Question

Cold Boxes Ltd. has 100 bonds outstanding (maturity value = $1,000). The nominal required rate of return on these bonds is currently 10 percent (Kd), and interest is paid semiannually. The bonds mature in 5 years, and their current market value is $768 per bond.
What is the annual coupon interest rate?

a.8%

b.6%

c.4%

d.2%

e.0%

Answer 1

Answer:

correct option is c.4%

Explanation:

given data

maturity value = $1,000

nominal rate of return r = 10 percent  = 5 % semi annually = 0.05

mature time t = 5 years  = 10  semi annually

current market value = $768

solution

we apply here present value formula that is

present value = coupon rate × maturity value × $\frac{1-(1+r)^{-t}}{r}$ + $\frac{mature\ value}{(1+r)^{-n}}$   ..............1

put here value and we get

$768 =  coupon rate × $1000 ×  $\frac{1-(1+0.05)^{-10}}{0.05}$ ×  $\frac{1000}{(1+0.05)^{-10}}$

solve it we get

coupon rate  = 1.99549 %  Semi-annual

so here annual coupon interest rate is = 2 × 1.99549 %

annual coupon interest rate is 3.99 = 4%

so correct option is c.4%