## Find the ytm and what is its roe, Finance Basics

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1. Find the price of the following bonds. They are all risk-free, and the risk-free rate is 10%.

(a) A fifteen-year zero coupon bond with face value \$1,000.

(b) A three year semiannual-pay 6% coupon bond with face value \$500.

2. Find the YTM of the following bonds. Be careful to report the YTM as an APR with appropriate compounding. These are not the same bonds as in question 1.

(a) A fifteen-year zero coupon bond with face value \$1,000 and price \$300. Use annual compounding for the YTM.

(b) A three year semiannual-pay 6% coupon bond with face value \$500 and price \$400. You will need to solve this in Excel using trial and error.

3. A one-year semiannual pay 10% coupon bond has a price of \$100 and a face value of \$100. Recall from class that when price=par value, YTM=coupon rate. I buy the bond today and hold it to maturity. I will reinvest the coupon I receive in six months in a bank account that pays a certain rate. I close out my investment in the bank account on the day the bond matures. What is my HPR if the rate at which I reinvest the coupon is (a) 10% (b) 4% (c) 16%? All rates are quoted as APRs with semiannual compounding.

What can you conclude about the relationship between YTM and HPR for a coupon bond that is held to maturity?

Guide: For each case, find the total dollar amount you will have at the end of the year.

The HPR is the total amount you get at the end of the year divided by the amount you paid to buy the bond (minus 1). Before comparing the HPR with the YTM make sure that they are both APRs with the same compounding frequency or both effective rates over the same period.

4. A company had net income of \$20,000 this year on equity of \$100,000 last year. Its ROE is expected to be constant. Answer the following questions:

(a) What is its ROE?

(b) The company retains 40% of its earnings. What are earnings next year expected to be? What are dividends next year expected to be?

(c) What is the growth rate of earnings? What is the growth rate of dividends?

(d) The beta of the returns on the stock has been 1. The risk-free rate is 5% and the return on the market is expected to be 10%. What is the discount rate (OCC) on the company's stock?

(e) The company has 20,000 shares outstanding. What should the price per share be today?

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