To expand its operation in Ontario, the Dundar Mifflin has applied for a $3,500,000 loan from the...

Question:

To expand its operation in Ontario, the Dundar Mifflin has applied for a $3,500,000 loan from the TD Bank. According to Dundar Mifflin financial analyst, the company can only afford a maximum yearly loan payment of $1,000,000. The bank has offered Dundar Mifflin the following:

Option 1: 3 year loan with an 8 percent interest rate

Option 2: 4 year loan with a 10 percent interest rate

Option 3: 5 year loan with a 12 percent interest rate

Which option should be chosen?

Equated Annual Installment:

Equated annual installment refers to an equal amount paid by an entity every year towards the repayment of a loan. Some part of an equated annual installment is toward the principal amount of loan, and the remaining part is towards the interest charged during the year.

Answer and Explanation:

Option 1 :

Computation of yearly installment amount.

{eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\$3,500,000 \times 0.08 \times \left ( 1+0.08 \right )^3}{\left (1+0.08\right )^3-1}\\&=\$1,358,117.30 \end{align*} {/eq}

Since the annual installment is greater than $1,000,000, "Dundar Mifflin" should not choose option 1.

Option 2:

Computation of yearly installment amount.

{eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\$3,500,000 \times 0.10 \times \left ( 1+0.10 \right )^4}{\left (1+0.10\right )^4-1}\\&=\$1,104,147.81 \end{align*} {/eq}

Since the annual installment is greater than $1,000,000, "Dundar Mifflin" should not choose option 2.

Option 3:

Computation of yearly installment amount.

{eq}\begin{align*}\text{Yearly Installment}&=\dfrac{P \times R \times \left ( 1+R \right )^n}{\left (1+r\right )^n-1}\\&=\dfrac{\$3,500,000 \times 0.12 \times \left ( 1+0.12 \right )^5}{\left (1+0.12\right )^5-1}\\&=\$970,934.06 \end{align*} {/eq}

Since the annual installment is less than $1,000,000, "Dundar Mifflin" should choose option 3.


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Sources of Long-Term Financing

from Business 100: Intro to Business

Chapter 23 / Lesson 4
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