Chapter 14, Problem 10P

(a)

To determine

Net present value.

Explanation of Solution

Given information:

Rate of interest (r) is 10%.

Cost is 30,000.

Calculation:

The general formula for calculating the present value of mixed stream is shown below:

$\text{NPV}=-\text{Cost}+\left(\frac{{\text{Cash flow}}_1}{{\left(1+\text{r}\right)}^1}\right)+\left(\frac{{\text{Cash flow}}_2}{{\left(1+\text{r}\right)}^2}\right)+\mathrm{...}+\left(\frac{{\text{Cash flow}}_{\text{n}}}{{\left(1+\text{r}\right)}^{\text{n}}}\right)$ (1)

The future earnings will increase $48,000, and currently Mr. M makes $40,000 in a year. Thus, increase in future earnings (AP) is $8000. Substitute the respective values in Equation (1) to calculate the net present value (NPV).

$\begin{array}{c}\text{NPV}=-30,0\text{00}+\left(\frac{8,000}{{\left(1+0.10\right)}^1}\right)+\left(\frac{8,000}{{\left(1+0.10\right)}^2}\right)+\left(\frac{8,000}{{\left(1+0.10\right)}^3}\right)+\left(\frac{8,000}{{\left(1+0.10\right)}^4}\right)+\left(\frac{8,000}{{\left(1+0.10\right)}^5}\right)\\ =-30,0\text{00}+\left(\frac{8,000}{1.1}\right)+\left(\frac{8,000}{1.21}\right)+\left(\frac{8,000}{1.331}\right)+\left(\frac{8,000}{1.4641}\right)+\left(\frac{8,000}{1.61051}\right)\\ =-30,0\text{00}+7,272.72+6,611.57+6,010.51+5,464.10+4,967.37\\ =-30,0\text{00}+30,326.2\\ =326.2\end{array}$

Net present value is $326.

(b)

To determine

Mr. M’s decision about career change.

Explanation of Solution

Since the net present value of earnings after career change is positive, the person should change his career.

(c)

To determine

Present value.

Explanation of Solution

Given information:

Rate of interest (r) is 10%.

Annual payment (AP) is $40,000 (from truck driving).

Future value (FV) is $48,000 (from florist).

Calculation:

The calculation of the present value is shown below:

$\text{Present}\text{value}=\left(\frac{{\text{Cash flow}}_1}{{\left(1+\text{interest}\right)}^{\text{1}}}\right)+\left(\frac{{\text{Cash flow}}_2}{{\left(1+\text{interest}\right)}^2}\right)+\mathrm{...}+\left(\frac{{\text{Cash flow}}_{\text{n}}}{{\left(1+\text{interest}\right)}^{\text{n}}}\right)$ (2)

Substitute the respective values in Equation (2) to calculate the PV of the earning for truck driving.

$\begin{array}{c}\text{PV}=\left(\frac{40,000}{{\left(1+0.10\right)}^{\text{1}}}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^2}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^3}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^4}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^5}\right)\\ =\left(\frac{40,000}{1.1}\right)+\left(\frac{40,000}{1.21}\right)+\left(\frac{40,000}{1.331}\right)+\left(\frac{40,000}{1.4641}\right)+\left(\frac{40,000}{1.61051}\right)\\ =36,363.63+33,057.85+30,052.59+27,320.53+24,836.85\\ =151,631.4\end{array}$

Present value from truck driving is $151,631.47.

Using the same Equation (2), calculation of the present value from florist is shown below:

$\begin{array}{c}\text{PV}=\left(\frac{48,000}{{\left(1+0.10\right)}^{\text{1}}}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^2}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^3}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^4}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^5}\right)\\ =\left(\frac{48,000}{1.1}\right)+\left(\frac{48,000}{1.21}\right)+\left(\frac{48,000}{1.331}\right)+\left(\frac{48,000}{1.4641}\right)+\left(\frac{48,000}{1.61051}\right)\\ =43,636.36+39,669.42+36,063.11+32,784.64+29,804,22\\ =181,957.80\end{array}$

Present value from florist is $181,957.80.

The present value of earnings from florist is greater by $30,326$\left(181,957.80-151,631.40\right)$ than the earning from truck driving. Since the excess earning from florist is greater than the cost of $30,000, it is justified to spend $30,000.

Economics Concept Introduction

Present value (PV): The present value refers to today’s value of a future amount.

(d)

To determine

Excess revenue from the florist business.

Explanation of Solution

Excess revenue earning from florist over the truck driving can be calculated as follows:

$\begin{array}{c}\text{Excess earning}=-\text{Cost}+\left(\begin{array}{l}{\text{Present value of earning}}_{\text{Florist}}\\ -{\text{Present value of earning}}_{\text{Truck driving}}\end{array}\right)\\ =\left(\begin{array}{l}-30,000+\left(\begin{array}{l}\left(\frac{48,000}{{\left(1+0.10\right)}^{\text{1}}}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^2}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^3}\right)\\ +\left(\frac{48,000}{{\left(1+0.10\right)}^4}\right)+\left(\frac{48,000}{{\left(1+0.10\right)}^5}\right)\end{array}\right)\\ -\left(\begin{array}{l}\left(\frac{40,000}{{\left(1+0.10\right)}^{\text{1}}}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^2}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^3}\right)\\ +\left(\frac{40,000}{{\left(1+0.10\right)}^4}\right)+\left(\frac{40,000}{{\left(1+0.10\right)}^5}\right)\end{array}\right)\end{array}\right)\\ =\left(\begin{array}{l}-30,000+\left(\begin{array}{l}\left(\frac{48,000}{1.1}\right)+\left(\frac{48,000}{1.21}\right)+\left(\frac{48,000}{1.331}\right)\\ +\left(\frac{48,000}{1.4641}\right)+\left(\frac{48,000}{1.61051}\right)\end{array}\right)\\ -\left(\begin{array}{l}\left(\frac{40,000}{1.1}\right)+\left(\frac{40,000}{1.21}\right)+\left(\frac{40,000}{1.331}\right)\\ +\left(\frac{40,000}{1.4641}\right)+\left(\frac{40,000}{1.61051}\right)\end{array}\right)\end{array}\right)\\ =\left(\begin{array}{l}-30,000\left(\begin{array}{l}43,636.36+39,669.42+36,063.11\\ +32,784.64+29,804,22\end{array}\right)\\ -\left(\begin{array}{l}36,363.63+33,057.85\\ +30,052.59+27,320.53+24,836.85\end{array}\right)\end{array}\right)\\ =326.4\end{array}$

The excess revenue is $326, which is equal to subpart ‘a’ answer.