Problem 1. You would like to buy a machine. The conditions of the sale are as follows:
Price without discount: $100,000;
Final bullet payment: $30,000
Repayment period: 7 years, compounded daily and payable weekly
APR equals 8 percent.
A choice must be made for borrowing the initial deposit of 15000. Is it more appropriate to borrow at the 6 percent p.a. payable as a lump sum after two years, or repay the debt in four equal semiannual installments of $4035.4. In the latter case the interest rate is 6 percent compounded semiannually.
What is the Effective Annual Rate?
Calculate the weekly payment?
How much would you still owe after 5 years?
Problem 2. Today is Janet’s 23rd birthday. Starting today, Janet plans to begin saving for her retirement. Her plan is to contribute $1,000 to a brokerage account each year on her birthday. Her first contribution will take place today. Her 42nd and final contribution will take place on her 64th birthday. Her aunt has decided to help Janet with her savings, which is why she gave Janet $10,000 today as a birthday present to help get her account started. Assume that the account has an expected annual return of 10 percent. How much will Janet expect to have in her account on her 65th birthday?
Problem 3. Acme Electronics Pty Ltd. issued a fifteen-year bond with a coupon payment of 8 percent paid semiannually. The price of the bond was $930 after two years. The yield to maturity was 5 percent after 5 years.
a) What is the value of the bond after the 10th interest payment?
b) After 10 years (20 interest payments) the value of the bond amounts to 1103.45. What is the yield to maturity?
Problem 4.
a) Impuls-acme Co. has just paid 2 dollars in dividends that will grow 12 percent during the next four years. After four years the dividend will increase 10 percent, after five years an increase will be 8 percent. Afterwards, it will continue growing 6 percent forever. The required rate of return is 8 percent. What is the price of the share?
b) It should be the explanation for the 12 percent growth in dividends? Would you expect abrupt changes in the dividend growth or rather gradual one as in this example? Discuss?
Problem 5.
a) Company pays $2.50 annual dividend and it will be soon raised by 8 percent per year, indefinitely. If the required return is 10 percent, what is the actual share price?
b) If the annual dividend is paid in equal quarterly installments, the same company has just paid $0.625 dividend per share. What is the value for the current share now?