\ =16,500\left(0.5\right)\left\{\frac{\left[{\left(1+0.12\right)}^{20}-1\right]}{0.12}\right\} +16,500\left(0.45\right)\left\{\left[\frac{{\left(1+0.05\right)}^{20}-1}{0.05}\right]\right\} \\ +16,500\left(0.05\right)\left\{\left[\frac{{\left(1+0.03\right)}^{20}-1}{0.03}\right]\right\}\\ =\$862,115\end{array}$

Option: 3

$\begin{array}{c}\text{Terminal value}=\left(\text{Contribution and return}\times \%\text{Equity}\times \frac{{\left(1+r\right)}^n-1}{r}\right)+\left(\text{Contribution and return}\times \%Bonds\times \frac{{\left(1+r\right)}^n-1}{r}\right)\\ +\left(\text{Contribution}\times \%\text{Money market securities}\times \frac{{\left(1+r\right)}^n-1}{r}\right)\\ =16,500\left(0.4\right)\left\{\frac{\left[{\left(1+0.12\right)}^{20}-1\right]}{0.12}\right\} +16,500\left(0.5\right)\left\{\left[\frac{{\left(1+0.05\right)}^{20}-1}{0.05}\right]\right\} \\ +16,500\left(0.1\right)\left\{\left[\frac{{\left(1+0.03\right)}^{20}-1}{0.03}\right]\right\}\\ =\$792,676\end{array}$