Chapter 7, Problem 71P

To determine

i.

Interest Rate.

Answer to Problem 71P

Interest Rate is 3.24%.

Explanation of Solution

Given:

Purchase Price: $ 380000

Time: 6 years

Salvage value is 15% of the first cost

Leased for $60000

Interest rate is 12%.

Calculation:

Formula to calculate the net present value is as follows:

$NPV=-P+A(P/A,i,n)+F(P/F,i,n)$

P = $320000

A = $60000

F = $57000

I = ?

n = 5 years for A and 6 years for F.

Now substituting the value of variables into formula, when interest rate is 3%.

$NPV=-P+A(P/A,i,n)+F(P/F,i,n)$

NPV=

$\begin{array}{l}-\$320000+\$60000(P/A,i,5)+\$57000(P/F,i,6)\\ -\$320000+60000(4.515)+\$57000(0.8135)\\ \$317,269.5\end{array}$

Therefore, net present value is $317.269.5

The rate of return, which is between 3.00% and 3.50% may indeed be computed by linear interpolation.

$IRR=i{\%}_{low}+(i{\%}_{high}-i{\%}_{low)}\left[\frac{F_{low}-P}{F_{low}-F_{high}}\right]$

Substituting, the values in equation, the result is as follows:

$\begin{array}{l}IRR=3\%+\left(3.5\%-3\%\right)\left[\frac{\$322537.5-\$320000}{\$322537.5-\$\mathrm{317.269.5}}\right]\\ IRR=3\%+0.5\%\left[\frac{\$2537.5}{\$5268}\right]\\ IRR=0.0324\end{array}$.

Conclusion:

Therefore, the internal rate of return is 0.0324 or 3.24%

Therefore, B is the best financing plan in leasing.

To determine

ii.

Rate of return for the bulldozer using the best financing plan.

Answer to Problem 71P

Rate of return for the bulldozer using the best financing plan is 8.34%.

Explanation of Solution

Given:

If the firm will receive $65000 more each year than it spends on operating and maintenance costs.

Calculation:

Calculation of Present worth of leasing to check whether company buy the bulldozer or not is as follows:

Formula to calculate the net present value is as follows:

$NPV=-P+A(P/A,i,n)+F(P/F,i,n)$

P = $320000

A = $60000

F = $57000

I = ?

n = 8 years for A

n = 9 years for F

Now, substituting the value of variables into the formula(1), when interest rate is 8%

$NPV=-P+A(P/A,i,n)+F(P/F,i,n)$

NPV =

$\begin{array}{l}=-\$60000+\$5000(P/A,i,5)+\$65000(P/F,i,6)\\ =-\$60000+\$5000(3.993)+\$65000(0.6302)\\ =\$60928\end{array}$

Therefore, net present value is $60928

Now, substituting the value of variables into the formula, when interest rate is 9%

$NPV=-P+A(P/A,i,n)+F(P/F,i,n)$

$\begin{array}{l}=-\$60000+\$5000(P/A,i,5)+\$65000(P/F,i,6)\\ =-\$60000+\$5000(3.890)+\$65000(0.5963)\\ =\$58209.5\end{array}$

Therefore, net present value is $58209.5

The rate of return, which is between 8.00% and 9.00% may indeed be computed by linear interpolation.

$IRR=i{\%}_{low}+(i{\%}_{high}-i{\%}_{low)}\left[\frac{F_{low}-P}{F_{low}-F_{high}}\right]$

Substituting the values in equation, the result is as follows:

$\begin{array}{l}IRR=8\%+\left(9\%-8\%\right)\left[\frac{\$60928-\$60000}{\$60928-\$58209.5}\right]\\ IRR=8\%+1\%\left[\frac{\$928}{\$2718.5}\right]\\ IRR=0.0834\end{array}$

Therefore, 8.34% is the rate of return for the bulldozer using the financing plan.

Conclusion:

Therefore, the internal rate of return is 0.0834 or 8.34%.