Chapter 11, Problem 36P

(a):

To determine

Calculate the annual worth.

Explanation of Solution

Defender: Upgrade cost (UC) is $79,000. Market value (MV) is $40,000. Annual operating cost (AC) is $85,000. Salvage value (SV) is $30,000. Interest rate (i) is 15%. Time period (n) is 3.

Challenger: First cost (FC) is $220,000. Annual operating cost (AC) is $45,000. Salvage value (SV) is $50,000. . Interest rate (i) is 15%. Time period (n) is 3.

Annual worth (AV) of defender can be calculated as follows:

$\begin{array}{c}\text{AV}=-\left(\text{MV}+\text{UC}\right)\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)-\text{AC}+\text{SV}\left(\frac{\text{i}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\\ =-\left(40,000+79,000\right)\left(\frac{0.15{\left(1+\text{0}\text{.15}\right)}^3}{{\left(1+\text{0}\text{.15}\right)}^3-1}\right)-85,000+30,000\left(\frac{0.15}{{\left(1+\text{0}\text{.15}\right)}^3-1}\right)\\ =-\left(119,000\right)\left(\frac{0.15\left(1.52088\right)}{1.52088-1}\right)-85,000+30,000\left(\frac{0.15}{1.52088-1}\right)\\ =-\left(119,000\right)\left(\frac{0.22813}{0.52088}\right)-85,000+30,000\left(\frac{0.15}{0.52088}\right)\\ =-\left(119,000\right)\left(0.43797\right)-85,000+30,000\left(0.28797\right)\\ =-52,118.43-85,000+8,639.1\\ =-128,479.33\end{array}$

The annual worth of the defender is -$128,479.33.

Annual worth (AV) of challenger can be calculated as follows:

$\begin{array}{c}\text{AV}=-\text{FC}\left(\frac{\text{i}{\left(1+\text{i}\right)}^{\text{n}}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)-\text{AC}+\text{SV}\left(\frac{\text{i}}{{\left(1+\text{i}\right)}^{\text{n}}-1}\right)\\ =-220,000\left(\frac{0.15{\left(1+\text{0}\text{.15}\right)}^3}{{\left(1+\text{0}\text{.15}\right)}^3-1}\right)-45,000+50,000\left(\frac{0.15}{{\left(1+\text{0}\text{.15}\right)}^3-1}\right)\\ =-220,000\left(\frac{0.15\left(1.52088\right)}{1.52088-1}\right)-45,000+50,000\left(\frac{0.15}{1.52088-1}\right)\\ =-22,000\left(\frac{0.22813}{0.52088}\right)-45,000+50,000\left(\frac{0.15}{0.52088}\right)\\ =-220,000\left(0.43797\right)-45,000+50,000\left(0.28797\right)\\ =-96,353.4-45,000+14,398.5\\ =126,954.9\end{array}$

The annual worth of the challenger is -$126,954.9.

The challenger can be replaced, if the annual cost of challenger is lower than the defender. Thus, the firm can replace the defender for the challenger.

(b):

To determine

Calculate the annual worth for the next three years.

Explanation of Solution

The annual worth for the next three years is -$126,954.9, which is calculated in the subpart ‘a’.

(c):

To determine

Calculate the annual worth through spreadsheet.

Explanation of Solution

The spreadsheet function to calculate the annual worth of defender through the spreadsheet is given below:

= -PMT(15%,3,-119000,30000)-85000

The above function gives the value of -$128,479.95.

The spreadsheet function to calculate the annual worth of challenger through the spreadsheet is given below:

= -PMT(15%,3,-220000,50000)-45000

The above function gives the value of -$126,956.08.

(d):

To determine

Calculate the annual worth through spreadsheet for 8 years.

Explanation of Solution

The spreadsheet function to calculate the annual worth of challenger for 8 years through the spreadsheet is given below:

= -PMT(15%,8,-220000,10000)-45000

The above function gives the value of -$93,298.52. This reveals that there is a reduction of $33,657.56 per year recovery from the annual worth of the challenger with the 3 year time period.