Financial Management

Unit IV Assignment

This assignment will allow you to demonstrate the following objectives:

• Calculate the annual payment on a loan using the present value of an annuity.
• Use discounting to determine the present value of an annuity.
• Calculate the future value of an annuity and periodic annuity payments.
• Determine the present value of a bond.

Instructions: Answer the questions directly on this document. When you are finished, select “Save As,” and save the document using this format: Student ID_UnitIV. Upload this document to BlackBoard as a .doc, docx, or .rtf file. Show all of your work.

1. Using the PVIFA table (table 9.4 in the textbook), determine the annual payment on a $600,000, 10 percent, business loan from a commercial bank that is to be amortized over a five-year period.

2. You are considering borrowing $200,000 to purchase a new home.

1. Calculate the monthly payment needed to amortize an 7% fixed-rate 30-year mortgage loan.
2. Calculate the monthly amortization payment if the loan in (a.) was for 15 years instead.
3. In a few sentences, explain the effect of a smaller loan period. How does it influence the monthly payment and interest?

3 Use a financial calculator or computer software program to answer the following questions:

1. Melanie is trying to save money for retirement and has a future goal of $450,000 at the end of 20 years. Determine the present value of her goal using a discount rate of 10%.
2. How would the present value change if the $450,000 is to be received at the end of 15 years instead? Explain the impact and show your work?

4. Assume you are planning to invest $200 each year for four years and will earn 8 percent per year.

1. Determine the future value of this annuity due problem if your first $200 is invested now. Show your work.
2. What is the difference between an annuity due and an ordinary annuity? Explain.

5. Jimmy has a bond with a $1,000 face value and a coupon rate of 9.5% paid semiannually. It has a eight-year life.

1. If investors are willing to accept a 12 percent rate of return on bonds of similar quality, what is the present value or worth of this bond? Show your work.
2. What is the impact of paying interest semi-annually rather than annually? Explain.

Sample Solution

1. The annual payment on a $600,000, 10 percent business loan amortized over a five-year period can be calculated using the PVIFA table as follows:

PVIFA (5 years, 10%) = 3.79079

Annual payment = $600,000 / 3.79079 = $158,304.61

Therefore, the annual payment on the loan is $158,304.61.

a. The monthly payment needed to amortize a $200,000, 7% fixed-rate 30-year mortgage loan can be calculated using the following formula:

Monthly payment = [P x (r/12) x (1 + r/12)^n] / [(1 + r/12)^n – 1]

Where P is the loan amount, r is the interest rate per year, and n is the number of payments (months).

Plugging in the given values, we get:

Monthly payment = [$200,000 x (0.07/12) x (1 + 0.07/12)^(30×12)] / [(1 + 0.07/12)^(30×12) – 1] = $1,330.60

Therefore, the monthly payment needed to amortize a 7% fixed-rate 30-year mortgage loan of $200,000 is $1,330.60.

b. The monthly amortization payment if the loan in (a.) was for 15 years instead can be calculated using the same formula as above, with n equal to 15×12=180:

Monthly payment = [$200,000 x (0.07/12) x (1 + 0.07/12)^(15×12)] / [(1 + 0.07/12)^(15×12) – 1] = $1,811.86

Therefore, the monthly payment needed to amortize a 7% fixed-rate 15-year mortgage loan of $200,000 is $1,811.86.

A smaller loan period means that the borrower will pay less interest over the life of the loan, but will have higher monthly payments. This is because the principal is being paid off over a shorter period of time, so each payment has to be higher to make up for it. The interest rate is usually lower on shorter-term loans, which helps offset the higher payments.

3. The present value of Melanie’s goal of $450,000 at the end of 20 years, using a discount rate of 10%, can be calculated using the following formula:

PV = FV / (1 + r)^n

Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods.

Plugging in the given values, we get:

PV = $450,000 / (1 + 0.10)^20 = $94,239.46

Therefore, the present value of Melanie’s goal is $94,239.46.

If the $450,000 is to be received at the end of 15 years instead, the present