Chapter 9, Problem 6AP

1. (a)

To determine

Identify the present value of the debt.

Answer to Problem 6AP

The present value of debt of Company E is $\left[\$1,361,160(1)+\$598,907(2)\right]$ $1,960,067.

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 $2,000,000 to be repaid in five years:

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.08\right)}^5}\times \$2,000,000\\ =\$1,361,160\end{array}$

Therefore, the present value of debt for the borrowed money of $2,000,000 to be repaid in five years is $1,361,160.

…… (1)

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

$\begin{array}{c}\text{Present Value =}\frac{\text{1}-{\left(1+\text{i}\right)}^{-\text{n}}}{\text{i}}\times \text{Amount}\\ =\frac{\text{1}-{\left(1+0.08\right)}^{-5}}{8\%}\times \$150,000\\ =3.99271\times \$150,000\\ =\$598,907\end{array}$

Therefore, the present value of annuity for an agreed amount interest each year for five years is $598,907.

…… (2)

2. (b)

To determine

Identify the single amount the company must deposit on January 1, 2014 and also to identify the total amount of interest revenue that will be earned.

Explanation of Solution

Determine the single amount that Company E must deposit on January 1, 2014:

$\begin{array}{c}\text{Present Value = }\frac{1}{{\left(1+\text{i}\right)}^{\text{n}}}\times \text{Amount}\\ =\text{}\frac{1}{{\left(1+0.08\right)}^{10}}\times \$1,000,000\\ =0.4632\times \$1,000,000\\ =\$463,200\end{array}$

Therefore, the single amount that Company E must deposit on January 1, 2014 is $463,200.

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

The total amount of interest revenue that will be earned by the Company E is $536,800$\left[\$1,000,000-\$463,200\right]$.

3. (c)

To determine

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

Explanation of Solution

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

$\begin{array}{c}\begin{array}{l}\text{Amount of equal annual}\\ \text{ payment for four years}\end{array}\}=\frac{\left(\begin{array}{l}\text{Machine purchased}-\text{Cash paid on }\\ \text{ machine purchased}\end{array}\right)}{\text{Annuity value for 4 years}}\\ =\frac{\left(\$750,000-\$400,000\right)}{3.3121(3)}\\ =\frac{\$350,000}{3.3121}\\ =\$105,673\end{array}$

Therefore, The amount of each of the equal annual payments that will be paid on the note by Company E is $105,673.

Working Note:

$\begin{array}{c}\text{Annuity value for 4 years = }\frac{\text{1}-{\left(1+0.08\right)}^{-4}}{8\%}\\ =\frac{0.264970147}{0.08}\\ =3.3121\end{array}$ (3)

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

$\begin{array}{c}\text{Total interest accrued = }\left(\begin{array}{l}\text{ Annual payment for one year }\times \\ \text{Number of years of annual payment }\end{array}\right)-\left(\begin{array}{l}\text{Remaining amount to}\\ \text{ be paid on purchase}\end{array}\right)\\ =\left(\$105,673\times 4\right)-\$350,000\\ =\$422,692-\$350,000\\ =\$72,692\end{array}$

Therefore, the total amount of interest expense that will be accrued by Company E is $72,692.