## Related questions with answers

James Kirk is a financial executive with McDowell Enterprises. Although James Kirk has not had any formal training in finance or accounting, he has a “good sense” for numbers and has helped the company grow from a very small company ($500,000 sales) to a large operation ($45 million in sales). With the business growing steadily, however, the company needs to make a number of difficult financial decisions in which James Kirk feels a little “overhis head.” He therefore has decided to hire a new employee with “numbers” expertise to help him. As a basis for determining whom to employ, he has decided to ask each prospective employee to prepare answers to questions relating to the following situations he has encountered recently. Here are the questions.

- a. In 2016, McDowell Enterprises negotiated and closed a long-term lease contract for newly constructed truck terminals and freight storage facilities. The buildings were constructed on land owned by the company. On January 1, 2017, McDowell took possession of the leased property. The 20-year lease is effective for the period January 1, 2017, through December 31, 2036. Advance rental payments of $800,000 are payable to the lessor (owner of facilities) on January 1 of each of the first 10 years of the lease term. Advance payments of$400,000 are due on January 1 for each of the last 10 years of the lease term. McDowell has an option to purchase all the leased facilities for $1 on December 31, 2036. At the time the lease was negotiated, the fair value of the truck terminals and freight storage facilities was approximately$7,200,000. If the company had borrowed the money to purchase the facilities, it would have had to pay 10% interest. Should the company have purchased rather than leased the facilities?
- b. Last year the company exchanged a piece of land for a non-interest-bearing note. The note is to be paid at the rate of $15,000 per year for 9 years, beginning one year from the date of disposal of the land. An appropriate rate of interest for the note was 11%. At the time the land was originally purchased, it cost$90,000. What is the fair value of the note?
- c. The company has always followed the policy to take any cash discounts on goods purchased. Recently, the company purchased a large amount of raw materials at a price of $800,000 with terms 1/10, n/30 on which it took the discount. McDowell has recently estimated its cost of funds at 10%. Should McDowell continue this policy of always taking the cash discount?

Solution

Verified$\textbf{A.}$

Step 1: Compute the present value of the rental payments.

Note:

Use the present value of annuity due formula for the first ten payments.

Use the present value of ordinary annuity formula for the last ten payments.

Given:

Advance rental payments for the first ten years = $800,000

Advance rental payments for the last ten years = $400,000

Lease contract = 20

Interest rate = 10%

Fair value of the facilities = $7,200,000

$\textbf{First ten payments:}$

$\begin{equation} \text{Present value of annuity due} = P\frac{{1 - (1+r)^{-n}}}{r}(1+r) \end{equation}$

$\begin{equation} \text{Present value of annuity due} = \$800,000\frac{{1 - (1+.10)^{-10}}}{.10}(1+.10) \end{equation}$

$\begin{equation} \text{Present value of annuity due} = \$800,000(6.144567106)(1.10) \end{equation}$

$\begin{equation} \textbf{Present value first ten payments} = \textbf{\$5,407,219} \end{equation}$

$\textbf{Last ten payments:}$

$\begin{equation} \text{Present value of ordinary annuity} = P(\frac{{1 - (1+r)^{-n}}}{r} - \frac{{1 - (1+r)^{-n}}}{r}) \end{equation}$

$\begin{equation} \text{Present value of ordinary annuity} = \$400,000(\frac{{1 - (1+.10)^{-19}}}{.10} - \frac{{1 - (1+.10)^{-9}}}{.10}) \end{equation}$

$\begin{equation} \text{Present value of ordinary annuity} = \$400,000(8.36492-5.75902) \end{equation}$

$\begin{equation} \text{Present value of ordinary annuity} = \$400,000(2.6059) \end{equation}$

$\begin{equation} \textbf{Present value last ten payments} = \textbf{\$1,042,360} \end{equation}$

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