Question

FIN322 Corporate Finance Homework Assignment I

Answer All Questions but my professor is picking two random to grade Show all your work (use of formula, etc.) in solving the problems. You still need to show your work even if you use the financial calculator to get the answers.

1. Suppose you wish to plan for your newborn’s college tuition payment. You intend to make equal semiannual deposits into an account offering 4% compounded semiannually on the child’s 3rd through 13th birthdays. You expect that tuition payments will be $50,000 semiannually by the time the child is ready to enter college. Therefore, your goal is to make eight semiannual withdrawals of $50,000 each starting on the child’s 18th birthday, each withdrawal to be used for semiannual tuition. Assume the account continues to offer 4 percent per year compounded semiannually throughout the entire period of deposits and withdrawals. How much must each of the semiannual deposits be such that there will be enough money accumulated in the account to exactly meet the goal? [Suggestion: Draw the cash flow diagram to aid you in solving this problem.]

2. You are planning to save for retirement over the next 40 years. To do this, you will invest $500 per month in a stock account and $2,500 semiannually in a bond account. The return of the stock account is expected to be 6 percent per year, and the bond account will pay 4 percent per year. When you retire, you will combine your money into an account with a 5 percent per year return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?

3. You are taking out a four-year loan of $30,000 from your bank. The interest rate is 5 percent per year, and the loan calls for equal monthly payments. How much principle is paid in the second month? How much total interest is paid after five months? (Draw an amortization table to answer the questions. Use of excel is highly encouraged.)

4. Bond J is a 4 percent coupon bond. Bond K is a 7 percent coupon bond. Both bonds have 10 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rate (YTM) changes from 6 percent to 8 percent, what is the percentage price change of these bonds? What if the YTM suddenly falls from 6 percent to 4 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?

5. Rizzi Co. is growing quickly. The company just paid a $2 per share dividend and dividends are expected to grow at a 15%, 8% and 4% rate respectively for the next three years, with the growth rate falling off to a constant 3 percent thereafter. If the required return is 10 percent, what is the current share price?

Answer 1

Part 2

Calculating Value of deposits into stocks account (as on the 40th Year) = 500*(1+6%)^40 + 500*(1+6%)^39 +.....+500*(1+6%)^1 = $82023.84

Calculating Value of deposits into bonds account (as on the 40th Year) = 2500*(1+2%)^80 + 2500*(1+2%)^79 +.....+2500*(1+2%)^1 = $494,118

Sum of the two = $576,142.

On, investing this amount in an account paying 5% per year = the resulting Cash flows are equivalent to the flows received by a lender when he lends the above amount at 5% per year for 25 years.

Running this on the MS Excel, we get = $ 40,878.71. This is the amount that can be withdrawn in each year for the next 25 years.

Part 3

Use MS Excel formula =PMT(5%/12,48,30000) to get EMI of $ 690.88.

Every month, interest payment is calculated as = Principal outstanding * 5%/12.

Using this, we get, principal paid in the 2nd month as $568.24.

Interest paid in the 5th month is $ 115.5

Part 4

Using MS Excel input formula = PV(6%/2,10*2,100*4%/2,100) to calculate the current value of bond J. It comes out to be $85.1. Similarly, for Bond K, the value comes out to be $107.4.

When YTM changed to 8%, use the above formula again but replace 6% with 8% to calculate the new value of both these bonds. They come out to be $72.8 and $93.2.

Percentage price change of Bond J is -14% and of Bond K is -13%.

When YTM drops to 4%, Bond J value moves to $100 and Bond K value moves to $124.5. The price of bonds J and K increase by 17% and 16% respectively.

It shows that bonds with lower coupons are more sensitive to interest rates (hence, higher interest rate sensitivity).

Part 5

Projecting dividends in the next few years (at the given growth rates), they are $2.3, $2.48, $2.58, $2.66 and so on.

Calculating the Present Value of these dividends with Required rate of 10% the value of the share comes out to be $ 34.64.