Question

ESTION 1

What is the price of a 4-year coupon bond with a face value of $2000 and an 8% annual coupon

rate when the interest rate is 3%?

QUESTION 2

What is the price of a 3-year coupon bond with a face value of $4000 and a 5% annual coupon

rate when the interest rate is 4%?

QUESTION 3

What is the price of a three-year zero-coupon bond with a face value of $2000 when the interest

rate is 6%?

QUESTION 4

Assume the current dividends on a stock are $9 per share, growing at the rate of 5% annually. If

the interest rate is 8%, what is the value of this stock?

QUESTION 5

Assume the current dividends on a stock are $6 per share, decreasing at the rate of 3% annually.

If the interest rate is 7%, what is the value of this stock?

Answer 1

1) Given that the coupon rate on the bond is 8%

hence cash flow from coupon each year = 8%* 2000=160

Cash flow from Principal payment = 2000

Value of bond is given by = CF1/(1+ interest rate)^time till first CF+CF2/(1+ interest rate)^time till second CF+CF3/(1+ interest rate)^time till third CF+CF4/(1+ interest rate)^time till fourth CF

=160/(1+3%)^1+160/(1+3%)^2+160/(1+3%)^3+(160+2000)/(1+3%)^4

= 155.34+150.82+146.42+1919.13

=2371.71

Hence price of the bond = 2371.71

(CF= Cash flow

CF4= Coupoun payment +principal)

2) Given that the coupon rate on the bond is 5%

hence cash flow from coupon each year = 5%* 4000=200

Cash flow from Principal payment = 4000

Value of bond is given by = CF1/(1+ interest rate)^time till first CF+CF2/(1+ interest rate)^time till second CF+CF3/(1+ interest rate)^time till third CF

=200/(1+4%)^1+200/(1+4%)^2+(200+4000)/(1+4%)^3

= 192.31+184.91+3733.78

= 4111

Hence price of the bond = 4111

(CF= Cash flow

CF3= Coupoun payment +principal)

3) Give Face value of zero coupon bond =$2000

Price of Zero coupon bond is given by = Face value of bond/(1+Interest rate)^time till maturity

=$2000/(1+6%)^3

=$1679.24

Hence price of Zero Coupon bond is 1679.24

4) For a dividend paying stock, Price of stock is derived as -

Current year dividend*(1+ growth rate)/(cost of equity - Growth rate)

Since Cost of equity is not given Interest rate is taken as substitute

Hence price of stock = $9*(1+5%)/(8%-5%)=9.45/3%

= $315

Price of stock is $315

4) For a dividend paying stock, Price of stock is derived as -

Current year dividend*(1+ growth rate)/(cost of equity - Growth rate)

Since Cost of equity is not given Interest rate is taken as substitute

Hence price of stock = $6*(1+(-3%))/(7%-(-3%))=5.82/10%

= $58.2

Price of stock is $58.2