Sky Enterprises has bonds on the market making annual payments, with 8 years to maturity, and selling for $950

Finance Nov 03, 2020

Sky Enterprises has bonds on the market making annual payments, with 8 years to maturity, and selling for $950. At this price, the bonds yield 11.0 percent. What must the coupon rate be on the bonds? Multiple Choice 10.56% 11.00%

Expert Solution

Price of the bond is calculated using the formula: P= C/(1+r)+C/(1+r)^2+....C/(1+r)^n+P/(1+r)^n; where C is the coupon payment per period, P is the face value of the bond, r is the yield to maturity and n is the number of years to maturity.

950= C/1.11+C/1.11^2+....C/1.11^8+1000/1.11^8.

For the coupons part, we can use the formula of present value of annuity which is C*(1-(1+r)^-n)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

So, we have,

950= (C*(1-1.11^-8)/0.11)+1000/1.11^8

516.07= C*5.146

C= 100.28.

So, Coupon rate is 10.028% (10.03% on rounding off).

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