Chapter 6, Problem 18P

(a)

To determine

Calculate the equivalent annual worth.

Explanation of Solution

Table-1 shows the cash flow of different projects.

Table -1

Projects	RK	SK
First cost (C)	-250,000	-170,000
AOC (MO) per year	-31,000	-35,000
Overhaul cost (O) in year (n1) 2		-26,000
Salvage value (SV)	40,000	10,000
Time period (n)	6	4
Interest (i)	10%	10%

The equivalent annual worth of Model RK (AWG) can be calculated as follows:

$\begin{array}{c}\text{AWG}=\text{C}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\text{+MO}+\text{SV}\left(\frac{\text{i}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\\ =-250\text{,000}\left(\frac{\text{0}\text{.1}{\left(1+\text{0}\text{.1}\right)}^{\text{6}}}{{\left(1+\text{0}\text{.1}\right)}^{\text{6}}-1}\right)-31,000+\text{40,000}\left(\frac{\text{0}\text{.1}}{{\left(1+\text{0}\text{.1}\right)}^{\text{6}}-1}\right)\\ =-250\text{,000}\left(\frac{\text{0}\text{.1}\left(1.771561\right)}{1.771561-1}\right)-31,000+\text{40,000}\left(\frac{\text{0}\text{.1}}{1.771561-1}\right)\\ =-250\text{,000}\left(\frac{\text{0}\text{.177156}}{0.771561}\right)-31,000+\text{40,000}\left(\frac{\text{0}\text{.1}}{0.771561}\right)\\ =-250\text{,000}\left(0.229607\right)-31,000+\text{40,000}\left(0.129607\right)\\ =-57,401.75-31,000+5,184.28\\ =-83,217.47\end{array}$

The annual worth of Model RK is -$83,217.47.

The equivalent annual worth of Model SK (AWF) can be calculated as follows:

$\begin{array}{c}\text{AWF}=\text{C}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)+\text{MO+}\left(\frac{\text{O}}{{\left(1+\text{i}\right)}^{\text{n1}}}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\right)+\text{SV}\left(\frac{\text{i}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\\ =\left(\begin{array}{l}-170\text{,000}\left(\frac{\text{0}\text{.1}{\left(1+\text{0}\text{.1}\right)}^{\text{4}}}{{\left(1+\text{0}\text{.1}\right)}^{\text{4}}-1}\right)-35,000-\left(\frac{26\text{,000}}{{\left(1+\text{0}\text{.1}\right)}^{\text{2}}}\left(\frac{\text{0}\text{.1}{\left(1+\text{0}\text{.1}\right)}^{\text{4}}}{{\left(1+\text{0}\text{.1}\right)}^{\text{4}}-1}\right)\right)\\ +\text{10,000}\left(\frac{\text{0}\text{.1}}{{\left(1+\text{0}\text{.1}\right)}^{\text{4}}-1}\right)\end{array}\right)\\ =\left(\begin{array}{l}-170\text{,000}\left(\frac{\text{0}\text{.1}\left(1.4641\right)}{1.4641-1}\right)-35,000-\left(\frac{26\text{,000}}{1.21}\left(\frac{\text{0}\text{.1}\left(1.4641\right)}{1.4641-1}\right)\right)\\ +\text{10,000}\left(\frac{\text{0}\text{.1}}{1.4641-1}\right)\end{array}\right)\\ =\left(\begin{array}{l}-170\text{,000}\left(\frac{\text{0}\text{.14641}}{0.4641}\right)-35,000-\left(21,487.6033\left(\frac{\text{0}\text{.14641}}{0.4641}\right)\right)\\ +\text{10,000}\left(\frac{\text{0}\text{.1}}{0.4641}\right)\end{array}\right)\\ =\left(\begin{array}{l}-170\text{,000}\left(0.315471\right)-35,000-\left(21,487.6033\left(0.315471\right)\right)\\ +\text{10,000}\left(0.215471\right)\end{array}\right)\\ =\left(-53,630.07-35,000-6,778.72+2,154.71\right)\\ =-93,254.08\end{array}$

The annual worth of Model SK is -$93,254.08. Since the annual worth of Model RK is greater than Model SK, select Model RK.

(b)

To determine

Calculate the annual worth using spreadsheet function.

Explanation of Solution

Spreadsheet function to calculate the annual worth of Model RK is given below:

=-PMT(10%,6,-250000,40000)-31000

The above function gives the value of $83,217.55.

Spreadsheet function to calculate the annual worth of Model SK is given below:

=-PMT(10%,4,-170000,10000)-35000-PMT(10%,4,-PV(10%,2,,-26000))

The above function gives the value of $93,254.04.