Financial Management Case

Final Assignment

Financial Management

Question 1:

You want to buy a condo 5 years from now, and you plan to save $ 3, 000 per year, beginning immediately. You will make 5 deposits in an account that pays 6 % interest. Under these assumptions, how much will you have 5 years from today?

Answer 1:

Here we have to calculate the future value using this formula:

FVn= [PV ((1+i) n -1)] / i

FV5 = 3,000 x (1.065) – 1] /0.06= $1,014.676 /0.06 = $16,911.28

You'll have $16,911.28 in 5 years from today.

Question 2:

You recently received a letter from Cut-to-the-Chase National Bank that offers you a new credit card that has no annual fee. It states that the annual percentage rate (APR) is 18 percent on outstanding balances with daily compounding. What is the effective annual interest rate?

Answer 2:

We have the annual percentage rate but we need the monthly rate.

Monthly percentage rate= 18% / 12 = 1.5%

To solve this problem we can use a base 100 (because we want a percentage).

Effective annual rate = 100 x 1.01512= 119.56 => 19.56%

The Effective annual interest rate is 19. 56%.

Question 3:

You have just taken out an installment loan for $ 100, 000. Assume that the loan will be repaid in 12 equal monthly installments of $ 9,456 and that the first payment will be due one month from today. How much of your third monthly payment will go toward the repayment of principal?

Answer 3:

I need a calculator to solve this problem because I need to know the interest per year first.

Because the loan will be repaid in monthly installments we need the interest per month now.

Interest Rate For One Period = Interest per year /12 = 0.24/12=0.02

We know that:

• INTt = Beginning balance x (Interest)

• END BAL = BEG BAL - PRIN

• PRIN = PMT – INT

So we can build the following table:

Year BEG BAL PMT INT PRIN END BAL

1 $100,000 $9,456 INT1 = 100,000 x (0.02) =$2,000 $7,456 $92,544

2 $92,544 $9,456 INT2=92,544 x(0.02) =$1,850.88 $7,605.12 $84,938.88

3 $84,938.88 $9,456 INT3 = 84,938.88 x(0.02)=1,698.78 $7,757.22 $77,181.66

We need just the first three rows to solve the problem but you could see the whole table in the Excel document.

For the third month, $7,757.22 will go towards the repayment of the principal.

Question 4:

Your bank account pays a nominal interest rate of 6 %, compounded daily. Your plan is to deposit $ 500 in the account today, and deposit $1, 000 in the account at the end of each of the next three years. How much will you have in the account at the end of three years, after making your final deposit?

Answer 4:

Years Number of period (cumulative)

1 365 days

2 730 days

3 1095 days

Here we have the calcite the future values.

V0= $500 (1+0.06)1 =$530

V1= $1000 (1+ (0.06/365)365) = $1061.83

V2= $1000 (1+ (0.06/730)2*365) =$1061.83

V3= $1000 (1+ (0.06/1095)3*365) =$1061.83

In order to know how much we'll have at the end of three years, after making our final deposit, we have to calculate the sum of the Vs.

FV3 = $530 + ($1000 x 1.061831) + ($1000 x 1.061834) + ($1000 x 1.0618348) = $530+ $1061.831311 +$1061.833928 + $1061.834801 = $3715.5

At the end of the third year we will have $3,715.5 in the account.

Question 5:

A 20-year, $ 1, 000 par value bond has a 9 % annual coupon. The bond currently sells for $ 925. If the yield to maturity remains at its current rate, what will the price be 5 years from now?

Answer 5:

I used Excel to resolve this problem.

First of all we have to solve the Yield to Maturity.

YTM:

We have all the information we need to calculate the yield to maturity, where:

Present Value = -$925

Number of Periods = 20

Future Value = $1,000

Annual Payment = $90

YTM (Excel formula) = TAUX (25; 85;-875; 1000; 0) = 9.873%

Present Value:

Now, we have all the information we need to calculate the price in 5 years from now.

Rate = 9. 873%

Number of Periods = 15 (20 - 5)

Future Value $ 1, 000

Annual Payment = $ 90

PV = =VA (9.873; 15; 90; 1000; 0) = $-933. 09

The price of the bond will be $933. 09 in 5 years.

Question 6:

You wish to purchase a 20 year, $1, 000 face value bond that makes semiannual interest payments of $ 40. If you require a 10 % nominal yield to maturity, what price should you be willing to pay for the bond?

Answer 6:

To solve this question we will use the following formula:

P0= [INT (1-(1/ (1+rd)) N)/rd] + per value/ (1+rd) N

We know that:

INT = $40

Rd = 10% / 2 = 0.05 or 5% (We have the annual rate in the question but we need the semiannual rate, so we just have to divided the annual rate by 2)

Number of Periods = 20 years x 2 =40 (It is a 20-years bond that makes semiannual interest payments. Therefore there are 2 payments per years and by consequence 40 periods.)

Par Value = $1,000

P = 40 [1-(1/1.05)40]/0.05]+ 1,000/1.0540

P= $686.363 + $142.0456 = $828.409

We will be willing to pay $828.41 for the bond.

Question 7:

The current price of a 10 year, $1, 000 par value bond is $1, 158. 91. Interest on this bond is paid every six months, and the nominal annual yield is 14 %. Given these facts, what is the annual coupon rate on this bond?

Answer 7:

I used the calculator to solve the PMT. Here you can see the inputs and outputs from the calculator.

Here are the instructions we have to follow to calculate when the interests on the bond are semiannual:

So, we have:

Annual coupon rate = 92.625 / 1,000 = 0.092625 = 9.26%

The annual coupon rate on this bond is 9.26%.

Question 8:

A $1,000 par value bond pays interest of $35 each quarter and will mature in 10 years. If your nominal yield to maturity is 12% with quarterly compounding, how much should you be willing to pay for this bond?

Answer 8:

Because there is 4 quarter in a year, we have to

• divided the yield to Maturity by 4

• Multiply the number of periods by 4

• Divided by 4 the annual payment but here we already have the quarterly Payment.

Yield To Maturity = 12%/4 = 3%

Number of Periods (4 quarter in a year) = 4 x 10=40

Future Value $1,000

INT = $35

We