Chapter 4, Problem 55QP

Summary Introduction

To determine: The offer’s present value when the rate of discount 9%.

Explanation of Solution

The computation of current value of salary offer is as follows:

$\begin{array}{l}\text{PV }=\text{C}\left\{\left[\frac{\text{1}}{\left(\text{r–g}\right)}\right]\text{ – }\left[\frac{\text{1}}{\left(\text{r–g}\right)}\right]\text{ × }{\left[\frac{\left(\text{1 +g}\right)}{\left(\text{1 +r}\right)}\right]}^{\text{t}}\right\}\hfill \\ =\$65,000\left\{\left[\frac{1}{\left(.09–.032\right)}\right]–\left[\frac{1}{\left(.09–.032\right)}\right]\times {\left[\frac{\left(1+.032\right)}{\left(1+.09\right)}\right]}^{35}\right\}\hfill \\ =\$955,361.30\hfill \end{array}$

The computation of next year’s bonus is as follows:

$\begin{array}{l}\text{Next year’s bonus = }\text{.10}\times \left(\text{\$65,000}\right)\hfill \\ =\$6,500\hfill \end{array}$

The computation of present value of annual bonus is as follows:

$\begin{array}{l}\text{PV }=\text{C}\left\{\left[\frac{\text{1}}{\left(\text{r–g}\right)}\right]\text{ – }\left[\frac{\text{1}}{\left(\text{r–g}\right)}\right]\text{ × }{\left[\frac{\left(\text{1 +g}\right)}{\left(\text{1 +r}\right)}\right]}^{\text{t}}\right\}\hfill \\ =\$6,500\left\{\left[\frac{1}{\left(.09–.032\right)}\right]–\left[\frac{1}{\left(.09–.032\right)}\right]\times {\left[\frac{\left(1+.032\right)}{\left(1+.09\right)}\right]}^{35}\right\}\hfill \\ =\$95,536.13\hfill \end{array}$

The computation of total value of offer is as follows:

$\begin{array}{l}\text{PV }=\text{ PV}\left(\text{Salary}\right)\text{ + PV}\left(\text{Bonus}\right)\text{ + Bonus paid today}\hfill \\ =\$955,361.30+95,536.13+12,000\hfill \\ =\$1,062,897.43\hfill \end{array}$ $\begin{array}{l}\text{PV }=\text{ PV}\left(\text{Salary}\right)\text{ + PV}\left(\text{Bonus}\right)\text{ + Bonus paid today}\hfill \\ =\$955,361.30+95,536.13+12,000\hfill \\ =\$1,062,897.43\hfill \end{array}$

Hence, the present value of total offer is $1,062,897.43.