Chapter 16.A, Problem 13P

(a):

To determine

Calculate the recovery rate.

Explanation of Solution

Straight line recovery rate (RRSL1) for Year 1 can be calculated as follows:

$\begin{array}{c}\text{RRSL1}=0.5\times \frac{1}{\text{n}}\\ =0.5\times \frac{1}{3}\\ =0.167\end{array}$

Thus, the recovery rate for Year 1 is 0.167.

Straight line recovery rate (RRSL2) for Year 2 can be calculated as follows:

$\begin{array}{c}\text{RRSL2}=\frac{1}{\text{n}}\\ =\times \frac{1}{3}\\ =0.333\end{array}$

Thus, the recovery rate for Year 2 is 0.333.

Straight line recovery rate (RRSL3) for Year 3 can be calculated as follows:

$\begin{array}{c}\text{RRSL3}=\frac{1}{\text{n}}\\ =\times \frac{1}{3}\\ =0.333\end{array}$

Thus, the recovery rate for Year 3 is 0.333.

The straight line recovery rate (RRSL4) for Year 4 can be calculated as follows:

$\begin{array}{c}\text{RRSL4}=0.5\times \frac{1}{\text{n}}\\ =0.5\times \frac{1}{3}\\ =0.167\end{array}$

Thus, the recovery rate for Year 4 is 0.167.

(b):

To determine

Calculate the present worth.

Explanation of Solution

The book value is $80,000. MACRS recovery rate for Year 1 (RR1) is 33.33%, Year 2 (RR20 is 44.5%, Year 3 (RR3) is 14.81%, and Year 4 (RR4) is 7.41%. Interest rate (i) is 15%.

The present worth of the MACRS (PWMACRS) depreciation can be calculated as follows:

$\begin{array}{c}\text{PWMACRS}=\left(\frac{\text{RR1}\times \text{B}}{{\left(1+\text{i}\right)}^1}\right)+\left(\frac{\text{RR2}\times \text{B}}{{\left(1+\text{i}\right)}^2}\right)+\left(\frac{\text{RR3}\times \text{B}}{{\left(1+\text{i}\right)}^3}\right)+\left(\frac{\text{RR4}\times \text{B}}{{\left(1+\text{i}\right)}^4}\right)\\ =\left(\frac{\text{0}\text{.3333}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)+\left(\frac{\text{0}\text{.4445}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)+\left(\frac{\text{0}\text{.1481}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^3}\right)+\left(\frac{\text{0}\text{.0741}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)\\ =\left(\frac{26,664}{1.15}\right)+\left(\frac{35,560}{1.3225}\right)+\left(\frac{11,848}{1.520875}\right)+\left(\frac{5,928}{1.74901}\right)\\ =61,253\end{array}$

Thus, the present worth of the depreciation that is calculated by MACRS is $61,253.

The present worth of the SL (PWSL) depreciation can be calculated as follows:

$\begin{array}{c}\text{PWSL}=\left(\frac{\text{RRSL1}\times \text{B}}{{\left(1+\text{i}\right)}^1}\right)+\left(\frac{\text{RRSL2}\times \text{B}}{{\left(1+\text{i}\right)}^2}\right)+\left(\frac{\text{RRSL3}\times \text{B}}{{\left(1+\text{i}\right)}^3}\right)+\left(\frac{\text{RRSL4}\times \text{B}}{{\left(1+\text{i}\right)}^4}\right)\\ =\left(\frac{\text{0}\text{.167}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)+\left(\frac{\text{0}\text{.333}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)+\left(\frac{\text{0}\text{.333}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^3}\right)+\left(\frac{\text{0}\text{.167}\times \text{80,000}}{{\left(1+\text{0}\text{.15}\right)}^1}\right)\\ =\left(\frac{13,360}{1.15}\right)+\left(\frac{26,640}{1.3225}\right)+\left(\frac{26,640}{1.520875}\right)+\left(\frac{13,360}{1.74901}\right)\\ =56,915\end{array}$

Thus, the present worth of the depreciation that is calculated by the SL method is $56,915.