Question

B. ANALYTICAL QUESTIONS QUESTION 1 What is the price of a 3-year coupon bond with a face value of $3000 and a 6% annual coupon rate when the interest rate is 2%? QUESTION What is the price of a two-year zero-coupon bond with a face value of $5000 when the interest rate is 5%? QUESTIONS Assume the current dividends on a stock are $12 per share, growing at the rate of 4% annually. If the interest rate is 10%, what is the value of this stock? QUESTION 4 Assume the current dividends on a stock are $11 per share, decreasing at the rate of 2% annually. If the interest rate is 6%, what is the value of this stock?

please answer all

Answer 1

Dear student, only one question is allowed at a time. I am answering the first question

1)

Price of a bond is the present value of all future cash flows receivable from the bond discounted at required rate of return

Future cash flows are periodic interest payments and maturity value of the bond

Face Value = $3,000

Coupon rate = 6% or 0.06

Periodic interest

= Face Value x Coupon Rate

= $3,000 x 6%

= $180

Time period = 3 Years

Interest rate for discounting = 2% or 0.02

Present value factor

= 1 / ( 1 + Rate of discounting ) ^ Number of periods

So, discounting factor for period 3

= 1 / ( 1.02 ^ 3 )

= 1 / 1.061208

= 0.942322

Now, Since the periodic cash flow of Coupons are same each year, we can use annuity factor for finding present value of these

Present value of Annuity

= Annuity Factor x Annual payments

Annuity Factor

= [ 1 – ( 1 + r ) ^ - n ] / r

= [ 1 – ( 1.02 ^ - 3 ] / 0.02

= [ 1 - 0.942322 ] / 0.02

= 0.057677 / 0.02

= 2.883883

So, Present value of Interest payments

= 2.883883 x $180

= $ 519.10

Now, Present value of Face value of the Bond

= Present value factor for year 3 x Face Value of Bond

= 0.942322 x $3,000

= $2,826.97

So, Price of the bond

= Present value of coupons + Present value of Face value

= $ 519.10 + $2,826.97

= $3,346.07

So, the price of the bond is $3,346.07