Chapter 9, Problem 11P

1.

To determine

Identify the present value of debt.

Answer to Problem 11P

The present value of debt of Company B is $\left[\$71,616+\$32,336\right]$ $103,952.

Explanation of Solution

Present value:

Present value is the current value of an amount that is to be paid or received in future. Present value is determined by using the formula:

$\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}$

 Annuity:

 An annuity is referred as a sequence of payment of fixed amount of cash flows that occurs over the equal intervals of time.

Working Notes:

Calculate the present value of debt for the borrowed money of $115,000 to be repaid in seven years:

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.07\right)}^7}\times \$115,000\\ =0.62275\times \$115,000\\ =\$71,616\end{array}$

Therefore, the present value of debt for the borrowed money of $115,000 to be repaid in seven years is $71,616.

Calculate the present value of annuity for an agreed amount interest each year for seven years:

$\begin{array}{c}\text{Present Value =}\frac{\text{1}-{\left(1+\text{i}\right)}^{-\text{n}}}{\text{i}}\times \text{Amount}\\ =\frac{\text{1}-{\left(1+0.07\right)}^{-7}}{7\%}\times \$6,000\\ =5.38929\times \$6,000\\ =\$32,336\end{array}$

Therefore, the present value of annuity for an agreed amount interest each year for seven years is $32,336.

2.

To determine

Identify the single amount the company must deposit on January 1 and also to identify the total amount of interest revenue that will be earned.

Explanation of Solution

Determine the single amount that Company B must deposit on January 1:

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.07\right)}^8}\times \$490,000\\ =0.58201\times \$490,000\\ =\$285,185\end{array}$

Therefore, the single amount that Company B must deposit on January 1 is $285,185.

Identify the total amount of interest revenue that will be earned by Company B:

The total amount of interest revenue that will be earned by the Company B is $204,815$\left[\$490,000-\$285,185\right]$.

3.

To determine

Identify the present value.

Answer to Problem 11P

The present value of Company B for given obligation is $\left[\$70,094+\$98,262+\$122,445\right]$ $29,801.

Explanation of Solution

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.07\right)}^1}\times \$75,000\\ =0.93458\times \$75,000\\ =\$70,094\end{array}$

Therefore, Company B’s present value to pay $75,000 to discharged employees at the end of first year is $70,094.

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.07\right)}^2}\times \$112,500\\ =0.87344\times \$112,500\\ =\$98,262\end{array}$

Therefore, Company B’s present value to pay $112,500 to discharged employees at the end of second year is $98,262.

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.07\right)}^3}\times \$150,000\\ =0.81630\times \$150,000\\ =\$122,445\end{array}$

Therefore, Company B’s present value to pay $150,000 to discharged employees at the end of third year is $122,445.

4.

To determine

Identify the amount of each of the equal annual payments that will be paid on the note by Company B and also to identify the total amount of interest expense that will be accrued by Company B.

Explanation of Solution

Identify the amount of each of the equal annual payments that will be paid on the note by Company B:

$\begin{array}{c}\begin{array}{l}\text{Amount of equal annual}\\ \text{ payment for four years}\end{array}\}=\frac{\left(\begin{array}{l}\text{Machine purchased}-\text{Cash paid on }\\ \text{ machine purchased}\end{array}\right)}{\text{Annuity value for 4 years}}\\ =\frac{\left(\$170,000-\$34,000\right)}{3.31213}\\ =\frac{\$136,000}{4.10020}\\ =\$33,169\end{array}$

Therefore, The amount of each of the equal annual payments that will be paid on the note by Company B is $33,169.

Working Note:

$\begin{array}{c}\text{Annuity value for 5 years = }\frac{\text{1}-{\left(1+0.07\right)}^{-5}}{7\%}\\ =\frac{0.264970147}{0.07}\\ =4.10020\end{array}$

Identify the total amount of interest expense that will be accrued by Company B:

$\begin{array}{c}\text{Total interest accrued = }\left(\begin{array}{l}\text{ Annual payment for one year }\times \\ \text{Number of years of annual payment }\end{array}\right)-\left(\begin{array}{l}\text{Remaining amount to}\\ \text{ be paid on purchase}\end{array}\right)\\ =\left(\$33,169\times 5\right)-\$136,000\\ =\$165,845-\$136,000\\ =\$29,845\end{array}$

Therefore, the total amount of interest expense that will be accrued by Company B is $29,845.