If the appropriate discount rate for the following cash flows is 9.75% per year, what is the present value of the cash flows? (8 points)

 

Year Cash Flow
1 $2,800
2 0
3 8,100
4 1,940

 

 

 

 

 

Solution

 

Present value PV) of the cash flow can be calculated as follows;

 

 

Hence the present value is

  1. You are to make monthly deposits of $150 into a retirement account that pays 11 percent interest compounded monthly. If your first deposit will be made one month from now, how large will your retirement account be in 20 years? (8 points)

 

Solution

This problem can be solved using the following formula;

Where  is the future value,

is the current value;

is the rate and t is time.

In this question, we have FVA=?, r=11% per month, t=20 years= and CV=$150

Inserting the values in the equation above;

 

 

 

 

 

 

Hence the retirement amount in 20 years will be

 

  1. Beginning three months from now, you want to be able to withdraw $1,200 each quarter from your bank account to cover college expenses over the next four years. If the account pays 0.50 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years? (8 points)

 

Solution

 

From the question above, we have quarterly withdrawal as $1200, interest being 0.5% per quarter, time being 4 years, equal to

 

We use the following equation to solve the problem;

 

 

 

Since we are dealing with quarterly, in 1 year, we have 4 periods, hence in 4 years, we have;

 

Inserting the values to the formula;

 

 

Hence the present value that should be available to complete school is

 

 

  1. You want to be a millionaire when you retire in 40 years. How much do you have to save each month if you can earn a 10 percent annual return? (8 points)

 

Solution

 

The amount to be saved monthly can be calculated having known that the future value, FVA is $1000000. We are also given the rate per month as 10% which is equal to 0.1 and the time is 40 years, equal to

 

To calculate the unknown value, which is CV, we use the formula,

 

 

Where in the question, , ,

Inserting the values to formula above;

 

 

 

 

Making the unknown the subject of the formula;

 

 

 

 

Hence the amount that should be saved monthly to become a millionaire in 40 years is

 

  1. While Steve was a college student, he borrowed $12,000 in student loans at an annual interest rate of 9 percent. If Steve repays $1,500 per year, how long will it take him to repay the loan? (8 points)

 

Solution

 

For this question, we use the formula;

 

 

Where,

,, and t=?

Inserting the values to the equation above,

 

 

 

Finding the value of t,

 

 

 

 

    1. You are looking at a bond that has 20 years to maturity. The coupon rate is 9% and coupons are paid semiannually. The yield-to-maturity is 7%. What is the current price? Is it a premium bond or a discount bond?

Solution

 

 

 

 

    1. You are looking at a bond that has 30 years to maturity. The coupon rate is 8% and coupons are paid semiannually. The current price is $950. What is the yield to maturity? Is it a premium bond or a discount bond?

Solution

Yield to maturity is calculated using the following formula;

It is a premium Bond

 

  1. (10 points) The Northwest Athletic Equipment Company has undergone tremendous growth over the past several years.  Things are slowing now but they still anticipate a 3% annual rate in the growth of dividends per year indefinitely.  If the market requires a 14% rate of return on comparable securities, and Northwest Athletic currently pays an annual dividend of $.50 per share, estimate a current per share price of the stock.

 

Solution

 

The value of stock in this question can be solved using the following formula;

We have annual dividend=0.50%

Rate of return=14%

Growth=3%